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Bioreactor Scale-Up

  1. Laura A. Palomares,
  2. Octavio T. Ramírez

Published Online: 15 DEC 2009

DOI: 10.1002/9780470054581.eib143

Encyclopedia of Industrial Biotechnology

Encyclopedia of Industrial Biotechnology

How to Cite

Palomares, L. A. and Ramírez, O. T. 2009. Bioreactor Scale-Up. Encyclopedia of Industrial Biotechnology. 1–22.

Author Information

  1. Instituto de Biotecnología, Universidad Nacional Autónoma de México, Departamento de Medicina Molecular y Bioprocesos, Cuernavaca, México

Publication History

  1. Published Online: 15 DEC 2009

1 Introduction

  1. Top of page
  2. Introduction
  3. Aspect Ratio, Homogeneity, and Gradients
  4. Heating and Cooling
  5. Nomenclature
  6. References

Bioprocess and bioreactor scale-up are clearly activities that strictly depend on the substance being produced. For many biotechnology products, such as antibiotics, alcohols, organic acids, amino acids, and enzymes, a commercially viable process is attained only if a final fermenter scale on the order of hundreds of thousands of liters is reached. Such large volumes are needed to satisfy markets requiring very large amounts (102 to 107 t/year) of products with very low added value (10−1 to 103 $/kg). In contrast, products derived from animal and plant cell culture are, in general, costly therapeutics or fine chemicals whose price can be as high as 104 to 109 $/kg, but their worldwide demand is only 10−1 to 103 kg/year. Such a behavior is depicted in Fig. 1 where an inverse logarithmic relationship between product costs and market size exists (1). Accordingly, for the production of many substances derived from tissue culture, at most only hundreds to thousands of liters per year are required to satisfy the demand, and, thus, the largest bioreactors needed hardly come close to the scales of other biotechnology products. This can be exemplified by two extreme cases, human erythropoietin (EPO) and taxol. EPO has the largest market for any therapeutic recombinant protein produced by mammalian cell culture. At an EPO selling price of $0.013/U (130,000 U/mg), the total 2006 demand ($11,500 × 106/yr) could be satisfied with only ca 7 kg/yr. Such production could be generated through a modest hypothetical bioprocess (batch operation, overall yield 500 U/mL cycle, 10-day cycles) in six bioreactors of less than 10,000 L. Similarly, the estimated world requirements of taxol (200 kg/yr at a bulk price of $500,000/kg) could be satisfied by a single 70,000 L plant cell bioreactor yielding 0.25 g/L of product and operated in 15-day cycles (assuming a 50% purification yield) (1, 2). These examples assume that a single manufacturer using a single vessel, which is a very improbable scenario, satisfies the market. Furthermore, the development of improved cell lines and bioreactor operation modes, such as perfusion culture, has resulted in substantial increases in cell and product concentrations, which would further reduce the bioreactor volumes calculated above.

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Figure 1. Relationship of chemical prices to annual production. Cell culture-derived products (open circles).

Adapted and reprinted with permission from Ref 1

In general, while the largest homogeneous cultures of suspended animal cells range between 4000 and 20,000 L, heterogeneous systems (microcarrier, packed beds, etc.) for anchorage-dependent animal cells usually do not exceed the 1000 L scale. Problems such as mass transfer limitations and concentration gradients, inherent to heterogenous systems, can explain their lower scales. Published data on the industrial production of products derived from cell culture is limited. Nonetheless, some of the largest cultures reported in the literature are summarized in Table 1. For example, the foot-and-mouth disease vaccine, obtained from baby hamster kidney (BHK-21) cells, has been produced by Wellcome for almost 30 years in a 1000 L reactor, and more recently at a 10,000 L scale (3). Cells from human origin (lymphoblastoid Namalwa cells) have been cultured for interferon production up to 8000 L (4), and hybridomas for Mab production have been cultured in 2000-L airlift bioreactors (5). Recombinant antibodies are nowadays routinely produced in bioreactors of 10,000 L. Some of the largest reported scales for microcarrier cultures, packed beds, and ceramic cartridges are 7000, 100 and 240 L, respectively (6, 7). Compared to animal cells, the scales of plant cell cultures tend to be larger. For instance, tobacco plant cells have been cultured in 20,000-L reactors (3), while a 75,000-L bioreactor is in operation for taxol production (2). Nevertheless, despite these successful experiences, large-scale culture of higher eukaryotic cells is still a challenge, particularly for anchorage-dependent cell lines or very fragile cells, such as insect cells.

