Verification of Energy Dissipation Rate Scalability in Pilot and Production Scale Bioreactors Using Computational Fluid Dynamics Chris Johnson, Venkatesh Natarajan, and Chris Antoniou Global Engineering Sciences, Biogen Idec Inc., 10 Cambridge Center, Cambridge, MA 02142 DOI 10.1002/btpr.1896 Published online March 10, 2014 in Wiley Online Library (wileyonlinelibrary.com)
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 scaledependence 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 C 2014 American Institute of Chemical Engineers Biotechnol. highly unlikely at all scales. V Prog., 30:760–764, 2014 Keywords: bioreactors, antibodies, CFD, Kolmogorov length scales, energy dissipation rates, scalability
Introduction Suspension mammalian cell culture in aerated stirred tank bioreactors is a commonly used upstream process in the manufacture of monoclonal antibodies. It is critical to maintain efficient mixing conditions and aeration rates in these bioreactors to promote spatial uniformity of nutrient concentrations and to ensure appropriate oxygen intake. Impeller agitation rates and aeration rates both contribute to the overall hydrodynamic stresses that could damage or decrease the productivity of mammalian cells.1 It has been reported in the literature that in suspension cultures, the hydrodynamic stresses induced by mechanical agitation are not sufficient to damage cells in the absence of sparging;1,2 however, these stresses cannot be ignored due to their potential to impact both the mass transfer properties and the shear lethality of the bubbles sparged into the cell culture media. The turbulent energy dissipation rate, e, is a common metric used to characterize flow conditions in mixing systems.3 This scalar quantity is a measure of the rate of increase in internal energy of a system per unit mass resulting from the conversion of input mechanical energy to heat via viscous shear. For mixing vessels, the energy dissipation rates have been estimated using computational fluid dynamics (CFD) simulations4 and/or empirical methods such as Laser Doppler Anemometry,5 Constant Temperature Anemometry,6 and Particle Tracking Velocimetry.3 In this communication, e Correspondence concerning this article should be addressed to V. Natarajan at [email protected]. 760
will consistently be multiplied by the fluid density (q) to quantify turbulent energy dissipation in the more recognizable engineering units of power per unit volume. Given that production scale cell culture operations are typically performed in very large bioreactors ( 10,000 L), bioreactor scale-up and scale-down become crucial in the development of robust cell culture processes. For a successful scale-up of a cell culture operation, it is important to understand the scale-dependence of the distribution of qe in a bioreactor. At the production scale, CFD methods are more practical and cost-effective than experimental methods in the estimation of qe, and this is reflected in the recent increase in CFD studies of bioreactor hydrodynamics.7,8 Rathore et al.9 generated a CFD model for a 3 L bioreactor and performed a full factorial design of experiments (DOE) which tested three levels of gas flow and agitation rates as well as two liquid levels. Subsequently, statistical techniques were used to generate a mixing design space for the bioreactor using the simulation DOE results. Other researchers have used CFD to characterize bioreactors with volumes ranging from microliters10 to cubic meters.11 Rathore and coworkers,7 in their review of biotechnology applications that have attracted CFD analysis, provide several examples of CFD being used to optimize impeller design, number and location; generate velocity fields; and evaluate mixing conditions. Most of these analyses take place at a single scale and in vessels in which design elements (some listed above) can be manipulated to optimize performance. We believe that the power of CFD simulations C 2014 American Institute of Chemical Engineers V
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Table 1. Pilot- and Production-Scale Bioreactors Analyzed for Hydrodynamic Scalability Set 1 Bioreactor 200 L 2,000 L 315 L Number of baffles Shaft angle # of Impellers, diameter Power number per impeller Impeller diameter/vessel diameter Impeller diameter/max liquid height Aspect ratio
Zero (h 1 1) One, D NP 1.06 (DI/DV) 1.61 (DI/HL) 1.13 (HL/DV)
Zero h One, 2.2 (D) NP 1.02 (DI/DV) 1.77 (DI/HL) (HL/DV)
Two (h 1 1) Two, 0.9 (D) 1.50 (NP) (DI/DV) (DI/HL) 1.73 (HL/DV)
Set 2 15,000 L A
15,000 L S
Two (h 2 1) Two, 3.5 (D) 1.50 (NP) (DI/DV) 1.08 (DI/HL) 1.58 (HL/DV)
Two 0 Two, 3.5 (D) 1.25 (NP) (DI/DV) 1.08 (DI/HL) 1.58 (HL/DV)
The dimensional ratios are presented in relative terms to protect the confidentiality of the bioreactor designs. The baseline for each category, represented by a letter variable, corresponds to the smallest ratio or non-zero value for the design parameter. Non-baseline values are represented as a function set in terms of the baseline. For example, the power number per impeller of the 315 L bioreactor is 1.53 that of the 200 L bioreactor. Italics in the bioreactor names indicate angled (A) or straight (S) shaft differentiation for the two 15,000 L bioreactors.
