CFD simulation coupled with population balance equations for aerated stirred bioreactors

Validation of a CFD model for cell culture bioreactors at large scale and its application in scale-up

Among all the operating parameters that control the cell culture environment inside bioreactors, appropriate mixing and aeration are crucial to ensure sufficient oxygen supply, homogeneous mixing, and CO2 stripping. A model-based manufacturing facility fit approach was applied to define agitation and bottom air flow rates during the process scale-up from laboratory to manufacturing, of which computational fluid dynamics (CFD) was the core modeling tool. The realizable k-ε turbulent dispersed Eulerian gas-liquid flow model was established and validated using experimental values for the volumetric oxygen transfer coefficient (kLa). Model validation defined the process operating parameter ranges for application of the model, identified mixing issues (e.g., impeller flooding, dissolved oxygen gradients, etc.) and the impact of antifoam on kLa. Using the CFD simulation results as inputs to the models for oxygen demand, gas entrance velocity, and CO2 stripping aided in the design of the agitation and bottom air flow rates needed to meet cellular oxygen demand, control CO2 levels, mitigate risks for cell damage due to shear, foaming, as well as fire hazards due to high O2 levels in the bioreactor gas outlet. The recommended operating conditions led to the completion of five manufacturing runs with a 100% success rate. This model-based approach achieved a seamless scale-up and reduced the required number of at-scale development batches, resulting in cost and time savings of a cell culture commercialization process.

Designing a Model-Driven Approach Towards Rational Experimental Design in Bioprocess Optimization

To enable a more rational optimization approach to drive the transition from lab-scale to large industrial bioprocesses, a systematic framework coupling both experimental design and integrated modeling was established to guide the workflow executed from small flask scale to bioreactor scale. The integrated model relies on the coupling of biotic cell factory kinetics to the abiotic bioreactor hydrodynamics to offer a rational means for an in-depth understanding of two-way spatiotemporal interactions between cell behaviors and environmental variations. This model could serve as a promising tool to inform experimental work with reduced efforts via full-factorial in silico predictions. This chapter thus describes the general workflow involved in designing and applying this modeling approach to drive the experimental design towards rational bioprocess optimization.

CFD modelling of a wave-mixed bioreactor with complex geometry and two degrees of freedom motion

Optimizing bioprocesses requires an in-depth understanding, from a bioengineering perspective, of the cultivation systems used. A bioengineering characterization is typically performed via experimental or numerical methods, which are particularly well-established for stirred bioreactors. For unstirred, non-rigid systems such as wave-mixed bioreactors, numerical methods prove to be problematic, as often only simplified geometries and motions can be assumed. In this work, a general approach for the numerical characterization of non-stirred cultivation systems is demonstrated using the CELL-tainer bioreactor with two degree of freedom motion as an example. In a first step, the motion is recorded via motion capturing, and a 3D model of the culture bag geometry is generated via 3D-scanning. Subsequently, the bioreactor is characterized with respect to mixing time, and oxygen transfer rate, as well as specific power input and temporal Kolmogorov length scale distribution. The results demonstrate that the CELL-tainer with two degrees of freedom outperforms classic wave-mixed bioreactors in terms of oxygen transport. In addition, it was shown that in the cell culture version of the CELL-tainer, the critical Kolmogorov length is not surpassed in any simulation.

Industrial Case-Study-Based Computational Fluid Dynamic (CFD) Modeling of Stirred and Aerated Bioreactors

Industrial bioreactors featuring inadequate geometry and operating conditions may depress the effectiveness and the efficiency of the hosted bioprocess. Computational fluid dynamics (CFD) can be used to find a suitable operating match between the target bioprocess and the available bioreactor. The aim of this work is to investigate the feasibility of addressing bioreactor improvement problems in the bioprocess industry with the aid of such mainstream tools as industry-standard CFD. This study illustrates how to effectively simulate both the impeller rotation and air supply and discusses the way toward model validation at the 4.1 m³ capacity scale. Referring to experimentally measured process values, the developed full-scale model successfully predicted the power draw, liquid phase level, and mixing time with errors lower than 4.6, 1.1, and 6.7%, respectively, thus suggesting the illustrated approach as a best practice design method for the bioprocess industry. The validated model was employed to improve performance by reducing the power draw in aerated conditions with a minimal operational derating.

