Primary
drying is the most time-consuming and energy-intensive
step in pharmaceutical freeze-drying. Minimizing the duration of this
stage is of paramount importance to speed up process development and
product manufacturing. In this study, we propose a stochastic modeling
framework that can help to reach this target. The framework is composed
of five sequential steps: model development, sensitivity analysis,
model calibration, model validation, and dynamic optimization. Three
critical issues are addressed and accounted for in the model structure,
namely, (i) the effect of time-varying operating conditions on the
process key performance indicators (KPIs); (ii) the dynamic evolution
of the water vapor partial pressure inside the drying chamber; and
(iii) the impact of drying heterogeneity on the primary drying duration.
We cope with the first two issues by introducing macroscopic energy
and mass balances within the model formulation. The third issue is
addressed by allocating intralot variability as a parametric uncertainty
in the model parameter with the strongest sensitivity toward the process
KPIs. The proposed stochastic model is calibrated and validated with
data generated from industrial experiments. Nonlinear dynamic optimization
is then exploited to minimize the duration of primary drying while
simultaneously guaranteeing the fulfillment of tight constraints on
the product temperature and sublimation rate. Experimental results
show a reduction of ∼20% of the primary drying duration with
the optimized protocol when compared to standard (i.e., at constant
shelf temperature and chamber pressure) protocols, while ensuring
the same product quality.