can be expanded to tackle a different set of challenges presented by the need to maintain consistent hydrodynamic conditions in bioreactors with fixed configurations at different scales. This is a crucial challenge that biopharmaceutical manufacturers often face in the process development and technology transfer stages of commercial operations. Biogen Idec has a unique collection of production bioreactors in its pilot and manufacturing facilities that must be well characterized to accurately design, scale, and model production cell culture processes. These bioreactors can be grouped into two sets corresponding to the scale of commercial manufacturing in which they are involved: one set contains a 2,000 L bioreactor used in small scale manufacturing and its 200 L pilot scale replica; the other contains two distinct 15,000 L bioreactors used in different large scale manufacturing facilities and the 315 L pilot bioreactor used to model both. The variability in the design of these vessels (e.g., the number and size of impellers, dimensional ratios, and shaft angle) is captured in Table 1. The objective of this study was to use CFD to assess the hydrodynamic environments in these five bioreactors over a wide range of operating conditions. CFD simulation and DOE have been used to compare hydrodynamics across scales and to assess the relative impact of fixed bioreactor design features in existing pilot and manufacturing plant production bioreactors. A new scalability constant, kb, has been defined to compare how power dissipation rates vary from vessel to vessel to assess whether or not traditional P/V matching is sufficient to maintain consistent hydrodynamic conditions across scales and designs.
Theory Liquid flow in a mixing vessel is characterized by the presence of turbulent eddies. Initially, the velocity and length scales of these turbulent eddies are both large enough to render the turbulent Reynolds number very large, i.e., inertial forces dominate viscous forces. “Vortex shedding” results in the cascade of turbulent kinetic energy from large to small eddies to satisfy the conservation of momentum. As shedding proceeds, smaller eddies with lower turbulent Reynolds numbers begin to appear.12,13 Near the end of this process, the turbulent Reynolds number approaches unity and viscous forces become important. At this point, viscous shear dissipates eddy turbulent kinetic energy at the energy dissipation rate (e) which, when multiplied by the fluid density (q), gives the share of power input per unit volume dissipated by turbulent viscosity.
Kolmogorov proposed a relationship for quantifying the eddy length scale at which viscous eddy energy dissipation occurs 3 1=4 m k e
(1)
where m is defined as the kinematic viscosity of the fluid. Several experimental studies have correlated cell death in simple culture systems with large e and correspondingly small k.14,15 The theory holds that turbulent eddies much larger or smaller than the biological cells do not inhibit cell viability; however, once k is similar to the cell diameter, the dissipating eddies expose the cells to damaging viscous shear.
CFD Tools and Methods TM R Workbench Software products in ANSYSV (R14.0) were used at each stage of the CFD modeling process. Computer aided design (CAD) geometries were created in Design Modeler based on technical drawings supplied by the bioreactor manufacturer. The finite volume grids consisting of 106 mesh cells were created for each vessel in ANSYS Mesh and R to be included in the case setup. exported to FLUENTV 16 Models were setup in FLUENT to accurately capture the hydrodynamics of the turbulent cell culture flow field within each of the bioreactor vessels. Impeller rotation has been simulated using a moving reference frame. The liquid surface was modeled as a zero-shear boundary condition; this simplification reduced the complexity of the model in a non-critical region to reduce the computation time required for each simulation. As the focus of this work was to analyze the spatial distribution of energy dissipation rates due to mechanical agitation, the cell culture was modeled as a single-phase liquid with the material properties of water at 37 C. Solution initialization consisted of 2,000 iterations using a standard twoequation k-e turbulence model, and solution refinement was performed using the seven-equation RSM turbulence model. A total of 80 simulations were performed by testing four impeller speeds at four culture volumes for each of the five bioreactors. Hydrodynamic scalability was defined as the uniformity of volume-average qe with P/V held constant across different vessels:
qe5kb P=V
(2)
where kb is a bioreactor-specific hydrodynamic coefficient that quantifies the fraction of power input dissipated via turbulence rather than bulk flow shear or wall effects. Results
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Figure 1.
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Comparison of experimentally measured and CFD-simulated bioreactor blending times at full volume and variable RPM in the 15,000 L centerline shaft bioreactor and the 315 L bioreactor.