A model-driven approach towards rational microbial bioprocess optimization

Due to sustainability concerns, bio-based production capitalizing on microbes as cell factories is in demand to synthesize valuable products. Nevertheless, the nonhomogenous variations of the extracellular environment in bioprocesses often challenge the biomass growth and the bioproduction yield. To enable a more rational bioprocess optimization, we have established a model-driven approach that systematically integrates experiments with modeling, executed from flask to bioreactor scale, and using ferulic acid to vanillin bioconversion as a case study. The impacts of mass transfer and aeration on the biomass growth and bioproduction performances were examined using minimal small-scale experiments. An integrated model coupling the cell factory kinetics with the three-dimensional computational hydrodynamics of bioreactor was developed to better capture the spatiotemporal distributions of bioproduction. Full-factorial predictions were then performed to identify the desired operating conditions. A bioconversion yield of 94% was achieved, which is one of the highest for recombinant Escherichia coli using ferulic acid as the precursor.

Computational fluid dynamics analysis of mixing and gas-liquid mass transfer in wave bag bioreactor

Single use bioreactors provide an attractive alternative to traditional deep-tank stainless steel bioreactors in process development and more recently manufacturing process. Wave bag bioreactors, in particular, have shown potential applications for cultivation of shear sensitive human and animal cells. However, the lack of knowledge about the complex fluid flow environment prevailing in wave bag bioreactors has so far hampered the development of a scientific rationale for their scale up. In this study, we use computational fluid dynamics (CFD) to investigate the details of the flow field in a 20-L wave bag bioreactor as a function of rocking angle and rocking speed. The results are presented in terms of local and mean velocities, mixing, and energy dissipation rates, which are used to create a process engineering framework for the scale-up of wave bag bioreactors. Proof-of-concept analysis of mixing and fluid flow in the 20-L wave bag bioreactor demonstrates the applicability of the CFD methodology and the temporal and spatial energy dissipation rates integrated and averaged over the liquid volume in the bag provide the means to correlate experimental volumetric oxygen transfer rates (k_L a) data with power per unit volume. This correlation could be used as a rule of thumb for scaling up and down the wave bag bioreactors.

Recommended turbulent energy dissipation rate for biomass and lipid production of Scenedesmus obliquus in an aerated photosynthetic culture system

Effects of turbulent energy dissipation rate (increased from 1.28 × 10^-6 to 1.67 × 10^-5 m² s^-3) on Scenedesmus obliquus biomass and lipid accumulation at different aeration rates (0.3, 0.6, 0.9, 1.2, and 1.5 L min^-1) were investigated. The turbulent energy dissipation rate was calculated by CFD model simulation. When the turbulent energy dissipation rate increased to 7.30 × 10^-6 m² s^-3, the biomass and lipid productivity increased gradually, and finally reached their maximum values of 1.11 × 10⁷ cells mL^-1 and 16.0 mg L^-1 day^-1, respectively. When it exceeded 7.30 × 10^-6 m² s^-3, the biomass and lipid productivity showed a decreasing trend. Therefore, the most favorable turbulent energy dissipation rate for S. obliquus growth and lipid accumulation was 7.30 × 10^-6 m² s^-3.

Approximate Moment Methods for Population Balance Equations in Particulate and Bioengineering Processes

Population balance modeling is an established framework to describe the dynamics of particle populations in disperse phase systems found in a broad field of industrial, civil, and medical applications. The resulting population balance equations account for the dynamics of the number density distribution functions and represent (systems of) partial differential equations which require sophisticated numerical solution techniques due to the general lack of analytical solutions. A specific class of solution algorithms, so-called moment methods, is based on the reduction of complex models to a set of ordinary differential equations characterizing dynamics of integral quantities of the number density distribution function. However, in general, a closed set of moment equations is not found and one has to rely on approximate closure methods. In this contribution, a concise overview of the most prominent approximate moment methods is given.

Numerical Simulation of Bubble-Liquid Two-Phase Turbulent Flows in Shallow Bioreactor

An improved second-order moment bubble-liquid two-phase turbulent model is developed to predict the hydrodynamic characteristics of the shallow bioreactor using two height-to-diameter ratios of H/D = 1.4 and H/D = 2.9. The two-phase hydrodynamic parameters, the bubble normal and shear stress, the bubble energy dissipation rate, the bubble turbulent kinetic energy, etc. were numerically simulated. These parameters increased along with flow direction and constituted a threat to cells living at far distance away from the gas jetting inlet regions, rather than a finding of higher cell damage at near the jetting inlet region, as reported by Babosa et al. 2003. A new correlation named the turbulent energy production of bubble-liquid two-phase flow was proposed to successfully verify this experimental observation. A smaller H/D ratio makes more contributions to the generation of lower turbulent energy productions, which are in favor of the alleviation of cell damage. The extremely long and narrow shape of the bioreactor is deteriorative for cell living.

