The biomanufacturing processes that produce biologic drugs has become an extremely important area of study within the pharmaceutical industry. Within such processes, the drug substance is typically produced by living organisms within stirred tank bioreactors that require a continuous supply of sparged oxygen. The overall oxygen transfer rate to the fluid is a nonlinear convolution of the gas bubble size distribution, fluid properties, local fluid energy dissipation rates, and local dissolved oxygen concentrations. The complexity of this process presents challenges to process scale-up and intensification. In this work, we propose, implement, and validate a mechanistic transport model for predicting oxygen transfer rates within stirred tank bioreactors. To begin, we describe the relevant conservation laws and key principles from turbulence theory that govern mass transfer. Next, we present a physics-based modeling approach for solving these equations in tandem and in real-time. We then systematically validate the model against experimental data at operating scales ranging from 5 L to 2000 L. By running the algorithm on graphics processing units (GPUs), the approach is shown to solve at timescales practical for industrial application.