Figure 2. Simulation results with qe plotted as function of P/V according to Eq. 2. Bioreactor Set 1 is plotted in blue; bioreactor Set 2 is plotted in red.
are also presented in the form of cumulative k distributions and hydrodynamic contour plots.
Model Verification Blending simulations were executed with the 315 L and 15,000 L centerline bioreactor models to compare model results to empirical data. Mixing experiments have been previously performed in these vessels using a discrete set of operating conditions (varying agitator revolutions per minute (RPM) and water for injection (WFI) volume) with 85% phosphoric acid (0.025 mL L21 of working volume) added at the liquid surface to an open tank under ambient conditions. The acid was introduced at the same location in each experiment. Two pH probes, inserted at different liquid heights, were used to measure pH for the duration of the experiment. Once the pH values stabilized, the sensor data was analyzed to identify the time at which pH at both probes was within 5% of the final pH value. The operating conditions used in the CFD model verification simulations were chosen to match those from a selection of the experiments described above. For the mixing simulations, monitor surfaces were defined in the CFD mesh to collect species concentration data in approximately the same location as the experimental probes. A tracer species was patched to the liquid volume near the top surface boundary of the mesh (at the same location as in the experiment) and a transient species
transport simulation (initialized by a steady-state flow simulation) was run until the concentration of the tracer species at both monitor surfaces converged to 6 5 % of the volumeaverage concentration. The calculated blend time was determined by the value of the final time step in these simulations. Acceptable agreement between CFD and experimental results was obtained for cases in which the simulated working volume was sufficient to submerge the top impeller by several inches (Figure 1). The model was able to capture data trends related to scale and impeller speed, with simulated blend times in a few cases being slightly shorter than the experimentally measured times. It is unknown whether these small discrepancies were caused by the modeling assumptions, measurement error, or pH probe lag time. The models used in this study are thus considered acceptably verified given that they produced blend results that closely match those generated by the physical experiments. Although mixing is not a perfect proxy for turbulence and energy dissipation, checking the turbulence models by comparing blend times was determined to be the best method available to verify the models given the limited availability of experimental data types at different operating conditions and vessel scales.
Results Simulation results show that an exceptional degree of overall qe scalability exists within each of the two bioreactor sets.
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Plotting qe as a function of P/V shows that the hydrodynamic performance of each bioreactor set can be accurately characterized by a single linear function (Figure 2). This indicates that quantitative design differences within each bioreactor set, including small variations in vessel dimensional ratios and even large disparities in shaft angle, do not have a major impact on the overall qe scalability of the bioreactors. The separation in the data belonging to different bioreactor sets demonstrates that having pilot bioreactors that are specifically designed for each production bioreactor is essential to maintaining qe scalability. The difference between the slopes of the best-fit lines in Figure 2, the scalability coefficients kb, shows that energy dissipation rates vary significantly between the two bioreactor sets. The fact that the calculated scalability coefficients of the baffled, dual impeller bioreactors (kb,2) are more than 1.5 times larger than those of the unbaffled, single impeller bioreactors (kb,1) indicates that a much greater share of power input is being dissipated at turbulent length scales in the 315 L and 15,000 L bioreactors than in the 200 L and 2,000 L bioreactors. The Kolmogorov length scale distributions derived from simulation data show a discernible difference in the eddy length scales produced by a given power per volume input
Figure 3. Histogram showing the distribution of Kolmogorov length scale exposure fractions measured as the percentage of time cells spend at k.
Figure 4.
for the two bioreactor styles: Set 2 has a greater share of shorter length scales while Set 1 distributions have similar minimum length scales with a higher percentage at longer length scales (Figure 3). As the shortest calculated length scales (40 lm for Set 2) are nearly twice the approximate cell diameter of 17 lm, the risk of catastrophic cell damage due to mechanical stirring is very low for both sets. Thus, both qe and k distributions support the conclusion that overall hydrodynamic scalability exists within, but not between, bioreactor sets. However, the increase in granularity going from volume averaged quantities to distributions shows that slight differences in hydrodynamic performance exist within the bioreactor sets due to subtle variations in vessel geometry. The leftward shift of the 15,000 L S distribution shows that the change going from an angled to centerline shaft does have an impact on local hydrodynamics—a larger effect than the 503 scale-up with nearly identical geometry going from the 315 L to the 15,000 L A. A final examination of the simulation results looks at the contours of qe on the central plane (Figure 4). An important difference to note between the profiles of Set 1 (top row) and Set 2 (bottom row) is that the single impeller Set 1 bioreactors have much more stratification of energy dissipation rates as a function of vessel depth. For Set 1, dissipation rates are high up around the impeller but generally lower near the bottom of the vessel. The dissipation rates at the top and bottom of the Set 2 bioreactors, by contrast, are more closely aligned. This phenomenon of lower turbulent energy dissipation at the bottom of the Set 1 bioreactors could have ripple effects to other cell culture considerations such as mass transfer and mixing. As the spargers are inserted at low culture depth and the mass transfer coefficient is a function of local turbulent dissipation rates and the liquid–gas interfacial surface area, this difference could have a significant impact on mass transfer resulting from lower energy dissipation in the high air volume fraction regions at the bottom of the tank. Additionally, greater bottom settling could result from lower turbulence at the bottom of the tank.
