Estimation of Parameters from Data

The purpose of process modeling is to predict the behavior of chemical and physical phenomena. More often than not, it is not practical to predict the behaviors involved with ab initio models. Instead, most process models employ phenomenological models to represent the complex underlying physical and molecular behavior. These are compact models giving the required characteristics in a manageable form. Typical examples of models for intrinsic behavior include those for thermodynamic properties, transport properties, and chemical kinetic rates. Models are also often used to embody empirical solutions to complex flow situations, for example the models of volumeintegrated behavior used to predict pressure drops and heat transfer coefficients. These models by nature rely on empirical data. They involve two components: (1) a model form, often an algebraic relation, containing one or more adjustable constants referred to as “parameters”, and (2) the values to be used for these parameters. The parameter values are adjusted so that the model predictions match the available empirical data. Such data-based models are sometimes also referred to as “correlations”. The sections below discuss methods for determining the unknown model parameters to obtain a good fit between the model predictions and the set of available data. The first section addresses basic model fitting without statistical arguments. In many cases the quantity of data available is limited, and the model fitting process relies upon judgment and physical intuition. When larger quantities of data are available, statistical methods become useful. These techniques introduce probability arguments to analyze the magnitudes of the errors, assess models, and predict probable ranges of the parameters.