Multiresolutional partial least squares and principal component analysis of fluidized bed drying

Abstract

Fluidized bed dryers are used in the pharmaceutical industry for the batch drying of pharmaceutical granulate. Maintaining optimal hydrodynamic conditions throughout the drying process is essential to product quality. Due to the complex interactions inherent in the fluidized bed drying process, mechanistic models capable of identifying these optimal modes of operation are either unavailable or limited in their capabilities. Therefore, empirical models based on experimentally generated data are relied upon to study these systems. Principal Component Analysis (PCA) and Partial Least Squares (PLS) are multivariate statistical techniques that project data onto linear subspaces that are the most descriptive of variance in a dataset. By modeling data in terms of these subspaces, a more parsimonious representation of the system is possible. In this study, PCA and PLS are applied to data collected from a fluidized bed dryer containing pharmaceutical granulate. System hydrodynamics were quantified in the models using high frequency pressure fluctuation measurements. These pressure fluctuations have previously been identified as a characteristic variable of hydrodynamics in fluidized bed systems. As such, contributions from the macroscale, mesoscale, and microscales of motion are encoded into the signals. A multiresolutional decomposition using a discrete wavelet transformation was used to resolve these signals into components more representative of these individual scales before modeling the data. The combination of multiresolutional analysis with PCA and PLS was shown to be an effective approach for modeling the conditions in the fluidized bed dryer. In this study, datasets from both steady state and transient operation of the dryer were analyzed. The steady state dataset contained measurements made on a bed of dry granulate and the transient dataset consisted of measurements taken during the batch drying of granulate from approximately 33 wt.% moisture to 5 wt.%. Correlations involving several scales of motion were identified in both studies. In the steady state study, deterministic behavior related to superficial velocity, pressure sensor position, and granulate particle size distribution was observed in PCA model parameters. It was determined that these properties could be characterized solely with the use of the high frequency pressure fluctuation data. Macroscopic hydrodynamic characteristics such as bubbling frequency and fluidization regime were identified in the low frequency components of the pressure signals and the particle scale interactions of the microscale were shown to be correlated to the highest frequency signal components. PLS models were able to characterize the effects of superficial velocity, pressure sensor position, and granulate particle size distribution in terms of the pressure signal components. Additionally, it was determined that statistical process control charts capable of monitoring the fluid bed hydrodynamics could be constructed using PCAIn the transient drying experiments, deterministic behaviors related to inlet air temperature, pressure sensor position, and initial bed mass were observed in PCA and PLS model parameters. The lowest frequency component of the pressure signal was found to be correlated to the overall temperature effects during the drying cycle. As in the steady state study, bubbling behavior was also observed in the low frequency components of the pressure signal. PLS was used to construct an inferential model of granulate moisture content. The model was found to be capable of predicting the moisture throughout the drying cycle. Preliminary statistical process control models were constructed to monitor the fluid bed hydrodynamics throughout the drying process. These models show promise but will require further investigation to better determine sensitivity to process upsets. In addition to PCA and PLS analyses, Multiway Principal Component Analysis (MPCA) was used to model the drying process. Several key states related to the mass transfer of moisture and changes in temperature throughout the drying cycle were identified in the MPCA model parameters. It was determined that the mass transfer of moisture throughout the drying process affects all scales of motion and overshadows other hydrodynamic behaviors found in the pressure signals.