Contours of qe on the central plane.
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Conclusions CFD can be used to add an additional layer of depth to bioreactor scalability analysis. CFD simulations at different scales can provide advanced theoretical data that can be used to assess the relative differences in qe and k profiles and the potential impact on cell culture performance. In addition, CFD can identify how certain design elements affect scalability in differently sized bioreactor vessels. For instance, if a perfectly proportional scaled down replica of the production vessel is not available, CFD can be used to gauge how design differences can impact cell culture performance characteristics. On the other hand, if the two bioreactors of interest are identically designed with scaled dimensions, CFD can assess the relative differences in shear profiles created by parameters that are not maintained constant in a typical constant P/V scale down (e.g., tip speed). In both cases, CFD can be used to generate robust, detailed theoretical data sets to compare bioreactor performance across scales for the purpose of process scale-up, scale-down experimentation, and technology transfers. In this communication, CFD simulations have been performed to generate qe and k distributions for five different production bioreactor configurations to evaluate their hydrodynamic performance within and across scales. The results show that hydrodynamic scalability is achievable as long as major design features (# of baffles, impellers) remain consistent across the scales. The analysis confirms that Biogen Idec has appropriately designed separate pilot scale vessels for use in scaled down experimentation for the 2,000 L and 15,000 L production bioreactors used in biologics manufacturing. Finally, in all configurations, the CFD analysis has calculated values for mean k that are substantially larger than the average cell diameter, indicating that catastrophic cell damage due to mechanical agitation is highly unlikely over a wide range of operating conditions for all five Biogen Idec production bioreactors analyzed in this study.
Acknowledgments The contributions of Kelly Wiltberger, Weiwei Hu, An Zhang, and Toby Blackburn of BIIB Cell Culture Technical Development, RTP, NC were essential to the CFD modeling process. The authors thank Peter Walls of BIIB GES for exceptional research work performed during his summer internship.
Notation DI DV HL DI/DV DI/HL
= = = = =
impeller diameter (m) vessel diameter (m) maximum liquid height (m) baseline impeller to vessel diameter ratio baseline impeller diameter to maximum liquid height ratio HL/Dv = baseline aspect ratio
kb = bioreactor hydrodynamic scalability coefficient NP = baseline impeller power number
Greek letters e= h= k= t= q=
turbulent dissipation rate (W kg21) baseline shaft angle from the vertical (deg) Kolmogorov length scale (lm) fluid kinematic viscosity (m2 s21) fluid density (kg m23)
Literature Cited 1. Chisti Y. Animal-cell damage in sparged bioreactors. Trends Biotechnol. 2000;18:420–432. Available at: http://www.ncbi.nlm. nih.gov/pubmed/10998508. Accessed November, 2013. 2. Michaels JD, Mallik AK, Papoutsakis ET. Injury of cultured animal cells: do cell-to-bubble interactions in the bulk liquid injure cells? Biotechnol Bioeng. 1996;51:399–409. 3. Mollet M, Ma N, Zhao Y, Brodkey R, Taticek R, Chalmers JJ. Bioprocess equipment: characterization of energy dissipation rate and its potential to damage cells. Biotechnol Progr. 2004; 20:1437–1448. doi:10.1021/bp0498488. 4. Zhang H, Zhang K, Fan S. CFD simulation coupled with population balance equations for aerated stirred bioreactors. Eng Life Sci. 2009;9:421–430. doi:10.1002/elsc.200800074. 5. Zhou G, Kresta SM. Impact of tank geometry on the maximum turbulence energy dissipation rate for impellers. AIChE J. 1996; 42:2476–2490. 6. Wernersson ES, Tragardh C. Scale-up of rushton turbineagitated tanks. Chem Eng Sci. 1999;54:4245–4256. 7. Sharma C, Malhotra D, Rathore AS. Review of computational fluid dynamics applications in biotechnology processes. Biotechnol Progr. 2011;27:1497–1510. doi:10.1002/btpr.689. 8. Werner S, Kaiser SC, Kraume M, Eibl D. Computational fluid dynamics as a modern tool for engineering characterization of bioreactors. Pharm Bioprocess. 2014;2:85–99. 9. Rathore AS, Sharma C, Persad AA. Use of computational fluid dynamics as a tool for establishing process design space for mixing in a bioreactor. Biotechnol Progr. 2011;28:382–391. doi: 10.1002/btpr.745. 