Evolutionary optimization of batch reactors using tendency models

A generic methodology called "Tendency Modeling" has been developed for modeling and optimization of batch/semibatch production of fine and specialty chemicals. The developed methodology is particularly suitable for those industrial processes where a detailed understanding of process fundamentals (reaction mechanism, process kinetics) is not available.;The approach consists of developing an approximate model of the process from available plant data, physical/chemical insight and a priori process knowledge. The modeling effort is aimed at developing a low-order, nonlinear model which is descriptive of the qualitative and approximate quantitative behavior of the overall process. Thus, a "Tendency Model" is more predictive than a completely empirical (Black-box) model and is less expensive to develop than a first principles (white) model derived from the knowledge of the elementary reaction mechanism.;The "Tendency Model" consists of approximate stoichiometric and kinetic models, coupled with material and energy balances accounting for the transport and mixing characteristics of the process. The approximate stoichiometric model consists of a set of independent reactions required to explain the observed macroscopic compositional changes. The number of reactions and the corresponding stoichiometric coefficients are determined from the plant data as a part of the identification process itself. The information on the effect of operating variables on various response variables (e.g. reactant and promoter conversions, product yield etc.) is used to select the functional form (power-law kinetics, Langmuir-Hinshelwood kinetics, etc.) of various rate equations in the kinetic model. A small number of kinetic parameters are then determined by matching the model prediction to the available data.;At the onset of the modeling and optimization cycle, a two-level factorial design is implemented to collect data for model identification and parameter estimation. The developed "Tendency Model" is used to optimize the process in an evolutionary manner. The new data collected at the end of each batch is used to update the structure and parameters of the model. This cycle is repeated until no additional improvement of the process is possible.;The developed methodology is experimentally validated using an example process related to the production of fatty acid epoxides which are used as stabilizers/plasticizers for PVC resins.