As process integration becomes increasingly valuable for energy recovery and material reuse in the process industries, the structural controllability of an integrated process becomes more and more important for its successful implementation. One of the major concerns of the structural controllability is how disturbances can be effectively rejected at the steady state through process design. In this regard, the characterization of disturbance propagation among process units is of a great importance. In this paper, a set of unique steady state disturbance propagation models is introduced for heat-integrated distillation column systems. The models are first-principles-based, but simplified in a linear matrix form. They are particularly useful for process analysis and evaluation in the early stages of process integration. The capability of the model applications is demonstrated by tackling two industrial problems.