The inner workings of many batch processes are not known in great detail. This is necessary for the development of an accurate knowledge-driven model. Then the data-driven route is a very effective way of addressing the modeling and optimization of such a process. Data-driven models ignore even the partial knowledge we have about a process, and this is a drawback. Some of our present research activities are aiming to develop data-driven models that also incorporate partial process knowledge in the form of approximate material and energy balances. These models will be called hybrid models.
While most of the technical details are left for the related publications, here we present a few simple examples.
Simple Reaction Network
Assume that we need to optimize the operation of a batch reactor in which a simple network of reactions takes place: A+B ↔ C → D+E. The desired product is C and we wish to maximize its concentration at the end of an 8-hour batch, provided the concentration of E is below 0.10 mol/lt. The main question we wish to answer is the temperature profile with the time that will lead to optimal operation.
Without quantitative knowledge on the kinetics and thermodynamics, we will design a small set of experiments, using initially linear and afterward quadratic temperature profiles in time. See the left and right figures below. The minimum number of experiments is equal to the number of parameters in the 2FI model plus three more for the estimation of the Lack-of-Fit (LoF) statistic.
(Details on this example are forthcoming)