Comments on the Industrial Application of Process Models

"Mathematical process models can be applied in several different ways to serve industry by inducing beneficial changes to process operation. This paper attempts to summarize the different uses, types, and attributes of these models, and to offer some ideas to consider when developing, using, and reporting on them. Process models range from empirical to mechanistic in nature and vary in complexity from simple analytical solutions to coupled, 3-D transient numerical simulations. They are classified here according to the way in which they are implemented in practice, viz. fully-online models, semi-online models, off-line models, and literature models. The purpose of the model should dictate how choices are made during its development. Ways to validate and compare the model with experiments are suggested. Examples are taken in the context of the author's experience in modeling the continuous casting of steel.IntroductionThe objective of this paper is to provide a partial introduction for this symposium by discussing some basic aspects of the application of mathematical process models in industry. Essentially, the aim is to explore how process models are used to benefit industry, and to offer some general comments and suggestions, based on the experience of the author, on how models can best meet this goal.This work is concerned with process models, which consist of systems of mathematical equations and constants that are solved on a computer to make quantitative predictions about some aspect(s) of the process. The specific variables required as input data and generated as output data are important features of the model. The equations often derive from a numerical solution to one or more differential equations and their boundary conditions. The model also includes the constants, which represent material properties, empirical relationships, and other knowledge about the process, and usually require considerable effort to obtain. Thus, general purpose commercial software packages, (ie. finite-element or finite-difference based codes), are not models in this context. They are useful tools, however, serving as frameworks for the development of process models."