How Good is Your Model?

Models, which underpin all chemical engineering design work, vary widely in their complexity, ranging from traditional dimensionless number correlations through to modern computer based techniques such as computational fluid dynamics (CFD) and discrete element method (DEM). Industrial users require confidence in a model under the conditions it is to be applied in order to use it for design purposes and this can be a reason for slow acceptance of new techniques. This paper explores the validity of models and their validation using a variety of examples from heat transfer, reaction kinetics as well as particle and fluid flow, considering both traditional and modern computational-based approaches. The examples highlight that when comparing models to experimental data the mathematical form of the equations can contribute to an apparently good 'fit' while the actual adjustable parameter values can be poorly predicted; residuals or least squares alone are not a reliable indicator of quality of model fit or of model discrimination. When fitting models to experimental data, confidence in the adjustable parameter values is essential. A finite set of experimental data can fit many different models and often with many sets of parameter values. Not all of these models are of course useful for design. For that purpose it needs to be founded upon the real physics of the system and the adjustable parameters represent real quantities which can be measured, computed or estimated independently. The examples show also the importance of validating a model against more than one output parameter; instances are shown where a too simplistic validation exercise can be misleading. This paper shows therefore across a range of modelling approaches and applications that extreme care is required when validating a model. Models require validation under the conditions they are to be applied and against more than one output parameter, using appropriate data across appropriate scales and the paper encourages the practice of validating models in order to better persuade industry to adopt more advanced modelling approaches in the future.