cfd prediction of gas-liquid mass transfer in a large ... · pdf fileaerobic cell culturing is...

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 6 (2016) pp 4500-4507 © Research India Publications. http://www.ripublication.com

4500

CFD Prediction of Gas-Liquid Mass Transfer in A Large Scale Spin Filter

Bioreactor

L. Niño

Department of Chemical Engineering, Bioprocess Group, Universidad de Antioquia, Carrera 53 N. 61-30. Medellín, Colombia.

M. Peñuela

Department of Chemical Engineering, Bioprocess Group, Universidad de Antioquia, Carrera 53 N. 61-30. Medellín, Colombia.

G.R. Gelves

Department of Chemical Engineering, Bioprocess Group, Universidad de Antioquia, Carrera 53 N.° 61-30. Medellín, Colombia.

Abstract

In this work simulations were developed in order to allow the examinations of heterogeneities in the scale up of gas-liquid mass transfer in 10 and 1000 L spin filter bioreactors using CFD simulations (Computational Fluid Dynamics). The effects of turbulence, rotating flow, drop breakage were simulated by using the k-e, MRF (Multiple Reference Frame) and PBM (Population Balance Model), respectively, providing detailed information of important bioreactor conditions. The numerical results based on typical animal culturing conditions are simulated and a decrease of 70 percent 𝑘𝐿𝑎 was found in large scale spin filter bioreactor concerning 10 L scale. So that, CFD modeling predicts hydrodynamic conditions, which can affect the gas-liquid mass transfer in large scale bioreactors. Motivated by these results, CFD simulations are qualified as a useful alternative for predicting scale up spin filter bioprocess in animal cell culture applications which are characterized by the constrain of achieving relatively high mass transfer conditions and avoiding cellular damage. Keywords: bioreactor, scale up, multiple reference frame (MRF), population balance model (PBM), spin filter

Introduction Global productivity in large scale processes depends on gas-liquid conditions. Supplying adequate oxygen levels in aerobic cell culturing is a common problem in fermentation technology. This problem is increased in high cell density bioreactors due to oxygen transfer rate limitations affecting cell growth and productivity [1]. Such limitations are common in perfusion cell cultures leading to anoxic process, cellular damage and therefore loss of cell viability [2]. Perfusion bioprocessing is used for improving the productivity of such cultures. One of the most common devices for perfusion processes is the Spin-Filter, which is used for animal and plant cell cultures in continuous production processes. Such bioreactors incorporate a rotating filter device

into a stirred tank reactor. Cells are inoculated and cultivated by continuous addition of fresh nutrient medium. The spin-filter device minimizes the loss of cells through the bioreactor harvest. Consequently biomass productivity is increased substantially compared to batch or fed batch mode [2]. However cell density is dependent on oxygen requirements and therefore mass transfer limitations take place. Additionally, the loss of complete mixing conditions with increasing scale could generate gradients leading to a departure from optimal conditions found in laboratory scale. Heterogeneities in 𝑘𝐿𝑎 gas-liquid mass transfer aplications are caused by poor mixing generated by empirical methods adopting as scale up strategies. Conventional bioprocess scale up methodologies are based on empirical approaches regardless gas-liquid mass transport phenomena governing the scale up process. Knowing the hydrodynamic behavior on the scale up bioreactors by using CFD allows identifying the degree of departure from perfect mixing conditions associated with scaling rules [3]. In recent years, there has been fast development in the hydrodynamic modeling by the application of computational fluid dynamics (CFD). Successful examples are given covering the range from stirred device systems, including models from single phase rotating impeller systems [4-8] to the use of population balance models [9-16]. The main purpose of these models is the knowledge of the flow fields in conventional stirred impellers related to mass transfer profiles. Although these models have been used for understanding flow field and particle dynamics, gas-liquid mass transfer phenomena and hydrodynamics in scale up bioprocesses are not studied so far for large scale spin filter bioreactors. Due the lack appropriate methodologies, spin filters for animal cell cultures in large scale bioreactors are currently developed by combining a broad knowledge of the previous product formulations with empirical experimentation. The evaluation of a scale up bioprocess is generally unpredictable because of the large examinations demanded in a laboratory scale before commercialization. Due to the very large number of possible formulation and processing combinations that need to be


4501

explored in a scale up process, the traditional trial-and-error approach requires significant time and resources [3, 17]. To the authors knowledge CFD methodologies for analyzing heterogeneities in gas-liquid mass transfer have never been used previously for large scale spin filter bioreactors. Hence it is the motivation of this work to present a CFD simulation approach for the estimation of heterogeneities in 𝑘𝐿𝑎 mass transfer due to the scale up bioprocess in a large scale spin filter bioreactor. Methods Bioreactor setup