Table 1. Some of the Largest Scale Cultures Reported
Cell LineScale (L)ReactorProductReference
  1. a

    Baby Hamster Kidney

  2. b

    Chinese Hamster Ovary

Taxus sp.75,000Agitated tankTaxol2
Tobacco cells20,000Agitated tankNicotine3
BHK-21a10,000Agitated tankFoot-and-mouth disease vaccine8
CHOb10,000Agitated tanktPA6
Namalwa cells8,000Agitated tankLymphoblastoid interferon4
Bowes melanoma7,000Agitated tank/microcarrierstPA6
Murine hybridomas2,000AirliftMab5
Vero cells1,000Agitated tank/microcarriersKilled polio virus vaccine7
Murine hybridomas1,000Stirred tankMab vs cell surface antigens of adenocarcinomas9
BHK cells500Agitated tank/perfusionFactor VIII10
Microorganisms400,000Bubble column11
Microorganisms400,000Airlift11
Yeast1,500,000Bubble columnBaker's yeast12

The first step to translate a cell culture process to a commercial scale is to define the product requirements and the overall production and downstream processing economics. A decision has to be taken whether a single large-scale batch reactor or smaller multiple continuous reactors are used. This decision can only be made after considering the whole process, operation and capital costs, available facilities, and even assessment of the consequences of a possible contamination during the culture. From a technical standpoint, one of the major issues for scaling up a cell culture bioreactor is the oxygen transfer problem. In general, the fragile nature of most higher eukaryotic cells and foaming associated problems due to the proteinaceous composition of many medium formulations limit the use of high power inputs and intense submerged aeration. As a process is scaled up, bioreactors must be more reliable, safe, cheap, and comply with regulations. In particular, the tight regulation imposed on the production of cell culture-derived therapeutics has significantly constrained the free development of improved and novel bioprocesses at a commercial scale. The dogma that the “process determines the product,” mostly hatched from our analytical limitations to fully characterize cell culture products, has resulted in a costly and treacherous path for any company trying to modify its approved process. Thus, many therapeutics are produced by suboptimal processes and scales; however, this should change as regulation moves toward placing its attention on the characterization of products rather than on the bioprocess.

2 Aspect Ratio, Homogeneity, and Gradients

  1. Top of page
  2. Introduction
  3. Aspect Ratio, Homogeneity, and Gradients
  4. Heating and Cooling
  5. Nomenclature
  6. References

