At low reduced temperatures and near the critical point, some numeric problems can arise:

Near the critical point, the pressure range in which three real solutions of the equation of state can be found becomes rather small. If only one real solution is found for an estimated pressure and phase composition, the algorithm fails. This can be corrected by breaking the calculation for this iteration step and starting the iteration with better estimates. A good idea in this case is to limit the allowed change in pressure and phase composition.

At low reduced temperatures, small changes in the liquid volume result in very large pressure changes. This can lead to convergence problems, even when the calculation is performed using double precision. If the changing pressure from one iteration to the next has a neglible effect on the liquid volume and liquid fugacity coefficients, the values of the last iteration should be kept and recalculation of the liquid phase can be skipped.