Lumped process models derived from first engineering principles are usually too detailed for control purposes where only the major dynamic characteristics of the system should be captured. Two common steps of simplifying dynamic process models, the steady-state variable removal and the variable lumping simplification steps are investigated in this paper, in order to show if they preserve the key properties: the structural controllability, observability and stability of the models. In order to enable the formal analysis, these simplification steps are represented as context sensitive graph transformations acting on the structure graphs of the dynamic process models. It is shown that the simplification transformations above preserve the structural controllability and observability of process models, But only the steady-state variable removal transformation has been found not to destroy their structural stability. The variable lumping structure simplification transformation is further specialized to the case of cascade process models. It is shown that the inverse of this transformation does exist in this case, and both transformations preserve structural controllability and observability.