Modeling profiles in chemical processes

Profiles are regularly encountered in chemical process modeling, and often arise in situations in which products are characterized by a distribution, such as in molecular weight distributions or particle size distributions in polymer production. Approaches for modeling such problems include using a specified distribution characterized by a small number of parameters, or discretization and application of multivariate statistical methods such as Partial Least Squares (PLS). In this paper, an alternative approach using functional regression is presented in which the distribution is expressed using a suitable set of basis functions such as splines, and the parameter estimation problem includes both the coefficients in this basis, as well as the model parameters. The efficacy of the functional regression and PLS approaches is compared using a polystyrene reactor example.