2.1 Stirred Tanks

The purpose of a bioreactor is to provide proper environmental conditions required for optimal growth and/or product production under a contained system. Ideally, the culture environment should also be homogeneous and controlled. These conditions can be better accomplished in agitated tanks, which are the preferred design for scaling up anchorage-independent cells. Stirred-tank bioreactors for cell culture are cylindrical vessels with an aspect ratio (liquid height-to-diameter ratio) usually in the range of 1:1–3:1 (3, 8). Nonetheless, the aspect ratio should be kept under 2:1 and impellers should be spaced properly (1.0–1.5 impeller diameters apart) to avoid top-to-bottom heterogeneity (13). Furthermore, oxygen transfer from the liquid surface, which is particularly important for animal cell culture, can be improved by keeping the aspect ratio close to unity. Special attention should be placed to the headspace dimensions if foaming problems are anticipated. In general, foam and liquid height increase from gas holdup are handled by leaving 20–30% of the vessel empty (13). A common feature of stirred-tank bioreactors is a hemispherical bottom, which prevents stagnant zones even under mild agitation rates. Nonetheless, as pointed out by Charles and Wilson (13), the cost of a hemispherical bottom vessel can increase by as much as 50%; yet, no clear evidence of its superior performance over a standard dished-bottom vessel exists. Probably the most distinguishing feature between different stirred-tank bioreactor designs is the impeller configuration. Many different types of impellers have been used for the culture of animal and plant cells in stirred tanks, including marine propellers, sails, pitched blades, Vibromixers (perforated discs placed on a vertically reciprocating shaft), anchors, paddles, helical screws, cell lift, and centrifugal impellers. Typical geometric characteristics of commonly used impellers are shown in Fig. 2. Many of such impellers have been designed with the objective of preventing mechanical damage to the fragile cells, but still maintaining a homogeneous environment and high oxygen transfer rates (OTR). Likewise, excluding baffles, and minimizing other inserts, while placing the impeller shaft eccentrically to avoid vortex formation, can reduce mechanical damage to the cells. Finally, vessel design should optimize the use of available materials; however, excessive costs are usually reduced by simply selecting a vessel among reactors already available from specialized vendors.

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Figure 2. Commonly used impellers, and their geometric characteristics, used in animal and plant cell culture. D = impeller diameter, Tv = vessel diameter. (a) Suspended magnetic bar, (b) spherical rotating flex stirrer, (c) sail impeller, (d) membrane basket agitator, (e) marine propeller, (f) disc turbine, (g) angled blade, (h) and (i) profiled impellers, (j) helical ribbon impeller, (k) gate-anchor impeller, (l) gate impeller, and (m) anchor impeller.

Adapted from Refs 14-16

Tank geometry must be carefully selected as it influences the homogeneity of the bioreactor, especially as scale increases. Furthermore, heat and mass transfer are directly influenced by mixing, which in turn depends on operating variables and geometric characteristics of the bioreactor. For instance, the mixing time (time required for the system to reach a specified degree of uniformity) for a nonaerated Newtonian fluid in a baffled stirred tank with a flat-blade turbine impeller can be obtained from Fig. 3 and Equation 1 (15, 17, 18).

  • mathml alt image(1)

where N* is dimensionless mixing time, N is impeller speed, tM is mixing time, g is gravitational acceleration, D is impeller diameter, Tv is vessel diameter, and H is liquid height.

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Figure 3. Dimensionless mixing time as a function of Reynolds number for turbine impellers in baffled vessels as determined from pH tracer experiments.

Reprinted with permission from Ref. 18

Mixing times of different culture systems have been summarized elsewhere (19). Only very scarce information exists of homogenization and concentration gradients in large-scale animal or plant cell bioreactors. Among such studies, Langheinrich et al. (20) obtained mixing time data for typical operation conditions (maximum agitation speed of 1 s−1, maximum air sparging rate of 0.005 VVM (volume of air per volume of liquid per minute), superficial air velocity of 2  ×  10−4 m/s) of an 8000-L stirred-tank bioreactor (Rushton turbine D = 2/9Tv) used for animal cell culture at Glaxo Wellcome Research and Development. As a draw-and-fill operation is employed during production, aspect ratios of 0.3, 1.0, and 1.3 were studied. It was shown that mixing time, obtained from pH tracer and decolorization experiments, could be correlated with the total energy dissipation rate, ɛ T (Figs 4 and 5), defined by Equation 2:

  • mathml alt image(2)

where Po is power number (Eq. 27), ρ is liquid density, V is liquid volume, and uG is superficial gas velocity. The first term on the right hand side of Equation 2 is the contribution from agitation, whereas the second term is from aeration. Interestingly, experimental data of Langheinrich et al. (20) fitted well literature correlations (Eqs 3 and 4) obtained under agitation and aeration conditions two orders of magnitude above those studied in the animal cell culture bioreactor.

