In this work, we present the development of a phenomenological-based semi-physical model for a 10 H P vertical fire-tube boiler. The model is intended to become a didactic element as part of a process control course, so that students will be able to use it to grasp the concepts of process control and to extrapolate this knowledge to real equipment. We explain the development of the PBSPM in detail and present all of the model equations. The model itself was set-up in the Python programming language, and complementary materials are available in a public website.