10. Barrett TA, Wu A, Zhang H, Levy MS, Lye GJ. Microwell engineering characterization for mammalian cell culture process development. Biotechnol Bioeng. 2010;105:260–275. doi: 10.1002/bit.22531. 11. Zou X, Xia J, Chu J, Zhuang Y, Zhang S. Real-time fluid dynamics investigation and physiological response for erythromycin fermentation scale-up from 50 L to 132 m3 fermenter. Bioprocess Biosyst Eng. 2012;35:789–800. doi:10.1007/s00449-011-0659-z. 12. Durbin PA, Pettersson Reif BA. Statistical Theory and Modeling for Turbulent Flows, 2nd ed. UK: Wiley; 2011. 13. Pope SB. Turbulent Flows. UK: Cambridge University Press; 2000. 14. McQueen A, Meilhoc E, Bailey JE. Flow effects on the viability and lysis of suspended mammalian cells. Biotechnol Lett. 1987; 9:831–836. 15. Croughan MS, Hamel J-F, Wang DIC. Hydrodynamic effects on animal cells grown in microcarrier cultures. Biotechnol Bioeng. 1987;29:130–141. doi:10.1002/bit.21158. 16. ANSYS. ANSYS FLUENT Theory Guide. In: ANSYS FLUENT Theory Guide, Vol. 15317. Release 14. ANSYS, Inc, Canonsburg, PA, USA. 2012:724–746. Manuscript received Nov. 18, 2013, and revision received Feb. 26, 2014.
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 scaledependence 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 C 2014 American Institute of Chemical Engineers Biotechnol. highly unlikely at all scales. V Prog., 30:760–764, 2014 Keywords: bioreactors, antibodies, CFD, Kolmogorov length scales, energy dissipation rates, scalability
Introduction Suspension mammalian cell culture in aerated stirred tank bioreactors is a commonly used upstream process in the manufacture of monoclonal antibodies. It is critical to maintain efficient mixing conditions and aeration rates in these bioreactors to promote spatial uniformity of nutrient concentrations and to ensure appropriate oxygen intake. Impeller agitation rates and aeration rates both contribute to the overall hydrodynamic stresses that could damage or decrease the productivity of mammalian cells.1 It has been reported in the literature that in suspension cultures, the hydrodynamic stresses induced by mechanical agitation are not sufficient to damage cells in the absence of sparging;1,2 however, these stresses cannot be ignored due to their potential to impact both the mass transfer properties and the shear lethality of the bubbles sparged into the cell culture media. The turbulent energy dissipation rate, e, is a common metric used to characterize flow conditions in mixing systems.3 This scalar quantity is a measure of the rate of increase in internal energy of a system per unit mass resulting from the conversion of input mechanical energy to heat via viscous shear. For mixing vessels, the energy dissipation rates have been estimated using computational fluid dynamics (CFD) simulations4 and/or empirical methods such as Laser Doppler Anemometry,5 Constant Temperature Anemometry,6 and Particle Tracking Velocimetry.3 In this communication, e Correspondence concerning this article should be addressed to V. Natarajan at [email protected]. 760
will consistently be multiplied by the fluid density (q) to quantify turbulent energy dissipation in the more recognizable engineering units of power per unit volume. Given that production scale cell culture operations are typically performed in very large bioreactors ( 10,000 L), bioreactor scale-up and scale-down become crucial in the development of robust cell culture processes. For a successful scale-up of a cell culture operation, it is important to understand the scale-dependence of the distribution of qe in a bioreactor. At the production scale, CFD methods are more practical and cost-effective than experimental methods in the estimation of qe, and this is reflected in the recent increase in CFD studies of bioreactor hydrodynamics.7,8 Rathore et al.9 generated a CFD model for a 3 L bioreactor and performed a full factorial design of experiments (DOE) which tested three levels of gas flow and agitation rates as well as two liquid levels. Subsequently, statistical techniques were used to generate a mixing design space for the bioreactor using the simulation DOE results. Other researchers have used CFD to characterize bioreactors with volumes ranging from microliters10 to cubic meters.11 Rathore and coworkers,7 in their review of biotechnology applications that have attracted CFD analysis, provide several examples of CFD being used to optimize impeller design, number and location; generate velocity fields; and evaluate mixing conditions. Most of these analyses take place at a single scale and in vessels in which design elements (some listed above) can be manipulated to optimize performance. We believe that the power of CFD simulations C 2014 American Institute of Chemical Engineers V
