Multivariable Batch Processes

Batch processes often exhibit some batch-to-batch variation. Variations in charging the production recipe, differences in types and levels of impurities in raw materials, shift changes of operators, and disturbances during the progress of the batch are some of the reasons for this behavior.

Monitoring the trajectories of the process variables provides four different types of monitoring and detection activities:

• End of batch quality control. This is similar to the traditional quality control approach. The ability to merge information from quality variables and process variable trajectories by multivariate statistical tools enables accurate decision-making. Since process variable trajectories are available immediately at the conclusion of the batch, product quality can be inferred from them without any time delay.

• Analysis of process variable trajectories after the conclusion of the batch: This "postmortem" analysis of the batch progress can indicate major deviations in process variable trajectories and enable plant personnel to find out significant changes that have occurred, trace the source causes of disturbances and prevent the repetition of abnormal behavior in future batches. It can also point out different phases of production during the batch, providing additional insight about the process. Since the analysis is carried out after the conclusion of the batch, it cannot be used to improve the product of that batch.

• Real-time on-line batch process monitoring: The ultimate goal in batch process monitoring is to monitor the batch during its progress. This provides information about the progress of the batch while the physical, biological and chemical changes are taking place, enabling the observation of deviations from desired trajectories, implementation of interventions to eliminate the effects of disturbances, and decision to abort the batch if saving it is too costly or impossible.

• Real-time on-line quality control. This is the most challenging and important problem. During the progress of the batch, frequently measured process variables can be used to estimate end of batch product quality. This will provide an opportunity to foresee if there is a tendency towards the inferior product quality and take necessary actions to prevent final product quality deterioration before it is too late.

This section focuses on the first two types of activities, the off-line SPM and quality control. On-line SPM and quality control are discussed in

Section 6.5. Section 6.4.1 focuses on reference databases describing normal process operation and introduces the penicillin fermentation data used in many examples. Section 6.4.2 represents various multivariate charts for SPM. SPM of completed batches by MPCA is discussed in Section 6.4.3 and MPLS based SPM is presented in Section 6.4.4. Use of multiway/multiblock techniques for monitoring multistage/multiphase processes is discussed in Section 6.4.5. The integration of wavelet decompositions and MPCA is presented in Section 6.4.6.

6.4.1 Reference Database of Normal Process Operation

Developing empirical models as well as multivariate control charts for MSPM require a reference database comprised of past successful batches run under normal operating conditions (NOC). The historical database containing only the common cause variation will provide a reference distribution against which future batches can be compared. Selection of the reference batch records set out of a historical database depends on the objective of the monitoring paradigm that will be implemented. MPCA-based modeling is suitable if only the process variables are of interest. MPLS model will allow inclusion of final quality variables in the monitoring scheme. Initial choice of the potential NOC reference set may contain outlying batches. These batches will be found and removed at the initial round of either MPCA or MPLS modeling. As described in the earlier sections, there will be a temporal variation, in addition to amplitude variation, in process trajectories for each batch resulting in unequal/unsynchronized data. Prior to model development, it is crucial to apply one of the three equalization/synchronization techniques proposed earlier in Sections 6.3.1 (IVT), 6.3.2 (DTW) and 6.3.3 (Curve Registration). Equalized/synchronized data form a three-way array. After transforming the data by unfolding this array into a matrix and by subtracting the mean trajectory set from each batch trajectory set to remove most of the nonlinearity, MPCA and/or MPLS models can be built to investigate if the choice of the reference set is suitable for use in SPM of new batches. Once that decision is made, multivariate control chart limits are constructed according to the formulations given in Section 6.4.2. Development of a multivariate statistical process monitoring scheme will be given by means of a case study based on the unstructured mathematical model of fed-batch penicillin fermentation introduced in Section 2.7.1. A reference set of NOC generated by this simulator (Figures 6.41 and 6.42) will be used where applicable throughout the examples representing different monitoring techniques such as MPCA and MPLS along with the construction of multivariate control charts. Only for the multiblock MPCA technique, an

Table 6.6. Process variables measured throughout the batches

No.

Process Variables

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