This paper, the first part of our three-part contribution, proposes a process modelling framework that captures integral continuous variable dynamics in discrete-time; the framework may be called discrete-time version of the Phase Transition Model of Hybrid Systems. The modelling of the system phases is performed through Activity States. The characterisation of Activity State is derived from the physical system vriables for easy modelling. The contributions of this paper are as follow. Transitions among activity states are time constrained with upper and lower time bounds relative to an external global clock. Composition of component models, essential for modelling of complex systems, is discussed in detail. The model proposed in this paper is used in two companion papers for solving the inferential problems of state estimation and fault diagnosis.