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Table 1. Pilot- and Production-Scale Bioreactors Analyzed for Hydrodynamic Scalability Set 1 Bioreactor 200 L 2,000 L 315 L Number of baffles Shaft angle # of Impellers, diameter Power number per impeller Impeller diameter/vessel diameter Impeller diameter/max liquid height Aspect ratio
Zero (h 1 1) One, D NP 1.06 (DI/DV) 1.61 (DI/HL) 1.13 (HL/DV)
Zero h One, 2.2 (D) NP 1.02 (DI/DV) 1.77 (DI/HL) (HL/DV)
Two (h 1 1) Two, 0.9 (D) 1.50 (NP) (DI/DV) (DI/HL) 1.73 (HL/DV)
Set 2 15,000 L A
15,000 L S
Two (h 2 1) Two, 3.5 (D) 1.50 (NP) (DI/DV) 1.08 (DI/HL) 1.58 (HL/DV)
Two 0 Two, 3.5 (D) 1.25 (NP) (DI/DV) 1.08 (DI/HL) 1.58 (HL/DV)
The dimensional ratios are presented in relative terms to protect the confidentiality of the bioreactor designs. The baseline for each category, represented by a letter variable, corresponds to the smallest ratio or non-zero value for the design parameter. Non-baseline values are represented as a function set in terms of the baseline. For example, the power number per impeller of the 315 L bioreactor is 1.53 that of the 200 L bioreactor. Italics in the bioreactor names indicate angled (A) or straight (S) shaft differentiation for the two 15,000 L bioreactors.
can be expanded to tackle a different set of challenges presented by the need to maintain consistent hydrodynamic conditions in bioreactors with fixed configurations at different scales. This is a crucial challenge that biopharmaceutical manufacturers often face in the process development and technology transfer stages of commercial operations. Biogen Idec has a unique collection of production bioreactors in its pilot and manufacturing facilities that must be well characterized to accurately design, scale, and model production cell culture processes. These bioreactors can be grouped into two sets corresponding to the scale of commercial manufacturing in which they are involved: one set contains a 2,000 L bioreactor used in small scale manufacturing and its 200 L pilot scale replica; the other contains two distinct 15,000 L bioreactors used in different large scale manufacturing facilities and the 315 L pilot bioreactor used to model both. The variability in the design of these vessels (e.g., the number and size of impellers, dimensional ratios, and shaft angle) is captured in Table 1. The objective of this study was to use CFD to assess the hydrodynamic environments in these five bioreactors over a wide range of operating conditions. CFD simulation and DOE have been used to compare hydrodynamics across scales and to assess the relative impact of fixed bioreactor design features in existing pilot and manufacturing plant production bioreactors. A new scalability constant, kb, has been defined to compare how power dissipation rates vary from vessel to vessel to assess whether or not traditional P/V matching is sufficient to maintain consistent hydrodynamic conditions across scales and designs.
Theory Liquid flow in a mixing vessel is characterized by the presence of turbulent eddies. Initially, the velocity and length scales of these turbulent eddies are both large enough to render the turbulent Reynolds number very large, i.e., inertial forces dominate viscous forces. “Vortex shedding” results in the cascade of turbulent kinetic energy from large to small eddies to satisfy the conservation of momentum. As shedding proceeds, smaller eddies with lower turbulent Reynolds numbers begin to appear.12,13 Near the end of this process, the turbulent Reynolds number approaches unity and viscous forces become important. At this point, viscous shear dissipates eddy turbulent kinetic energy at the energy dissipation rate (e) which, when multiplied by the fluid density (q), gives the share of power input per unit volume dissipated by turbulent viscosity.
Kolmogorov proposed a relationship for quantifying the eddy length scale at which viscous eddy energy dissipation occurs 3 1=4 m k e
(1)
where m is defined as the kinematic viscosity of the fluid. Several experimental studies have correlated cell death in simple culture systems with large e and correspondingly small k.14,15 The theory holds that turbulent eddies much larger or smaller than the biological cells do not inhibit cell viability; however, once k is similar to the cell diameter, the dissipating eddies expose the cells to damaging viscous shear.