A Spin Filter stirred tank bioreactor (New Brunswick Celligen 310) with 0.008 m3 working volume (T = 0.21 m) was used in this study. The mixing is driven by a conventional Pitched Blade Impeller (D = 0.1 m) mounted on a 0.02 m diameter shaft and placed at the center line of the bioreactor. The gas is supplied through a 0.02 m diameter cylinder micro-sparger. The operating conditions chosen were defined by typical settings used for culturing animal cells: Ni = 70, 140 and 210 rpm, aeration rate = 0.04 vvm. These settings were tested for defining the best condition [1] for being implemented in further scale up. The properties used in the primary phase (water) are: ρL: 998.2 kgm−3; μL: 0.001 kgm−1 s−1. σ: 0.07 Nm−1. Secondary phase properties (air) are: ρG: 1.225 kgm−3, μG = 1.789 10−5 kgm−1 s−1 [18]. For simulating heterogeneities in the scale up stage, a 1000 L virtual bioreactor was dimensioned (0.86 m diameter) maintaining a geometric similarity from the tested 10 L bioreactor. Operational conditions were defined based on the best condition found in lab scale bioreactor (10 l) and using the P/V (constant power input per liquid volume) empirical scale up criterion [19].

Computational Fluid Dynamic Model

The gas and liquid phase are treated as interpenetrating continua and conservation of mass and momentum equations are solved for each phase. The conservation equations for each phase are derived to obtain a set of equations, which have similar structure for all phases [15, 20-25]. The Eulerian model is a multiphase model in ANSYS FLUENT 13.0. It solves a system of n-momentum and continuity equations for each phase. The coupling is achieved through pressure and interfacial exchange coefficients. The mass conservation equation for each phase is shown (Eq. 1): 𝜕

𝜕𝑡(𝜌𝑖𝛼𝑖) + 𝛻 ∙ (𝛼𝑖𝜌𝑖�⃗⃗� 𝑖) = 0

(1) Where 𝜌𝑖, 𝛼𝑖 𝑎𝑛𝑑 �⃗⃗� 𝑖 represent the density, volume fraction and mean velocity, respectively, of phase i (L or G). It is assumed that the liquid phase and the gaseous phase share space proportional to their volume, such that their volume fractions sum up to unity in the cell domain (Eq. 2): ∝𝐺+∝𝐿 = 1.0

(2) The momentum equation for phase i is described below (Eq. 3):

𝜕

𝜕𝑡(𝜌𝑖𝛼𝑖�⃗⃗� 𝑖) + 𝛻 ∙ (𝛼𝑖𝜌𝑖�⃗⃗� 𝑖�⃗⃗� 𝑖)

= 𝛼𝑖𝛻𝑝 + 𝛻 ∙ 𝜏�̿�𝑓𝑓𝑖 + �⃗� 𝑖 + 𝐹 𝑖 + 𝛼𝑖𝜌𝑖𝑔 (3)

𝑝 is the pressure shared by both phases and �⃗� 𝑖 represents the interfacial momentum exchange. The 𝐹 𝑖 term represents the Coriolis and centrifugal forces expressed in the MRF (Multiple Reference Frame) model for rotating flows and is represented as (Eq. 4): 𝐹 𝑖 = −2𝛼𝑖𝜌𝑖�⃗⃗� × �⃗⃗� 𝑖 − 𝛼𝑖𝜌𝑖�⃗⃗� × (�⃗⃗� × 𝑟 )

(4) �⃗⃗� is the angular velocity, 𝑟 , is the position vector. The Reynolds stress tensor 𝜏�̿�𝑓𝑓𝑖 (Eq. 5) is related to the mean velocity gradients through the Boussinesq hypothesis [20]: 𝜏�̿�𝑓𝑓𝑖 = 𝛼𝑖(𝜇𝑙𝑎𝑚,𝑖 + 𝜇𝑡,𝑖)(𝛻�⃗⃗� 𝑖 + 𝛻�⃗⃗� 𝑖

𝑇)

−2

3𝛼𝑖(𝜌𝑖𝑘𝑖 + (𝜇𝑙𝑎𝑚,𝑖 + 𝜇𝑡,𝑖𝑡)𝛻 ∙ �⃗⃗� 𝑖)𝐼 ̿

(5) 𝜇𝑙𝑎𝑚,𝑖 is the molecular viscosity of phase i, 𝐼,̿ is the strain tensor. The most important interphase force is the drag force acting on the bubbles. This force (Eq. 6) depends on friction, pressure, cohesion, and other hydrodynamic effects [26]. 𝑅𝐿 = −𝑅𝐺 = 𝐾(�⃗⃗� 𝐺 − �⃗⃗� 𝐿)

