Applying Computational Fluid Dynamics Technology in Bioprocesses-Part 2

ABSTRACT

Computational fluid dynamics (CFD) has been widely applied as a trouble-shooting and Quality by Design (QbD) tool for bioprocess from downstream, to upstream, to fill–finish. Part 1 of this article series provided an overview of the technology, and the model setup. Here in part 2, we provide a detailed review of the applications of CFD in cell culture and fermentation processes, including flow characterization, mixing, resuspension, scale-up, and cell damage.

Computational fluid dynamics (CFD) is applied in bioprocesses to collect a wide variety of information from many diverse and complex systems comprising complex bio-fluids and particulate matter. Work has ranged from trouble-shooting to process design and optimization. Processes such as filtration, centrifugation, chromatography, product freezing, thawing, and drying have benefited from CFD analysis in many ways. Here, however, we will focus on how bioreactor operations can benefit from CFD. Reviews of the applications of CFD to other processes shared with pharmaceutical industry, including material transport and storage, blending, granulation, milling, compression, film coating, and spray drying, appear in the literature.^1,2

(AMGEN, INC.)

Mechanically agitated or sparged tanks with single or multiple impeller systems are used extensively in the biopharmaceutical industry for various mixing processes, such as fermentation, cell culture, crystallization and emulsification, and resuspension. The empirical approach is still the prevailing practice for process scale-up and scale-down and technology transfer. This article shows how CFD has been used as a Quality by Design tool and for troubleshooting bioreactors.

Process development engineers frequently face biopharmaceutical performance problems such as cell damage, optimizing hardware configurations including sparger design and impeller choice, and system equivalency for technology transfer. CFD can address the critical operating parameters of mixing time, power consumption, particle size distribution, gas distribution, and the just-suspended agitation speed.

FLOW CHARACTERIZATION

The flow field in an agitated bioreactor under turbulent flow conditions is quite complex, consisting of several time-dependent flow systems, including discharge flow originating from the impeller, blade wake, trailing vortex systems, impinging jets on the wall, boundary layers on the wall, baffle-bound vortex systems, and large recirculation zones. Primary flow patterns depend on the impeller geometry, impeller clearance, the presence of baffles, liquid height, and blade pitch. Because the tanks and impellers used in bioprocessing come in all sizes and shapes, flow characterization is difficult.

CFD has been widely used to investigate the flow dynamics in agitated and sparged tanks because it can provide detailed three-dimensional information about velocity and pressure. It can reproduce the key flow pattern—the radial flow generated by a Rushton impeller and the axial flow caused by a pitched-blade impeller. Moreover, it has been used successfully to capture and predict important flow characteristics, such as the large recirculation patterns, the trailing vortex structure in the vicinity of the impeller and cavity formation, and even three distinctly different stable flow patterns (parallel, merging and diverging) in a tank equipped with dual Rushton impellers.^3–10

Recently, numerous studies have verified the existence of the macro-instability (MI), a large-scale low-frequency phenomenon occurring in a baffle-agitated tank.^11–18 The MI, when it appears, scales with the rotational speed of the impeller, N. Its occurrence is dependent on both the impeller geometry and the location of the impeller relative to the tank walls. MIs can cause practical concerns, such as massive vibrations that lead to significant damage to the tank interior wall, impeller shaft, and impeller, and also may be responsible for some observed phenomena in agitated tanks, such as large dissolved oxygen (DO) fluctuations, which can lead to serious control problems.

Three frequencies have been discovered, with the lowest being 0.02 N, the highest around 0.2 N, and various intermediate frequencies in between. These MIs are associated with the mean velocity as determined over a short time interval, rather than with turbulent velocity fluctuations. The MI of the lowest frequency, only under specific conditions and primarily in a region in front of the baffle, is induced by a precessing vortex,¹⁷ whereas the MI of the highest frequency may be related to circulation and is present for a wide range of conditions and geometries across a significant part of the vessel volume.¹⁶ The existence of intermediate MIs indicates that there is some cross talk between the low- and high-frequency motions for a wide range of frequencies.¹³ One intermediate frequency MI, 0.06 N, appears between the turbine and the liquid surface, characterizing an organized modification of the flow pattern that creates a transient violent flow activity in the upper part of the vessel.¹⁴

