(45a) Maximizing Batch Yield in the Presence of Upstream Disturbances with Multivariate Modeling and Numerical Optimization

Tightly controlled batch processes typically aim to replicate “optimized” results by restricting variation from an established operating profile. However, this operating strategy, by design, limits the ability to adapt to process disturbances. Even a small relaxation of control limits on key variables can make a significant impact on the ability to achieve the desired final batch quality in the presence of a disturbance.

This presentation will include a batch reactor case study that demonstrates a 40% predicted improvement in process yield by adjusting the pre-established operating profile to account for a feed quality disturbance using multivariate analysis (MVA) and numerical optimization.

MVA is a proven method for analyzing and interpreting diverse industrial Big Data. MVA has been successfully applied to data from batch processes for a variety of goals, such as improving yield and product quality, and reducing operating costs. Numerical optimization in this case study is a true and formal mathematical optimization, in which the solution is distinctly different from the pre-established operating profile coined as “optimized”. In many cases, the pre-established profile is often simply the historical batch that produced the best quality (or yield in this case) and is used as an initial feasible starting point.

In this application, a PCA model is developed to reduce the dataset from the upstream process to a small number of latent variables that are easily monitored on a score plot for any feed quality disturbance to the downstream batch reactor. A multi-block PLS is then developed to correlate upstream conditions (from the PCA model results) and batch reactor process conditions to final batch yield.

Next, numerical optimization is performed to calculate the batch operating profiles that will maximize batch yield. The Sequential Least Squares Programming (SLSQP) algorithm included in the SciPy Optimization package in Python is used to solve the nonlinear programming (NLP) problem. Extrapolation in the optimization step is constrained through the use of the nonlinear SPE and HT2 terms from the PLS model, which ensure that resulting profiles are within historical operating limits.

Finally, the optimization results are compared to the pre-established operating profile results.

This presentation will introduce the concepts of MVA in the context of the case study, and will discuss typical challenges and dataset limitations for tightly controlled batch processes.