(6) 𝐾 is the exchange coefficient of liquid and gaseous phases and is determined by (Eq. 7):

𝐾 =3

4𝜌𝐿𝛼𝐿𝛼𝐺

𝐶𝐷

𝑑|�⃗⃗� 𝐺 − �⃗⃗� 𝐿|

(7) 𝑑 is the bubble diameter, and the drag coefficient 𝐶𝐷 is defined as a function of Reynolds number (Eq. 8):

𝑅𝑒𝑝 =𝜌𝐿|�⃗⃗� 𝐺 − �⃗⃗� 𝐿|𝑑

𝜇𝐿

(8) To calculate the drag coefficient the standard correlation [27] was applied (Eq. 9):

𝐶𝐷 = {

24(1 + 0.15𝑅𝑒𝑝0.687)

𝑅𝑒𝑝

, 𝑅𝑒𝑝 ≤ 1000

0.44, 𝑅𝑒𝑝 > 1000

}

(9) The dispersed turbulence 𝑘 − 𝜀 model can be considered as the multiphase standard turbulence approach. It represents the extension of the single phase 𝑘 − 𝜀 model and is used when the secondary phase concentrations are diluted on primary phase. 𝑘 and 𝜀 equations describing this model are as follows (Eqs. 10 and 11): 𝜕

𝜕𝑡(𝜌𝐿𝛼𝐿𝑘𝐿) + 𝛻 ∙ (𝜌𝐿𝛼𝐿�⃗⃗� 𝐿𝑘𝐿)

= 𝛻 ∙ (𝛼𝐿

𝜇𝑡,𝐿𝛻𝑘𝐿

𝜎𝑘) + 𝛼𝐿𝐺𝑘,𝐿 − 𝛼𝐿𝜌𝐿𝜀 𝐿

+ 𝛼𝐿𝜌𝐿𝛱𝐾,𝐿 (10)


4502

𝜕

𝜕𝑡(𝜌𝐿𝛼𝐿𝑘𝐿𝜀𝐿) + 𝛻 ∙ (𝜌𝐿𝛼𝐿�⃗⃗� 𝐿𝜀𝐿)

= 𝛻 ∙ (𝛼𝐿

𝜇𝑡,𝐿𝛻𝜀𝐿

𝜎𝜀)

+ 𝛼𝐿

𝜀𝐿

𝑘𝐿

(𝐶1𝜀𝐺𝑘,𝐿 − 𝐶2𝜀𝜌𝐿𝜀𝐿) + 𝛼𝐿𝜌𝐿𝛱𝜀,𝐿

(11) In these equations, 𝐺𝑘,𝐿 represents the generation of turbulent kinetic energy, 𝑘𝐿 of the liquid phase due to mean velocity gradients, 𝜀𝐿 is the turbulent dissipation energy. 𝛱𝐾,𝐿 and 𝛱𝜀,𝐿 represent the influence of the dispersed phase in the continuous phase, respectively [28]. The turbulent viscosity 𝜇𝑡,𝐿, is calculated from (Eq. 12):

𝜇𝑡,𝐿 = 𝜌𝐿𝐶𝜇

𝑘𝐿2

𝜀𝐿

(12) The values of the constants used in this experiment were 𝐶1𝜀: 1.44, 𝐶2𝜀: 1.92, 𝐶𝜇:0.09 𝜎𝑘: 1.00 and 𝜎𝜀: 1.30. 𝜎𝑘 and 𝜎𝜀 represent turbulent Prandtl number for 𝑘 and 𝜀, respectively [28]. The discrete method [29-31] is used herein to solve the population balance equations. The bubble population is discretized into a finite number of intervals of bubble diameters. The population balance equations (Eq. 13) for different bubble classes can be written as [32-34]: 𝜕

𝜕𝑡(𝜌𝐺𝑛𝑖) + 𝛻 ∙ (𝜌𝐺 �⃗⃗� 𝐺𝑛𝑖) = 𝜌𝐺 (Γ𝐵𝑖𝐶

− Γ𝐷𝑖𝐶+ Γ𝐵𝑖𝐵

− Γ𝐷𝑖𝐵)

(13) Where 𝑛𝑖 is the number of bubbles per class 𝑖, Γ𝐵𝑖𝐶

and Γ𝐵𝑖𝐵

are birth rates due to coalescence and breakage, respectively, Γ𝐷𝑖𝐶

and Γ𝐷𝑖𝐵 are the death rates.

