Scaling-up of a bioprocess involves replicating the cell growth behavior observed in laboratory-scale vessels within larger manufacturing settings, typically with operating volumes ranging from 1000 L to 10,000 L, or potentially larger. Maintaining a consistent growth environment, as characterized by parameters such as the specific power dissipation rate, mixing time, and/or oxygen mass transfer rate, becomes challenging (and often impossible) across this range of vessel sizes(Paul et al., 2004). Instead, as a general rule, scale-up necessarily involves trade-offs between culture uniformity, system control, and process yield (Nienow, 2009; Megawati et al., 2018). Moreover, beyond these unavoidable differences in culture hydrodynamics, a multiple order-of-magnitude variation in operating volume also changes the vessel/impeller topology and the structure of the auxiliary control systems (e.g., in-line oxygen control, nutrient feed pumps, gas spargers, etc.) (Hall, 2010). Although empirical design correlations can provide general guidance, most process scale-up campaigns are empirically and/or heuristically driven (Delvigne and Noorman, 2017).

For bioprocess scale-up, the power per unit volume (P/V) is often used as a scale-up criterion. However, despite its widespread use in the industry, a shortcoming that often occurs while scaling up by P/V is longer mixing times, which can lead to unoptimized distribution of nutrients throughout the culture and the occurrence of hydrodynamic microenvironments at large scale (Alavijeh et al., 2022). Additionally, higher strain rate across the liquid phase at large scale can be particularly consequential to the health of mammalian cells that are sensitive to shear (Kreitmayer et al., 2023). The ultimate aim for biological systems in particular is often focused on maintaining a consistent dissolved oxygen (DO), pH, and nutrient concentration within the cell culture across all operating volumes (Alavijeh et al., 2022). Dissolved oxygen levels in laboratory-scale systems are easy to maintain at set point, as blend time is typically fast relative to the oxygen transfer and consumption rates. At larger production scales, however, the competition between oxygen transfer, nutrient mixing, and oxygen consumption can produce low oxygen zones across the fluid (Hanspal et al., 2022). Similarly, pH gradients can often impact the cellular growth and productivity within the culture. Nutrient gradients across the culture, especially for larger systems with continuous supplement feeding, can also be problematic: high glucose concentrations near a nutrient source, for example, can lead to unanticipated protein glycation and glycoxidation. Conversely, low nutrient concentrations in other regions of the culture can lead to improper protein expression and poor cell growth. These variations tend to reduce process efficiency and yield in production-scale reactors, when compared to laboratory-scale test systems (Carpio, 2020).

Multiple researchers have used computational fluid dynamics (CFD) simulations to characterize the effects of operating scale on hydrodynamics in bioreactors (Villiger et al., 2018; Scully et al., 2020). Some of these CFD models consider chemical reactions in tandem with hydrodynamics (Farzan and Ierapetritou, 2017; Elqotbi et al., 2013). In most, however, the fluid dynamics are not directly coupled to any cell growth kinetics. As such, although the CFD simulations improve the granularity with which the flow field across the vessel is understood, the net effect of this velocity field on biomass growth and process yield can be unclear. Moreover, very few CFD models consider the time-varying dynamics of embedded feedback logic systems, such as in-line oxygen, pH, or nutrient control (Bhatia et al., 2018; Oliveira et al., 2023). These missing components limit the generality of most CFD models, as they do not capture the dynamic interactions and feedback mechanisms that occur in physical systems.

In this work, an approach for building time-accurate, three-dimensional bioreactor CFD models with fully coupled fluid mixing, auxiliary control system dynamics, and cell reaction kinetics is developed. Like traditional CFD simulations, this work shows particular interest in generalized, first-principles modeling techniques to develop mechanistic models that appeal to the conservation of mass/momentum and require minimal numerical re-tuning with changes in operating scale and reactor topology. Beyond these traditional CFD models, an extended approach to include physical and time-dependent coupling with the in-line process controllers and the cell growth reaction kinetics was developed. The present work intends to develop a physics-based digital twin that can predict process outcome and yield across operating scales directly from the reactor operating conditions, in-line controller logic, and underlying cell growth kinetics.

The proposed approach presents a unifying bridge between the fluid eddy, system controller, and cell growth timescales. The fluid eddy timescale, which is characterized by physics such as the eddy turnover times and bubble break-up timescale, is on the order of 10−3 seconds (Pope, 2000; Ravelet, Colin, and Risso, 2011). The controller response timescale, which is characterized by the controller gain and reset time, is on the order of 102 seconds (Oliveira et al., 2023). The production timescale, which is characterized by the cell growth rate, is on the order of 106 seconds (López-Meza et al., 2016). Bridging the eddy/bubble timescales with the controller timescale is straightforward due to advances in graphics processing unit (GPU)-based computing paradigms (Haringa, 2022; Shu and Yang, 2018; Shu et al., 2020). Bridging the eddy/bubble timescales with the cell growth timescale, in a practical sense, requires some degree of self-similar reaction time scaling, which is introduced and discussed in this manuscript. The combined effects of GPU-acceleration and reaction scaling result in a fully coupled model that can simulate a multi-week manufacturing process in a practical industrial runtime.