CFD simulations have identified all three MI frequencies.^{6,11,12,16,19–24} A low-frequency precessional vortex motion in a vessel stirred by a Rushton turbine has MI frequency values nearly identical to the lowest reported frequency.²³ Large-eddy simulation (LES) models have revealed unsteady asymmetric flow patterns with intermediate frequency MIs in a pitched-blade turbine (PBT) impeller stirred-tank that is consistent with reported digital particle image velocimetry data.^19,13 Frequency analysis of CFD results has revealed an MI with a frequency of 0.186 N in a PBT tank with a Reynolds number >20,000, also matching experimental results from different scales of tank.¹⁶

These studies may provide valuable insights for interpreting many previously unexplained hydrodynamic phenomena observed in stirred-tanks, such as the time-dependent settling of solids in dilute suspensions, bi-modal and tri-model velocity histograms in laser-Doppler experiments, and large fluctuations of measured DO and pCO₂.

MIXING AND RESUSPENSION

The published literature on the liquid-phase mixing in a turbulent flow regime presents mathematical models and experimental techniques for determining mixing time, and reveals the effects of the hardware configuration on the mixing performance.²⁴ Mixing is very important for cell culture and fermentation because non-ideal mixing can lead to concentration gradients in nutrients, oxygen, and pH, among others. These gradients are likely to influence cellular behavior, growth, or process yield. Moving oxygen-limiting zones in large fed-batch bioreactors, a result of poor mixing, induce both metabolic and stress responses, which may account for the reduced biomass yield on scale-up and altered physiological properties of cells grown under large-scale conditions.²⁵ CFD has been used to investigate mixing performance in stirred-tanks because it overcomes the limitations of classical reactor flow models, such as compartment and recirculation models.^26–33 One of the applications is to understand local runaways and the quenching of runaway reactions in a tank under imperfect mixing conditions in an effort to develop operating protocols that prevent runaways in stirred reactors.⁹

CFD also can provide a reliable prediction of mixing time.^26–32,34 After a flow field is set up, an unsteady solution of a tracer transport equation leads to the prediction of the evolution of the tracer concentration inside the tank over time. Figure 1 shows the typical profiles of tracer concentration in a stirred-tank in CFD simulations when a Reynolds Average Navier-Stokes (RANS) model is used. The procedure to obtain the mixing time in CFD simulations is similar to the experimental approach.³⁵ Tracer is added and monitors are turned to trace the concentration of the tracer at randomly chosen locations in the tank. Although it is hard for a RANS-based CFD model to exactly match the transient responses recorded by experimental conductivity probes, the predicted mixing time is in agreement with experiments, especially for single-phase flow. The curve of tracer response predicted by LES was found to be in better agreement with the experimental curve because of the LES's capability of accurately capturing the scalar fluctuations in the tank.^36,32

Figure 1

The measured mixing time depends on the location of the added tracer.^29,35,37 The simulation should be in agreement with experimental values and empirical predictions as long as the addition point is kept away from the wall. In addition, accurately predicting the mean flow-field is key to successfully predicting the mixing time.^28,38,39 Mixing time as a function of agitation speed is also plotted in Figure 1. The simulations can provide correlations of the mixing time to operating and geometry parameters such as agitation speed (N), impeller diameter (D), tank diameter (T), and power number of the impeller (P₀), as indicated by the solid line in the plot. This information can greatly help the scale-up and scale-down processes if the mixing time is the primary concern.

The presence of solid particles will dramatically change the flow characteristics in agitated tanks. CFD simulations can provide detailed insight into the behavior of particles and how the liquid flow is altered by the presence of particles.⁴⁰ The presence of solids in a fluid actually slows down the mixing process, sometimes by more than 10-fold that of a single-phase state.⁴¹ LES confirmed that particles heavier than the fluid tend to rise slowly to the top in unbaffled, tall, turbulently stirred-tanks.⁴²

CFD simulations have been widely applied to investigate the multi-phase mixing (resuspension) process in an agitated or sparged tank, using either the Euler–Euler approach for dense systems or the Euler–Lagrange approach for dilute-to-moderate dense systems, the former being more popular than the latter because it is less demanding on computation resources. The two-fluid (Euler–Euler) approach can determine the flow pattern and the concentration field in a dense solid–liquid suspension in industrial vessels, when a kinetic theory of granular flow for the solid stress and the solid pressure is adopted, taking into account particle–particle interactions.⁴³ Predictions for solid distribution in an industrial crystallizer show agreement with experiments for several agitation speeds and mean concentrations.

