Abstract
A long-cycle oscillation sometimes appears in the iterative solution of nonlinear simultaneous equations. It occurred in simulation of extractive distillation by the successive approximation method and the cause of instability was investigated. A small deviation of the pressure and the total flow rate calculated from the material balance was found to travel down the column as a growing wave because of a poor temperature updating algorithm. An algorithm was proposed to stabilize it by revising the composition before updating temperature using information on the difference between the total flow rates calculated from the material and heat balances. The stability of the algorithm was quantitatively analyzed by evaluating the transformation matrix which corresponds to the successive deviation of the temperature profile. The absolute value of the dominant eigenvalue became less than unity, while that for the conventional method exceeded unity. The conventional method when stabilized by this algorithm was found to be competitive with the full Newton method.