The terms of breakage and coalescence are (Eqs. 14-17):

Γ𝐵𝑖𝐶=

1

2∫ 𝑎(𝑣 – 𝑣 ′, 𝑣 )𝑛(𝑣 – 𝑣 ′, 𝑡)𝑛(𝑣 ′, 𝑡)

𝑣

0

𝑑𝑣 ′

(14)

Γ𝐷𝑖𝐶= 𝑛(𝑣)∫ 𝑎(𝑣, v′)𝑛(𝑣 ′, 𝑡)𝑛(𝑣 ′ , 𝑡)

∝

0

𝑑𝑣 ′

(15)

Γ𝐵𝑖𝐵= ∫ 𝑝𝑔(𝑣 ′)𝛽(𝑣|𝑣 ′)𝑛(𝑣 ′, 𝑡)𝑑𝑣 ′

𝛺𝑣

(16) Γ𝐷𝑖𝐵

= 𝑔(𝑣)𝑛(𝑣, 𝑡) (17)

𝑎(𝑣, 𝑣 ′) is the coalescence rate between bubbles of size 𝑣 and 𝑣 ′; 𝑔(𝑣) is the breakup rate of bubbles of size 𝑣; 𝑔(𝑣 ′), is the breakup frequency of bubble 𝑣 ′and 𝛽(𝑣|𝑣 ′) is the probability density function of bubbles broken from the volume 𝑣 ′ in a bubble of volume . The bubble breakup is analyzed in terms of bubbles interaction with turbulent eddies. These turbulent eddies increase the bubble surface energy to cause deformation. The breakup occurs if the increase in the surface energy reaches a critical value. The break up rate (Eqs. 18-20) is defined as [5]:

𝑔(𝑣 ′)𝛽(𝑣|𝑣 ′) = 𝑘 ∫(1 + 𝜉)2

𝜉11

3⁄𝑒𝑥𝑝

1

𝜉𝑚𝑖𝑛

(−𝑏𝜉−11

3⁄ ) 𝑑𝜉

(18)

𝑘 = 0.9238𝜀1

3⁄ 𝑑−23⁄ 𝛼

(19) 𝑏 = 12 (𝑓

23⁄ +(1 − 𝑓)

23⁄ − 1)𝜎𝜌−1𝜀−2

3⁄ 𝑑−53⁄

(20) Where 𝑑 is the bubble diameter, 𝜉 is the dimensionless eddy size, 𝑓 is the breakage frequency. The bubble coalescence is modeled by considering the bubble collision due to turbulence, buoyancy and laminar shear. The coalescence rate (Eq. 21) is defined as the product of the collision frequency ωag(𝑣𝑖 , 𝑣𝑗) and coalescence probability 𝑃𝑎𝑔(𝑣𝑖 , 𝑣𝑗) and is defined as [5]: 𝑎(𝑣, 𝑣 ′) = ωag(𝑣𝑖 , 𝑣𝑗)Pag(𝑣𝑖 , 𝑣𝑗)

(21) The collision frequency is defined as (Eq. 22): 𝜔𝑎𝑔(𝑣𝑖 , 𝑣𝑗) =

𝜋

4(𝑑𝑖

2 + 𝑑𝑗2)𝑛𝑖𝑛𝑗�̅�𝑖𝑗

(22) Where �̅�𝑖𝑗 is the characteristic collision velocity of two bubbles with diameter 𝑑𝑖 𝑎𝑛𝑑 𝑑𝑗 and bubble density 𝑛𝑖 and 𝑛𝑗 (Eq. 23):

𝑃𝑎𝑔(𝑣𝑖, 𝑣𝑗) = exp(−𝑐1

[0.75(1 + 𝑥𝑖𝑗2 )(1 + 𝑥𝑖𝑗

3 )]

(𝜌2

𝜌1⁄ + 0.5)

12⁄(1 + 𝑥𝑖𝑗

3 )

12⁄

(𝜌𝑙𝑑𝑖(�̅�𝑖

2 + �̅�𝑗2)

12⁄

𝜎)

12⁄

)

(23) Where 𝑐1 is a first order constant, 𝑥𝑖𝑗 = 𝑑𝑖/𝑑𝑗 𝜌1 𝑎𝑛𝑑 𝜌2 the densities of primary and secondary phase. The number of bubbles per class 𝑖, 𝑛𝑖 is related to the gas phase volume fraction as follows (Eq. 24): 𝑛𝑖𝑣𝑖 =∝𝑖

(24) The sum of the volume fractions of each group of bubbles is equal to the volume fraction of the dispersed phase (Eq. 25): ∑ ∝𝑖=∝𝐺

𝑖

(25) The volume fraction of each group sizes is expressed in terms of the total fraction of the dispersed phase (Eq. 26):

𝑓𝑖 =∝𝑖

∝𝐺

(26) Therefore, including Eq. (26) in Eq. (13), is (Eq. 27): 𝜕

𝜕𝑡(∝𝐺 𝜌𝐺𝑓𝑖) + 𝛻 ∙ (∝𝐺 𝜌𝐺 �⃗⃗� 𝐺𝑓𝑖)