The two-fluid model, in conjunction with the slide-mesh algorithm, also is used to model the resuspension process in stirred-tanks.^44,45 The model is not only able to predict the formation of the clear liquid layer in the upper part of the tank, but also can provide quantitative agreement with experimental data on suspension height. The model also can predict the critical impeller speed over a wide range of design and operating conditions, e.g., solid loading (0.34–15% wt), different impeller designs (Rushton turbine, pitched blade down- and up-flow turbines),⁴⁵ solid particle sizes (120–1,000 mm) and for various superficial gas velocities (0–10 mm/s). However, it has been observed that the drag coefficient may sometimes need to be fine-tuned to match the available experimental data.⁴⁶

The performed studies demonstrate that the Euler–Euler approach, when applied to multi-phase flows without consideration for bubble coalescence or break-up, can agree with experiments, particularly when the bubble-flow is dominant.⁴⁷ When bubble breakup and coalescence are accounted for, and bubble size distribution is important, many researchers have used population balance models to model the spatial evolution of gas bubbles in bioreactors.^48–50 The mechanisms responsible for bubble coalescence and breakage are complex and not yet fully understood. For turbulent flows, most models formulate the kernel functions for the bubble coalescence according to random collision driven by turbulence and wake entrainment and the kernel functions for bubble breakage to turbulent eddies.⁵⁰

Although a uniformly mixed flow-field is optimal, CFD simulations indicate that full homogeneity of the gas–liquid mixture may never be achieved.⁵¹ Figure 2 shows the distribution of bubbles in a production-scale cell culture bioreactor, which is strongly dependent on the impeller type, sparger design, agitation rate, and sparging rate.

Figure 2

Power draw, another important parameter for bioreactor operation, depends primarily on the impeller geometry and fluid dynamics around the impeller blades.⁵² CFD provides a convenient and reliable tool to calibrate the power number of the impellers and the power consumption for a given bioreactor using the torque on the impeller surface and shaft. For a multiple impeller system, the calculated overall power number is less than the value expected if each of the impellers had the same power number as the single ones because of interference between adjacent impellers.⁵³ Power usage for a sparged tank depends on bubble coalescence, generally lower than the ungassed case.⁵⁴

FERMENTATION AND CELL CULTURE

It has been observed that the biomass yield on the carbon and energy source is decreased by the scale-up of aerobic processes. For example, in an E. coli-based recombinant protein process, the biomass yield of glucose and the maximum cell density reached in the process dropped by about 20% when scaling up from 3 to 9,000 L.⁵⁵ In large-scale fed-batch processes, poor mixing may cause a large gradient of the concentration of the limiting substrate. Streptomyces fradiae, has been shown to have a change of 55-fold in the rates of oxygen and nutrient consumption as it circulates through different micro-environments of varying concentrations of oxygen and nutrient.⁵⁶ Two possible scenarios may come up—the formation of moving oxygen-limiting zones when the cell density is high enough, caused by the fast use of sugar by cells, and the occurrence of overflow metabolism responded by the many microorganisms being exposed to glucose concentration above a critical level—Saccaromyces cerevisiae producing ethanol and E. coli-producing acetate.^25,57 Furthermore, the occurrence of oxygen-limitation may result in anaerobic reactions and concomitant stress responses.⁵⁸

Aeration is an essential requirement for aerobic cell lines. However, DO gradients are likely to occur when the characteristic time for oxygen uptake is shorter than the mixing time. In aerobic fermentation systems, the rate of oxygen transfer to the cells usually is the limiting factor. A key factor that influences oxygen transfer is bubble size distribution, which depend on turbulent characteristics in the reactor.⁵⁹ The bubble sizes dictate the available interfacial area for gas–liquid mass transfer. The scale-up and design of bioreactors must meet oxygen transfer requirements while maintaining low shear rates and a controlled flow pattern. Therefore, understanding the hydrodynamic environment is critical for fermentation processes.⁶⁰

One of the challenges for fermentation process scale-up is to prevent concentration gradients (from the feed zone to the interior of the tank) resulting in further limitations and unwanted byproduct formation or inhibition of product rate. The following examples indicate that CFD simulations can be applied for the optimization of fed batch processes to avoid oxygen limitations, overflow metabolism, or catabolite regulation.