CFD Tools and Methods TM R Workbench Software products in ANSYSV (R14.0) were used at each stage of the CFD modeling process. Computer aided design (CAD) geometries were created in Design Modeler based on technical drawings supplied by the bioreactor manufacturer. The finite volume grids consisting of 106 mesh cells were created for each vessel in ANSYS Mesh and R to be included in the case setup. exported to FLUENTV 16 Models were setup in FLUENT to accurately capture the hydrodynamics of the turbulent cell culture flow field within each of the bioreactor vessels. Impeller rotation has been simulated using a moving reference frame. The liquid surface was modeled as a zero-shear boundary condition; this simplification reduced the complexity of the model in a non-critical region to reduce the computation time required for each simulation. As the focus of this work was to analyze the spatial distribution of energy dissipation rates due to mechanical agitation, the cell culture was modeled as a single-phase liquid with the material properties of water at 37 C. Solution initialization consisted of 2,000 iterations using a standard twoequation k-e turbulence model, and solution refinement was performed using the seven-equation RSM turbulence model. A total of 80 simulations were performed by testing four impeller speeds at four culture volumes for each of the five bioreactors. Hydrodynamic scalability was defined as the uniformity of volume-average qe with P/V held constant across different vessels:
qe5kb P=V
(2)
where kb is a bioreactor-specific hydrodynamic coefficient that quantifies the fraction of power input dissipated via turbulence rather than bulk flow shear or wall effects. Results
762
Figure 1.
Biotechnol. Prog., 2014, Vol. 30, No. 3
Comparison of experimentally measured and CFD-simulated bioreactor blending times at full volume and variable RPM in the 15,000 L centerline shaft bioreactor and the 315 L bioreactor.
Figure 2. Simulation results with qe plotted as function of P/V according to Eq. 2. Bioreactor Set 1 is plotted in blue; bioreactor Set 2 is plotted in red.
are also presented in the form of cumulative k distributions and hydrodynamic contour plots.
Model Verification Blending simulations were executed with the 315 L and 15,000 L centerline bioreactor models to compare model results to empirical data. Mixing experiments have been previously performed in these vessels using a discrete set of operating conditions (varying agitator revolutions per minute (RPM) and water for injection (WFI) volume) with 85% phosphoric acid (0.025 mL L21 of working volume) added at the liquid surface to an open tank under ambient conditions. The acid was introduced at the same location in each experiment. Two pH probes, inserted at different liquid heights, were used to measure pH for the duration of the experiment. Once the pH values stabilized, the sensor data was analyzed to identify the time at which pH at both probes was within 5% of the final pH value. The operating conditions used in the CFD model verification simulations were chosen to match those from a selection of the experiments described above. For the mixing simulations, monitor surfaces were defined in the CFD mesh to collect species concentration data in approximately the same location as the experimental probes. A tracer species was patched to the liquid volume near the top surface boundary of the mesh (at the same location as in the experiment) and a transient species
transport simulation (initialized by a steady-state flow simulation) was run until the concentration of the tracer species at both monitor surfaces converged to 6 5 % of the volumeaverage concentration. The calculated blend time was determined by the value of the final time step in these simulations. Acceptable agreement between CFD and experimental results was obtained for cases in which the simulated working volume was sufficient to submerge the top impeller by several inches (Figure 1). The model was able to capture data trends related to scale and impeller speed, with simulated blend times in a few cases being slightly shorter than the experimentally measured times. It is unknown whether these small discrepancies were caused by the modeling assumptions, measurement error, or pH probe lag time. The models used in this study are thus considered acceptably verified given that they produced blend results that closely match those generated by the physical experiments. Although mixing is not a perfect proxy for turbulence and energy dissipation, checking the turbulence models by comparing blend times was determined to be the best method available to verify the models given the limited availability of experimental data types at different operating conditions and vessel scales.
Results Simulation results show that an exceptional degree of overall qe scalability exists within each of the two bioreactor sets.
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Plotting qe as a function of P/V shows that the hydrodynamic performance of each bioreactor set can be accurately characterized by a single linear function (Figure 2). This indicates that quantitative design differences within each bioreactor set, including small variations in vessel dimensional ratios and even large disparities in shaft angle, do not have a major impact on the overall qe scalability of the bioreactors. The separation in the data belonging to different bioreactor sets demonstrates that having pilot bioreactors that are specifically designed for each production bioreactor is essential to maintaining qe scalability. The difference between the slopes of the best-fit lines in Figure 2, the scalability coefficients kb, shows that energy dissipation rates vary significantly between the two bioreactor sets. The fact that the calculated scalability coefficients of the baffled, dual impeller bioreactors (kb,2) are more than 1.5 times larger than those of the unbaffled, single impeller bioreactors (kb,1) indicates that a much greater share of power input is being dissipated at turbulent length scales in the 315 L and 15,000 L bioreactors than in the 200 L and 2,000 L bioreactors. The Kolmogorov length scale distributions derived from simulation data show a discernible difference in the eddy length scales produced by a given power per volume input
Figure 3. Histogram showing the distribution of Kolmogorov length scale exposure fractions measured as the percentage of time cells spend at k.