= 𝜌𝐺𝑣𝑖(𝐵𝑖𝐶 − 𝐷𝑖𝐶 + 𝐵𝑖𝐵 − 𝐷𝑖𝐵) (27)

The Sauter diameter 𝑑32 is used to fit the population balance equations with the bioreactor hydrodynamics (Eq. 28):

𝑑32 =∑ 𝑛𝑖𝑑𝑖

3𝑖

∑ 𝑛𝑖𝑑𝑖2

𝑖

(28) A fine 3D mesh is composed for hybrid cells with ~1000 computational k cells for both 10 and 1000 L spin filter bioreactors, (Figures 1-2) Similar previus works for stirred tanks biorreactors [1,15,35] reported grid independence at one million grid cells, which is why the latter have been employed in the current study. The finite volume technique implemented in the CFD code Ansys Fluent 13.0 Software was used to convert the Navier-


4503

Stokes equations into algebraic equations which can be solved numerically. Tank walls, stirrer surfaces and baffles are treated with no slip conditions and standard wall functions. The gas flow rate at the cylinder micro-sparger was defined via inlet-velocity type boundary condition with gas volume fraction equal to unity. MRF model was applied for the impeller (Pitched Blade) and Spin Filter device. PC SIMPLE algorithm was used for solving the partial differential equations. The second order upwind scheme was applied for the spatial terms. It was assumed that the solution converges when the scaled residuals remain with values smaller than 10-5

and when the pseudo-regime for hold-up is reached [3, 10-11]. The size of the bubbles was set by the discretization scheme based on the geometric ratio [10]. The size of the bubbles for the Spin Filter Bioreactor was assumed from 75 to 3500 µm in diameter. 13 size classes were used to discretize the population balance equations [11], who analyzed hydrodynamics of a propeller type stirrer and found satisfactory results using the same classifiers.

Figure 1: Mesh generation for the 10 L Spin Filter Bioreactor

Figure 2: Mesh generation for the 1000 L Spin Filter Bioreactor

Experimental 𝑘𝐿𝑎 measurements in 10 liters spin filter bioreactor were performed applying the N2-stripping approach in aqueous medium. Time courses of increasing dissolved oxygen levels were monitored via an O2-probe (Mettler

Toledo, Germany). 𝑘𝐿𝑎 estimations (Eq. 29) resulted from non-linear parameter fitting using equation [1, 15]:

𝑘𝐿𝑎 = −

𝑙𝑛 (𝐶𝑂2

∗ − 𝐶𝑂2,𝑖−1

𝐶𝑂2

∗ − 𝐶𝑂2,𝑖)

𝑡𝑖 − 𝑡𝑖−1

(29) with i coding for subsequent time points t and * indicating the saturating dissolved oxygen levels 𝐶𝑂2 . Time series of dissolved oxygen were corrected with respect to the delayed probe responses which had been identified as ~28 seconds, relating to τ=0.035 1/s [1]. Results The mean goal of this work was to study the heterogeneities in a large spin filter bioreactor due to loss of complete mixing conditions with increasing scale, using CFD simulations. Special emphasis was given to the elucidation of gas-liquid mass transfer and bubble size distributions. Operational conditions were defined based on the best condition found in the 10 L lab scale spin filter bioreactor [1] and using the P/V (constant power input per liquid volume) empirical scale up criterion. Figures 3-4 show the CFD air volume fractions of the Spin Filter bioreactor at 10 and 1000 liters. Simulating the scale up in 1000 L (Figure 4), it can be seen that relatively low volume fraction dispersion occurs especially in bottom of bioreactor because of low centrifugal forces generated by the Rushton turbine. Obviously, these centrifugal forces could not overcome the air buoyancy [15] and the appearance of heterogeneous environment is becoming important in the large scale spin filter bioreactor. Contrarily, volume fractions gradients are minimal when the spin filter bioreactor is operated at lab scale (10 L) due to increase in drag forces reached. The latter are calculated from CFD by calling drag coefficient and values of 2.51 and 0.68 were found in 10 and 1000 bioreactors, respectively.

Figure 3: Air volume fraction [-] contours calculated for 10 L spin filter bioreactor.


4504

In aerobic fermentations, air flows continuously through the stirred tank reactor. The bubble size distribution results from physical interactions imposed on uprising bubbles and considers mechanisms such as coalescence and breakage. These phenomena together with hydrodynamics, trigger the formation of dissolved oxygen and trace gases gradients of which can affect productivity in aerobic plant cell cultures. For that reason, when breakage phenomenon prevails, bubble size decreases, the interfacial area for mass transfer thereof is increased and consequently, the oxygen transfer is promoted. On the other hand, large bubbles generated by coalescence are characterized by higher rising velocities and short residence times. Thereby, bubbles cannot be uniformly dispersed for the agitation system. The most relevant parameter for analyzing these hydrodynamic mechanisms is the Sauter mean diameter [1]. It can be interpreted as a parameter, summarizing all individual impacts affecting the bubble sizes and their distributions in one single value [15].