Large-Scale Tanks

Model simulations for large-scale tanks with multiple Rushton and axial flow impellers of different combinations shows that feeding the concentrated sugar solution into the impeller region and axial flow impellers leads to the best equidistribution of substrate.⁶¹ Bacillus subtilis is used as a model for an oxygen sensitive culture for the characterization of the effects of inhomogeneities on the intensity of oxygen transfer gas liquid in stirred-tank reactor. CFD predictions for DO concentration and the production rate of butanediol show qualitative agreement with experimental observations.⁶¹

Gradients of glucose in time and space are found in a 30 m³ fed-batch cultivation of S. cerevisiae grown in minimal medium to a cell density of 20 g/1, which were shown to depend on the feed position. Simulations with an integrated CFD and biokinetic model are performed to investigate the glucose gradients of this model.⁶² The simulations show a glucose gradient formed according to a change in the point of feeding and caused by a different cell concentration. The glucose concentration is high near the feed inlet and declines further away. The effect of the feed position appears as a generally higher mean concentration for the top feed compared with the bottom.

Scale-up

It is not rare to observe abnormal performances such as lower cell viabilities, higher death rates, and a drop of titer when cell culture processes are scaled up from laboratory-scale to pilot or product scale. The potentially lethal events in a mechanically agitated and sparged bioreactor have been identified.^63–66 They are bubble formation and detachment at the sparger, bubble interaction with the impeller in the impeller zones, bubbles rising along their path surfacing to the interface, and bubbles bursting at the media–air interface. Sparging gas into a tank generates strong turbulent flow and high shearing force at the sparger.⁶⁷ Without surfactant additives such as Pluronic F68, cells tend to attach to bubbles and thus experience shearing forces in the thin film surrounding rising bubbles and in the wake behind bubbles.^68–71

A complex dynamic takes place in the impeller zones when stable air-filled cavities are formed. Centrifugal force competes with buoyancy force in the impeller zones, of which the coupling interactions determine the bubble residence time, bubble breakup frequency, and bubble size distribution.^52,72 The existence of the medium–air interface has a large effect on cell damage.^73–80 If the air–medium interface at the top of the tank is eliminated, no cell damage is observed at impeller speeds up to 600 rpm for hydridoma cells.⁸¹ When a bubble approaches the air–liquid interface and subsequently bursts as a result of film draining, the shear stress in the resultant rimming flow is estimated at up to 200 Pa.⁷⁵ On average, about 1,000 cells are killed per 2 mm of bubble rupture.⁷⁹ Computer simulations of bubble rupture processes indicate that the rupture of small air bubbles in pure water generates an energy dissipation rate three to four orders of magnitude higher than that typically created in bioreactors solely because of agitation.^82–84 The energy dissipation rate increases rapidly with a decrease in bubble size.

CFD can provide information on the parameters most closely linked to cell damage, such as shear stress, power consumption, Kolmogrov eddy length scale distribution, turbulence characteristics including Reynolds stress, kinetic energy, and energy dissipation rate.^85,86 CFD models also can predict process conditions that will cause vortices to occur and also the product vortex strength, compute cell residence time, and provide bubble size distribution, etc. With these kinds of information, one can easily trouble-shoot process performance issues. CFD simulation results show that shear force on the impeller surface, Reynolds stress, and turbulence energy dissipation rate in the impeller zones are unlikely to cause cell damage under typical cell culture process conditions. On the other hand, the interaction between the impeller and bubbles, which leads to bubble breakup in the impeller zones, and bubble bursting at the air–media interface are more likely to be responsible for observed cell damage.^87,88

SUMMARY

A detailed review has been provided of how computational fluid dynamics (CFD) can be used to analyze bioreactor and fermentater unit operations, including flow characterization, mixing, resuspension, scale-up, and cell damage. CFD technology is a useful approach that provides detailed information that helps process development scientists understand cell culture and fermentation process performance problems encountered during technology transfer. However, some of the studied cases also indicate the inadequacy of the modeling efforts because of the complexity of biological systems and inaccurate physical models. Understanding a process physically and biologically is key to the success of the CFD modeling and simulations with regard to biopharmaceutical processes.

Zhiwu (David) Fang is the founder and principal consultant of Systems Quality-by-Design, Inc., Newbury Park, CA, 626.716.2016, zfang@systemsqbd.com.

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