The heat integrated distillation column (HIDiC) has a larger energy-saving potential but more complex dynamics stemming from thermal coupling. A nonlinear natural wave velocity for different stages of HIDiC is derived and reveals the local wave propagation dynamics. From the distribution of the natural wave velocity, the process of the disturbance propagation is observed clearly. Also, the coexistence of self-sharpening and non-sharpening waves can be easily understood. Then, a simplified nonlinear wave model from the perspective of the whole profile propagation is proposed, and clearly illustrates the nonlinear dynamic behaviors of HIDiC such as the dependence of response on the magnitudes and directions of disturbance, the asymmetric behavior of the transitions between two steady states, and the different dynamics between the rectifying and stripping columns. (C) 2015 Elsevier B.V. All rights reserved.