  • mathml alt image(3)

for aspect ratios of 1 (21), and

  • mathml alt image(4)

for aspect ratios of 1–3 (22).

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Figure 4. Effect of specific energy dissipation rate from agitation on mixing time. Determinations based on pH tracer experiments for various aspect ratios in an unaerated large-scale bioreactor. (a) H = 0.3 Tv (open triangle), H = 1.3 Tv (open square), dashed line = prediction by Cooke et al. (22) and (b) H = Tv (open triangle), H = 1.3 Tv (open circle), dashed line—prediction by Ruszkowski et al. (21).

Reprinted with permission from Ref. 20

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Figure 5. Effect of specific energy dissipation rate from agitation and aeration on mixing time. Determinations based on pH tracer experiments for various aspect ratios in a large-scale bioreactor. Closed symbols, determinations at the liquid surface and open symbols, determinations at the end of impeller discharge stream. Unaerated (triangles) and aerated (circles) at uG = 2 × 10−4 m/s.

Adapted and reprinted with permission from Ref. 20

Several important conclusions, for the particular system used, are drawn from the study of Langheinrich et al. (20). First, gradients in pH and dissolved oxygen can potentially occur in large-scale animal cell culture since high mixing times, in the range of 40–200 s, were obtained under typical operation conditions. Computational fluid dynamics (CFD) has been used to predict gradients in microbial cultures (23, 24). Secondly, homogenization is dramatically affected by geometric characteristics, as a fourfold increase in mixing times can occur as aspect ratios increase from 0.3 to 1.3 (Fig. 4). And finally, sparging substantially enhances mixing, particularly in the upper parts of the vessel and at aspect ratios greater than 1 (Fig. 5).

Poor mixing in stirred-tank reactors has been reported to cause significant problems in Escherichia coli, other microbial cultures, myeloma, hybridoma, Chinese hamster ovary (CHO), and insect cell cultures at high cell density (25-30). Undesirable carbon dioxide accumulation has been found to occur in 110–1000-L reactors as a result of low mass transfer characteristics of the systems (31, 32). Furthermore, heterogeneities in microcarrier concentration and pH gradients have been found in large-scale stirred vessels (33-35). For instance, severe localized cell lysis problems at the point of base addition, allegedly caused by high mixing times, were observed in a 15-L reactor with cell retention (30). Another problem aggravated by deficient mixing is culture segregation, which originates from the formation of cell aggregates and clumps during high cell density cultures (30). Problems related to mixing can negatively affect overall culture performance. However, due to the fragile nature of animal cells, increasing agitation intensity cannot solve such problems. Therefore, other solutions must be found. For instance, pH gradients can be eliminated by adding base through multiple points properly localized in the reactor (30), while carbon dioxide removal can be enhanced by manipulation of air bubble size through proper design of the sparging system (29).

2.2 Disposable Bioreactors

Disposable bioreactors represent a novel development that is increasingly employed (36, 37), particularly within the pharmaceutical area. This new paradigm in bioprocess technology has been motivated by several advantages that disposable bioreactors have over traditional stainless steel systems. Regulatory aspects impose important constraints in the pharmaceutical industry; among them, the most important is the need to guarantee that all bioprocess equipment in contact with the product has been perfectly cleaned between operation runs. This requirement substantially increases capital investment in a stainless steel-based facility since costly and sophisticated equipment such as steam-in-place and clean-in-place systems, as well as those needed for associated services such as clean steam generators, must be considered in the manufacturing plant. In addition, the initial cost of a stainless steel bioreactor can be several-fold higher than that of a disposable system of equivalent volume. Altogether, capital costs for a plant based on stainless steel bioreactors can be between three- and fourfold higher than an equivalent one based on disposable systems (38). In addition, operating costs for disposables are lower than for stainless steel bioreactors, as the former systems do not require labor-intensive procedures such as cleaning and sterilization validation, and shorter turnaround times between lots can be attained. Furthermore, stainless steel bioreactors require laborious specification and purchasing procedures, long times for design, construction and delivery, long times and high costs of installation and qualification, and precious facility space is occupied by hard pipe installations and ancillary equipment. Accordingly, in addition to the higher capital and operating costs, a facility based on stainless steel bioreactors has limited flexibility, and compared to disposables, has higher risks of contamination and longer start-up times. Such issues are important for multipurpose plants and new start-up companies, as well as for rapid development, scale-up, and manufacture of new drug substances or drug candidates. Criteria and analysis tools for aiding in the decision process for selecting between disposable and stainless steel systems can be found elsewhere (39).

