Modeling in process engineering

As an alternative to a trial-and-error strategy, modeling has demonstrated its importance in many fields: medicine, nuclear energy, aeronautics, meteorology... Modeling is used in all scientific disciplines, as well as in other disciplines such as economics, finance and the humanities. In all cases, the aim is to build a representation as close as possible to the way a real system works, in order to analyze or react to its behavior.

A model is a formalized structure used to account for a set of phenomena that possess certain interrelationships. Depending on the discipline, the formalism can be very different, and a distinction is made between the living model ("animal" model for medicine, pharmacy, miniaturization for flow studies, etc.) and the virtual model, for which the formalism is mathematical. In process engineering, the term "model" refers to a set of mathematical equations constructed on the basis of experimental data acquired on the real system, and used to represent the relationships between the system's outputs and inputs.

The aim of modeling is therefore to establish a system of equations:

which, knowing the model inputs (u), calculates the model outputs (s). For transient systems, the system of equations is differential, involving time (t) in addition to inputs and outputs. For non-homogeneous systems, the notion of space can be introduced (x, y, z).

To limit oneself to this definition might lead one to think that mastering the system is all that's needed to develop a model. But writing down the equations, however easy it may seem to a physicist, is only part of the modeler's task. They also need to be able to solve them and find a solution, and a physical solution at that. Modeling is therefore a skilful blend of the physicist's knowledge of the system's physics and chemistry, and the mathematician's ability to solve the resulting equations.

This dossier begins with a general overview of unit operation modeling in process engineering, then focuses on the phenomenological analysis approach based on the fundamental laws of physics. The various aspects of the modeling process are presented: representation of the material system, model formulation. Examples are given to illustrate the importance of careful model formulation in order to minimize...