Figure 4: Air volume fraction [-] contours calculated for 1000 L spin filter bioreactor.

Moreover, Figures 5-6 depict another reason for explaining the high discrepancy between 10 and 1000 L 𝑘𝐿𝑎 mass transfer. Sauter mean diamter profiles in both scales are significantly different. Interestingly, lowest values of ~400 µm were found close to the blades in the cross-sectional areas of the agitator speed direction. These regions mirror relatively high, buble breakage rates. In the case of 1000 L spin filter bioreactor (Figure 6) the sauter diameter was higher (3500 µm) than the values found for 10 L spin filter bioreactor (Figure 5). Besides, the 1000 L bioreactor reveals a significantly non-homogeneous sauter mean diameter distribution, while special differences are minimal using the 10 L bioreactor. The latter is the consequence of the improved hydrodynamics which promotes the formation of uniform bubble sizes and higher gas-liquid mass transfer rates, generally caused by the mixing. While the 10 L scale spin filter bioreactor shows well-defined

bubble dispersions (calculated as drag coefficient from CFD as showed before), the 1000 L bioreactor shows dead zones especially on top bioreactor and lateral walls of the spin filter. Consequently, poor mixed region are more significant due to loss of complete mixing conditions in large-scale bioreactors. This is probably due to the high tangential velocities and low turbulent kinetic dissipation energy developed in these zones of spin filter. Further, this problem should be overcome by improving the design of spin filter walls.

Figure 5: Sauter diameter contours [m] calculated for 10 L spin filter bioreactor.

Figure 6 Sauter diameter contours [m] calculated for 1000 L spin filter bioreactor.

The heterogeneities showed in sauter mean diameter contours are also checked by the analysis of Kolmogorov length scale 𝜆𝐾 [16]. Following this definition, the Kolmogorov diameter investigates eddies, created at the “hot spots” of energy input


4505

[15]. According to the hypothesis, only eddies with length scale smaller than bubble diameters can induce breakage. Larger eddies lead to bubble transport and coalescence instead. Figures 7-8 show the Kolmogorov length scale 𝜆𝐾 simulated by CFD in both scales (10 and 1000L). Considering these results, smaller length scales, which dominate high breakage phenomenon, are present in lab scale bioreactor than 1000 L bioreactor. This finding can also explain the heterogeneities found at 1000 L scale.

Figure 7: Kolmogorov length scales λk calculated for 10 L spin filter bioreactor.

Maintaining an adequate oxygen supply to aerobic cell cultures has been a long-standing problem in fermentation technology. This problem is particularly amplified in high cell density cultures, in which insufficient oxygen transfer rates limit cell growth and ultimately process productivity [37].

Figure 8: Kolmogorov length scales λk calculated for 1000 L spin filter bioreactor.

𝑘𝐿𝑎 values (Figures 9-10) are considered as the principal criterion to analyze the gas/liquid mass transfer. In this work, Higbies’ penetration theory is used for simulating 𝑘𝐿𝑎 from CFD. These values are obtained by the product of liquid mass transfer 𝑘𝐿𝑎 and interfacial area 𝑘𝐿𝑎 [34]. Interfacial area is expressed as a function of the local gas fraction and the local Sauter diameter.

Figure 9: 𝑘𝐿𝑎 mass transfer coefficient [1/h] calculated for 10 L spin filter bioreactor.

Given the biochemical constraint that cell cultivations require optimum dissolved oxygen levels for growth ensuring a minimum of 5 % (at atmospheric conditions) [37], sufficient oxygen transfer rates are obviously only achieved if 𝑘𝐿𝑎 values reach fairly high levels [15]. Simulating the large scale Spin Filter Bioreactor, oxygen mass transfer, expressed by 𝑘𝐿𝑎 (Figure 10), was found to be about 70 percent lower than values obtained at 10 L bioreactor. At the given scale up criterion (P/V), the 1000 L Spin Filter system reached only an integral 𝑘𝐿𝑎 of 16.93 1/h while simulating the 10 L bioreactor the 𝑘𝐿𝑎 values attained 60.0 1/h. The latter is the consequence of the improved gas-liquid mass transfer which ensures the formation of uniform bubble sizes, generally caused by the hydrodynamics. Conclusions The numerical results from a scale up bioprocess of gas-liquid mass transfer in a large spin filter bioreactor is analyzed using CFD. Possible heterogeneities were simulated at 1000 L spin filter bioreactor due to poor mixing conditions reached at this scale. Motivated by these simulated and experimental results CFD simulations are qualified as a very promising methodology for predicting heterogeneities in gas-liquid mass transfer applications for large scale spin filter bioreactors. Drag coefficient, bubble size diameter and Kolmogorov length scales can be treated as main criteria for scaling up spin filter bioreactors due to its influence on gas-liquid mass transfer heterogeneities found in this work.