Disposable bioreactors consist of Γ-irradiated presterilized multilayered bags formed by films of polyester, polyethylene, ethylene vinyl alcohol polymer, and other US Pharmacopoeia (USP) class VI materials with low or negligible leaching of extractable compounds. Bags are placed in various types of containers for conferring them structural rigidity. Various types of ports and accessories are attached to the bags, such as exhaust gas filters and aseptic rapid-type connectors. Different designs exist to attain homogeneity and to transfer gases to the liquid medium, the most common being those consisting of bags placed on rocking platforms that create a wave-like liquid movement (40), reciprocating bellows, and bags integrated to various types of molded polyethylene impellers and impeller shafts that are then placed into cylindrical containers (38, 41). The latter systems allow the design of bioreactors with conventional geometric ratios, although unlike traditional stainless steel equipment, the bottom of the vessels is flat. Different design challenges exist; in particular, the need for mechanically agitated shafts and impellers contained within a closed presterilized bag. This has been solved by different means, including bottom-driven magnetically levitated impellers or impellers connected to sheaths for inserting an external top-driven shaft. Another challenge is placement of sensors, such as pH and dissolved oxygen, which has been solved using disposable probes based on optical sensor technology or alternatively using traditional probes sterilized in disposable bellows that are inserted through quick-connectors to the sterile bag. Liquid transfer, inoculation, and sampling from and to the bags are usually performed through sterile tubing welding equipment, and in some systems aeration is performed through porous patch membranes, open-end tubing, or jet nozzle diffusers. Disposable bioreactor systems are available in volumes ranging form 100 mL to 1000 L. Some companies are developing bioreactors of 2000 L, which could be the highest volume attainable for disposable technology.

In addition to bioreactors, there is a growing trend for designing and developing other disposable process equipment for extending the advantages of disposable bioreactors to other bioprocess operations. At present, there is a widespread use of disposable bags for buffer preparation and media containers. Likewise, disposable cartridges for microfiltration and ultrafiltration are commonly employed in manufacturing facilities. Also, there is a growing interest for developing disposable downstream processing equipment, such as chromatography media and columns (36). In particular, disposable bags have been designed for use in special continuous centrifuges. Such equipment, placed in series to disposable bioreactors, offer important advantages for separating cells during perfusion culture mode in a complete sterile and disposable operation.

In spite of the convenient features of disposable bioreactors, there still exist important disadvantages that limit their application in fields other than production of certain pharmaceuticals. In general, operation is limited to low agitation rates (< 200 rpm), low aeration rates (< 0.02 VVM), and low total pressure (< 0.5 psig). Accordingly, the maximum volumetric oxygen transfer coefficients and OTR that can be attained are below 18 h−1 and 15 mmol/L h, respectively. Such constraints usually restrict the application of disposable bioreactors to animal and plant cell cultures operated at low or medium cell concentrations, although applications in microbial cultures are starting to appear (42). In addition, the maximum bioreactor volume available to date (1000 L) implies that multiple systems operated simultaneously will be required for manufacturing products requiring production outputs above 100 kg/yr. Finally, disposable bags are expensive and disposing the used bags and accessories must be considered under environmentally sustainable practices. Risk of puncture during operation must also be considered. Qualification of extractables and leachables must be necessary for particular processes that have not been previously validated by the bag vendors.

