Rational function ridge regression in kinetic modeling: A case study

Abstract

Rational functions appear in many theoretical formulae in chemistry, chemical engineering, and biochemistry. However, rational functions have not been used much in empirical multivariate modeling. This study is a continuation to developments in [1] and [3]. In this study, the focus is on empirical modeling using rational function in a case study of estimating the kinetics of esterification of ethanol with acetic acid. The results are compared with those obtained by traditional mechanistic modeling using nonlinear parameter estimation. The motivation for the approach is to find good models with less effort. Currently, developing and testing different mechanistic kinetic models are time consuming, and in spite of the effort, the performance of the resulting candidate models can be virtually the same. An alternative approach is to use empirical generic models. In this study, this approach is shown to require less effort than the mechanistic modeling approach.The proposed method is based on modeling the reaction rate by an empirical second order rational function. The rational function is first transformed into a linear form which is used to estimate the unknown model parameters using ridge regression. After this, the linear model is back-transformed into the original rational form which is then used for calculating both the fitted values and the predicted values. Finally, the estimated rational function for the rate expression is used to solve numerically the system of differential equations corresponding to the reaction kinetics.The data is obtained from [4], and it consists of several batch reactions between ethanol and acetic acid with different initial concentrations. Six of the eight batches are used for model estimation, and two of these are omitted for model validation (prediction).The results are very promising, and both the fitted and the predicted values are comparable to those obtained using traditional mechanistic modeling with nonlinear parameter estimation. It also seems that the method is able to take into account the non-ideal behavior of the reactants. The proposed method offers a flexible and fast method for developing kinetic models for reactor design and control, even in cases where the kinetic rate expression is not known by theory.