Thermodynamic Balance vs. Computational Fluid Dynamics Approach for the Outlet Temperature Estimation of a Benchtop Spray Dryer

The use of design space (DS) is a key milestone in the quality by design (QbD) of pharmaceutical processes. It should be considered from early laboratory development to industrial production, in order to support scientists with making decisions at each step of the product's development life. Presently, there are no available data or methodologies for developing models for the implementation of design space (DS) on laboratory-scale spray dryers. Therefore, in this work, a comparison between two different modeling approaches, thermodynamics and computational fluid dynamics (CFD), to a laboratory spray dryer model have been evaluated. The models computed the outlet temperature (T-out) of the process with a new modeling strategy that includes machine learning to improve the model prediction. The model metrics calculated indicate how the thermodynamic model fits T-out data better than CFD; indeed, the error of the CFD model increases towards higher values of T-out and feed rate (FR), with a final mean absolute error of 10.43 K, compared to the 1.74 K error of the thermodynamic model. Successively, a DS of the studied spray dryer equipment has been implemented, showing how T-out is strongly affected by FR variation, which accounts for about 40 times more than the gas flow rate (G(in)) in the DS. The thermodynamic model, combined with the machine learning approach here proposed, could be used as a valid tool in the QbD development of spray-dried pharmaceutical products, starting from their early laboratory stages, replacing traditional trial-and-error methodologies, preventing process errors, and helping scientists with the following scale-up.