Using CFD simulations and statistical analysis to correlate oxygen mass transfer coefficient to both geometrical parameters and operating conditions in a stirred-tank bioreactor

Optimization of a bioreactor design can be an especially challenging process. For instance, testing different bioreactor vessel geometries and different impeller and sparger types, locations, and dimensions can lead to an exceedingly large number of configurations and necessary experiments. Computational fluid dynamics (CFD), therefore, has been widely used to model multiphase flow in stirred-tank bioreactors to minimize the number of optimization experiments. In this study, a multiphase CFD model with population balance equations are used to model gas-liquid mixing, as well as gas bubble distribution, in a 50 L single-use bioreactor vessel. The vessel is the larger chamber in an early prototype of a multichamber bioreactor for mammalian cell culture. The model results are validated with oxygen mass transfer coefficient (k_L a) measurements within the prototype. The validated model is projected to predict the effect of using ring or pipe spargers of different sizes and the effect of varying the impeller diameter on k_L a. The simulations show that ring spargers result in a superior k_L a compared to pipe spargers, with an optimum sparger-to-impeller diameter ratio of 0.8. In addition, larger impellers are shown to improve k_L a. A correlation of k_L a is presented as a function of both the reactor geometry (i.e., sparger-to-impeller diameter ratio and impeller-to-vessel diameter ratio) and operating conditions (i.e., Reynolds number and gas flow rate). The resulting correlation can be used to predict k_L a in a bioreactor and to optimize its design, geometry, and operating conditions.

Characterizing the fluid dynamics in the flow fields of cylindrical orbitally shaken bioreactors with different geometry sizes

Orbitally shaken bioreactors (OSRs) are commonly used for the cultivation of mammalian cells in suspension. To aid the geometry designing and optimizing of OSRs, we conducted a three-dimensional computational fluid dynamics (CFD) simulation to characterize the flow fields in a 10 L cylindrical OSR with different vessel diameters. The liquid wave shape captured by a camera experimentally validated the CFD models established for the cylindrical OSR. The geometry size effect on volumetric mass transfer coefficient (k_La) and hydromechanical stress was analyzed by varying the ratio of vessel diameter (d) to liquid height at static (h _L), d/h _L. The highest value of k_La about 30 h^-1 was observed in the cylindrical vessel with the d/h _L of 6.35. Moreover, the magnitudes of shear stress and energy dissipation rate in all the vessels tested were below their minimum values causing cells damage separately, which indicated that the hydromechanical-stress environment in OSRs is suitable for cells cultivation in suspension. Finally, the CFD results suggested that the d/h _L higher than 8.80 should not be adopted for the 10 L cylindrical OSR at the shaking speed of 180 rpm because the "out of phase" state probably will happen there.

Population Balance Modeling: Current Status and Future Prospects

Population balance modeling is undergoing phenomenal growth in its applications, and this growth is accompanied by multifarious reviews. This review aims to fortify the model's fundamental base, as well as point to a variety of new applications, including modeling of crystal morphology, cell growth and differentiation, gene regulatory processes, and transfer of drug resistance. This is accomplished by presenting the many faces of population balance equations that arise in the foregoing applications.

Verification of energy dissipation rate scalability in pilot and production scale bioreactors using computational fluid dynamics

Suspension mammalian cell cultures in aerated stirred tank bioreactors are widely used in the production of monoclonal antibodies. Given that production scale cell culture operations are typically performed in very large bioreactors (≥ 10,000 L), bioreactor scale-down and scale-up become crucial in the development of robust cell-culture processes. For successful scale-up and scale-down of cell culture operations, it is important to understand the scale-dependence of the distribution of the energy dissipation rates in a bioreactor. Computational fluid dynamics (CFD) simulations can provide an additional layer of depth to bioreactor scalability analysis. In this communication, we use CFD analyses of five bioreactor configurations to evaluate energy dissipation rates and Kolmogorov length scale distributions at various scales. The results show that hydrodynamic scalability is achievable as long as major design features (# of baffles, impellers) remain consistent across the scales. Finally, in all configurations, the mean Kolmogorov length scale is substantially higher than the average cell size, indicating that catastrophic cell damage due to mechanical agitation is highly unlikely at all scales.