A New Integrated Modeling Approach with Case Studies for Gas Transmission of Container Closure Headspace

This article presents a new theoretical integrated modeling approach for calculating container closure integrity (CCI) that concurrently accounts for both diffusion and mass/volumetric flow in real time; practical case studies are also presented. For pharmaceutical, biological, cell, and gene therapies, container closure systems (CCSs) must ensure drug sterility and stability by safeguarding against microbial contamination and gaseous ingress (e.g., oxygen, carbon dioxide, moisture) according to product requirements. In addition to the testing approach for evaluating CCI performance, a modeling approach can be an important part of a CCI control strategy. Modeling is a powerful tool that provides information in situations where testing is not feasible, technically impossible, too time-consuming, or too expensive. Previously published models have lacked a systematic approach or the versatility needed to coherently and concurrently integrate both diffusion and effusion to solve problems arising in field applications. The new integrated modeling approach described in this article applies a robust numerical method to real-world applications. The model is based on the law of conservation and continuity for molecular flow, Fick's law of diffusion, and the Darcy-Weisbach theory of frictional mass/volumetric flow. This new integrated modeling approach handles time-dependent diffusion and effusion by combining diffusion and mass/volumetric flow seamlessly in real time. For a CCS under vacuum filled with nitrogen, this new modeling approach is able to reveal that oxygen ingress into the CCS through a leak path will enter in two phases, starting with effusion and continuously followed by diffusion in a seamless transition. Our integrated modeling approach is able to calculate and capture the exact timing of the phase transition point, providing unique understanding of complicated CCS problems. Using the finite difference method, all modeling results are numerically solved from the governing equations along with initial and boundary conditions for each individual case. The modeling results were precise and consistent with previously published testing results. This new integrated modeling approach displayed its capability and versatility to handle complicated leakage scenarios in practical applications. As a part of CCI control strategy, the modeling approach is a powerful tool for evaluating leaks, gauging their leak sizes, determining whether the CCS conforms to product requirements, and making informed decisions accordingly. Although additional studies are to be carried out to fully develop the potential of this model, the applications hold great promise and in addition provide insight into CCI and may also provide a solid foundation for CCI testing method development and validation for CCI performance.