Figure 4.
for the two bioreactor styles: Set 2 has a greater share of shorter length scales while Set 1 distributions have similar minimum length scales with a higher percentage at longer length scales (Figure 3). As the shortest calculated length scales (40 lm for Set 2) are nearly twice the approximate cell diameter of 17 lm, the risk of catastrophic cell damage due to mechanical stirring is very low for both sets. Thus, both qe and k distributions support the conclusion that overall hydrodynamic scalability exists within, but not between, bioreactor sets. However, the increase in granularity going from volume averaged quantities to distributions shows that slight differences in hydrodynamic performance exist within the bioreactor sets due to subtle variations in vessel geometry. The leftward shift of the 15,000 L S distribution shows that the change going from an angled to centerline shaft does have an impact on local hydrodynamics—a larger effect than the 503 scale-up with nearly identical geometry going from the 315 L to the 15,000 L A. A final examination of the simulation results looks at the contours of qe on the central plane (Figure 4). An important difference to note between the profiles of Set 1 (top row) and Set 2 (bottom row) is that the single impeller Set 1 bioreactors have much more stratification of energy dissipation rates as a function of vessel depth. For Set 1, dissipation rates are high up around the impeller but generally lower near the bottom of the vessel. The dissipation rates at the top and bottom of the Set 2 bioreactors, by contrast, are more closely aligned. This phenomenon of lower turbulent energy dissipation at the bottom of the Set 1 bioreactors could have ripple effects to other cell culture considerations such as mass transfer and mixing. As the spargers are inserted at low culture depth and the mass transfer coefficient is a function of local turbulent dissipation rates and the liquid–gas interfacial surface area, this difference could have a significant impact on mass transfer resulting from lower energy dissipation in the high air volume fraction regions at the bottom of the tank. Additionally, greater bottom settling could result from lower turbulence at the bottom of the tank.
Contours of qe on the central plane.
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Conclusions CFD can be used to add an additional layer of depth to bioreactor scalability analysis. CFD simulations at different scales can provide advanced theoretical data that can be used to assess the relative differences in qe and k profiles and the potential impact on cell culture performance. In addition, CFD can identify how certain design elements affect scalability in differently sized bioreactor vessels. For instance, if a perfectly proportional scaled down replica of the production vessel is not available, CFD can be used to gauge how design differences can impact cell culture performance characteristics. On the other hand, if the two bioreactors of interest are identically designed with scaled dimensions, CFD can assess the relative differences in shear profiles created by parameters that are not maintained constant in a typical constant P/V scale down (e.g., tip speed). In both cases, CFD can be used to generate robust, detailed theoretical data sets to compare bioreactor performance across scales for the purpose of process scale-up, scale-down experimentation, and technology transfers. In this communication, CFD simulations have been performed to generate qe and k distributions for five different production bioreactor configurations to evaluate their hydrodynamic performance within and across scales. The results show that hydrodynamic scalability is achievable as long as major design features (# of baffles, impellers) remain consistent across the scales. The analysis confirms that Biogen Idec has appropriately designed separate pilot scale vessels for use in scaled down experimentation for the 2,000 L and 15,000 L production bioreactors used in biologics manufacturing. Finally, in all configurations, the CFD analysis has calculated values for mean k that are substantially larger than the average cell diameter, indicating that catastrophic cell damage due to mechanical agitation is highly unlikely over a wide range of operating conditions for all five Biogen Idec production bioreactors analyzed in this study.
Acknowledgments The contributions of Kelly Wiltberger, Weiwei Hu, An Zhang, and Toby Blackburn of BIIB Cell Culture Technical Development, RTP, NC were essential to the CFD modeling process. The authors thank Peter Walls of BIIB GES for exceptional research work performed during his summer internship.
Notation DI DV HL DI/DV DI/HL
= = = = =
impeller diameter (m) vessel diameter (m) maximum liquid height (m) baseline impeller to vessel diameter ratio baseline impeller diameter to maximum liquid height ratio HL/Dv = baseline aspect ratio
kb = bioreactor hydrodynamic scalability coefficient NP = baseline impeller power number
Greek letters e= h= k= t= q=
turbulent dissipation rate (W kg21) baseline shaft angle from the vertical (deg) Kolmogorov length scale (lm) fluid kinematic viscosity (m2 s21) fluid density (kg m23)
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