4506

Figure 10: 𝑘𝐿𝑎 mass transfer coefficient [1/h] calculated for 1000 L spin filter bioreactor.

References

[1] L. Niño, R. Gelves. “Simulating gas-liquid mass transfer in a spin filter bioreactor”. Rev Fac Ing Univ Antioquia. N. º 75. pp. 163-174. 2015.

[2] S. Sens, P. Roychoudhury. “Step-up/step-down perfusion approach for increased mAb 520C9 production by a hybridoma cell line”. Biotechnol Lett. Vol. 35. pp. 153-163. 2013.

[3] R. Gelves, L. Niño. “CFD prediction of heterogeneities in the scale up of liquid-liquid dispertions”. International Journal of Chemical Engineering and Applications. Vol. 5. pp. 79-84. 2014.

[4] M. Jenne, M. Reuss. “A critical assessment on the use of k–e turbulence models for simulation of the turbulent liquid flow induced by Rushton turbine in baffled stirred-tank reactors”. Chem Eng Sci. Vol. 54. pp. 3921-3941. 1999.

[5] J. Luo, R. Issa, A. Gosman. “Prediction of impeller induced flows in mixing vessels using multiple frames of reference”. Inst. Chem. Eng. Symposium Series. Vol. 136. pp. 549-556. 1994.

[6] G. Micale, F. Grisafi. “Prediction of flow fields in a dual-impeller stirred tank”. AICHE J. Vol. 45. pp. 445-464. 1999.

[7] K. Rutherford, C. Lee, S. Mahmoudi, M. Yianneskis. “Hydrodynamic characteristics of dual Rushton impeller stirred vessels”. AICHE J. Vol. 42. pp. 332-346. 1996.

[8] A. Tabor, G. Gosman, R. Issa. “Numerical simulation of the flow in a mixing vessel stirred by a Rushton Turbine”. Inst. Chem. Eng. Symposium Series. Vol. 140. pp. 25-34.

[9]. V. Bakker, V. Akker. “A computational model for the gas–liquid flow in stirred reactors”. Transactions

of the Institution of Chemical Engineers. Vol. 72. 1994. pp. 594-606. 1996.

[10] F. Kerdouss, A. Bannari, P. Proulx, R. Bannari, M. Skrga, Y. Labrecque. “Two-phase mass transfer coefficient prediction in stirred vessel with a CFD model”. Comput and Chem Eng. Vol. 32. pp. 1943-1955. 2008.

[11] F. Kerdouss, L. Kiss, P. Proulx, J. Bilodeau, C. Dupuis. “Mixing characteristics of an axial flow rotor: Experimental and numerical study”. Int J of Chem React Eng. Vol. 3. pp. 35. 2005.

[12] F. Kerdouss, A. Bannari, P. Proulx, R. Bannari, M. Skrga, Y. Labrecque. “Two-phase mass transfer coefficient prediction in stirred vessel with a CFD model”. Comput and Chem Eng. Vol. 3. pp. 1-13. 2007.

[13] G. Lane, M. Schwarz, G. Evans. “Numerical modeling of gas–liquid flow in stirred tank”. Chem Eng Sci. Vol. 60. pp. 2203-2214. 2005.

[14] C. Venneker, V. Derksen. “Population balance modeling of aerated stirred vessels based on CFD”. AICHE J. Vol. 48. pp. 673-684. 2002.

[15] R. Gelves, A. Dietrich, R. Takors. “Modeling of gas-liquid mass transfer in a stirred tank bioreactor agitated by a rushton turbine or a new pitched blade impeller”. Bioprocess and Biosystem Engineering. Vol. 37. pp. 365-375. 2014.

[16] Y. Deo, M. Mahadevan, R. Fuchs. “Practical Considerations in Operation and Scale-up of Spin-Filter Based Bioreactors for Monoclonal Antibody Production”. Biotechnol Prog. Vol. 12. pp. 57-64. 1996.

[17] B. Raikar, R. Bhatia, F. Malone and A. Henson, “Experimental studies and population balance equation models for breakage prediction of emulsion drop size distributions” in Chemical Engineering Science Vol. 64. pp. 2433-2447. 2009.

[18] D. Lide. CRC Handbook of Chemistry and Physics. 83rd ed. Ed. CRC Press. Boca Raton, USA. pp. 8-232. 2002.

