The dynamic simulation of a chemical process is carried out to quantify the potential consequences that may arise in response to a deviation propagation. For this purpose, a case study is based on the industrial alkylation of benzene by propene to cumene with the production of a by-product (diisopropylbenzene). It consists of a packed bed reactor and a train of three distillation columns (C-1 to C-3). The presence of a recycle stream from the second distillation column to the reactor feed should be noted. This study examines various scenarios that describe the dynamic response of the alkylation process to a temperature reduction of the reboiler steam in one of the distillation columns. Then, the behaviour of the reactor and the separation unit is analysed to determine the consequences. The computational results show that the effects associated with a temperature reduction of 20 °C of the steam in C-1 can propagate through all the units of the chemical process. This result is due to an increased concentration of light hydrocarbons in downstream equipment. Therefore, a permanent overpressure and a vent release are observed at the top of C-2. On the contrary, C-3 only has a temporary pressure increase that is not high enough to open the safety valve of this column. The objective of this study is to examine the influence of the characteristics of the process safety valve installed at the top of C-2 on the deviation propagation consequences. The results show how these effects are determined not only by the operating conditions of the equipment but also by the vent relief specifications. This study demonstrates in particular that dynamic simulations can be recognized as an important tool for safer industrial operations due to their capability of studying the process deviation propagation.