[19] A. Junker. “Scale-Up Methodologies for Escherichia coli and Yeast Fermentation Processes”, Journal of Bioscience And Bioengineering. Vol. 97. pp. 347-364. 2004.

[20] G. Kasat, A. Pandit, V. Ranade. “CFD Simulation of Gas-Liquid Flows in a Reactor Stirred by Dual Rushton Turbines”. Int J of Chem React Eng. Vol. 6. pp. 1-28. 2008.

[21] L. Wei. Multiple Impeller Gas-Liquid Contactors. Technical report, National Taiwan University. Taipei, Taiwan. pp. 13-47. 2004

[22] V. Ranade, J. Dommeti. “Computational Snapshot of flow generated by axial impellers in baffled stirred vessels”. J. Chem. Vol. 74. pp. 476-484. 1990.

[23] V. Ranade. Computational Flow Modeling for Chemical Reactor Engineering, Process Systems Engineering Series. 1st ed. Ed. Academic Press. New York, USA. pp. 35-54. 2002.

[24] M. Jahoda, L. Tomášková, M. Moštěk. “CFD prediction of liquid homogenization in a gas-liquid

http://www.sciencedirect.com/science/article/pii/S0098135407002633?_alid=1838092556&_rdoc=4&_fmt=high&_origin=search&_docanchor=&_ct=1009&_zone=rslt_list_item&md5=715f59d3fb29d5fce2a8deccd699d3b6




4507

stirred tank”. Chem Eng Res and Des. Vol. 87. 2009. pp. 460-467.

[25] E. Marshall, A. Bakker. Computational fluid mixing. Technical report. Ed. Fluent-Inc. Lebanon, New Hampshire, USA. pp. 1-94. 2002.

[26] R. Gelves, A. Benavides, J. Quintero. “Predicción del comportamiento hidrodinámico en el escalado de un reactor de tanque agitado para procesos aerobios, mediante CFD”. Ingeniare. Rev. chil. ing. Vol. 21. pp. 347-361. 2013.

[27] M. Ishii, N. Zuber. “Drag coefficient and relative velocity in bubbly, droplet or particulate flows”. AIChE J. Vol. 25. pp. 843-855. 1979.

[28] S. Elgobashi, M. Rizk. “A two-equation turbulence model for dispersed dilute confined two-phase flows”. Int J of Multiph Flow. Vol. 15. pp. 119-133. 1989.

[29] M. Hounslow, R. Ryall, V. Marschall. “A Discretized Population Balance for Nucleation, Growth and Aggregation”. AIChE J. Vol. 34. pp. 1821-1832. 1988.

[30] J. Litster, D. Smit, M. Hounslow. “Adjustable Discretization Population Balance for Growth and Aggregation”. AIChE J. Vol. 41. pp. 591-603. 1995.

[31] D. Ramkrishna. Population Balances: Theory and Applications to Particulate Systems in Engineering. 1st ed. Ed. Academic Press. New York, USA. pp. 47-116. 2000.

[32] P. Chen, M. Dudukovic, J. Sanyal. “Numerical simulation of bubble columns flows: effect of different breakup and coalescence closures”. Chem Eng Sci. Vol. 60. 1085-1101. 2005.

[33] L. Hagesaether, H. Jakobsen, A. Hjarbo, H. Svendsen. “A coalescence and breakup module for implementation in CFD-codes”. European Symposium on Computer Aided Process Engineering. Vol. 8. pp. 367-372. 2000.

[34] J. Sanyal, D. Marchisio, R. Fox, K. Dhanasekharan. “On the comparison between population balance models for CFD simulation of bubble columns”. Ind Eng and Chem Res. Vol. 44. pp. 5063-5072. 2005.

[35] J. Gimbun. “Scale-up of gas-liquid stirred tanks using coupled computational fluid dynamics and population balance modelling“. PhD Thesis, Loughborough University Instititional Repository. Leicestershire, UK. pp 1-281. 2009.

[36] B. Pocurull. Mechanistic modeling of increased oxygen transport using functionalized magnetic fluids in bioreactors. PhD Thesis, Massachusetts Institute of Technology. Cambridge, USA. pp. 1-180. 2005.

[37] S. Oh, A. Nienow, M. Al-Rubeai, A. Emery. “The effects of agitation intensity with and without continuous sparging on the growth and antibody production of hybridoma cells”. J of Biotechnol. Vol. 12. pp. 45-61. 1989.

https://dspace.lboro.ac.uk/dspace-jspui/browse?type=author&value=Gimbun%2C+Jolius

cfd prediction of gas-liquid mass transfer in a large ... · pdf fileaerobic cell culturing is...

Documents