2.3 Airlift and Bubble Column Bioreactors

Airlift and bubble columns are also commonly used bioreactor configurations for the culture of suspended cells (typical geometric characteristics are shown in Fig. 6). These bioreactors are useful for culture broths with Newtonian behavior. They have higher energy efficiency than stirred tanks. Also, they have no moving parts, which can decrease maintenance time and costs, and in general they provide low shear. However, foaming can be a major problem, while bubble coalescence can reduce their performance (43). The height-to-diameter ratio of these reactors can range between 6:1 and as high as 12:1, but is typically 10:1. Nonetheless, airlift reactors with aspect ratios even below 2 have been reported for animal and plant cell cultures. As in stirred-tank vessels, geometric characteristic directly influence homogeneity, mass, and heat transfer in airlift and bubble column bioreactors. For instance, the relationship between geometric characteristics and mixing time is shown in Equations 5 and 6 (15, 44):

  • mathml alt image(5)

where B is a constant equal to 3.5 and 5.2 for internal- and external-loop airlift reactors, respectively, Ad and Ar are the downcomer and riser cross-sectional areas, respectively, and tc is the circulation time or time taken for a liquid element to complete a circulation cycle in the reactor. Circulation time of airlift reactors (either internal loop or external loop with short horizontal top and bottom sections) can be determined from the superficial liquid velocity and geometric parameters according to

  • mathml alt image(6)

where Hr and Hd are the riser and downcomer heights, respectively, and uLr is the superficial liquid velocity in the riser. uLr is affected, among other variables, by liquid density, gas holdups, frictional loss coefficients, and frictional pressure drops, in riser and downcomer, through complex relationships usually solved by iterative algorithms. However, simplified correlations between uLr and geometric characteristics and operation parameters have been developed for particular conditions. For instance, Popovic and Robinson (45) proposed the following equation for a pseudoplastic fluid in an external-loop airlift (uGr ≥ 0.04 m/s, H = 1.88 m, and Ad/Ar of 0.111, 0.25 and 0.44):

  • mathml alt image(7)

where uGr is superficial gas velocity in the riser and μapp is the apparent viscosity (Pa s), this last variable being important only in some plant cell cultures.

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Figure 6. Typical geometric characteristics of common airlift and bubble column bioreactors used for cell culture. For all vessels shown, H/Tv > 2. For internal-loop airlifts, Tr/Tv > 0.6. For external-loop airlifts, Tr/Td ≈ 2. (a) bubble column, (b) and (c) internal-loop airlifts, (d) external-loop airlift, and (e) airlift with impeller. Arrows indicate direction of liquid flow and “s” indicates sparger position.

Adapted from Ref. 14

Using Equations 1, 5, 6, and 7, Doran (15) compared the time constants of hypothetical 10,000-L stirred tank and external-loop airlift plant cell reactors of typical dimensions [details of geometric characteristics given in Doran (15)]. From the results of such simulation, shown in Fig. 7, several conclusions can be drawn. First, under typical operation conditions, the mixing time for a large-scale airlift can be substantially longer than that for a stirred vessel of the same volume. For instance, while mixing times from 200 to as high as 1000 s were predicted for the airlift, the range of mixing times for the stirred vessel was only between 20 and 200 s. A similar conclusion was reported by Bello et al. (44) where the mixing time per unit volume of stirred tanks was three to five times shorter than that of airlifts (either internal- or external loop) at the same total power input per unit volume. It is interesting to note that the calculations shown in Fig. 7 are in close agreement with experimental determinations by Langheinrich et al. (20), discussed in the previous section, for an animal cell stirred-tank reactor of similar size. Doran (15) also calculated the time constants for oxygen consumption, trxn (ratio of equilibrium oxygen concentration in the culture liquid to the volumetric oxygen consumption rate), and for mass transfer, tmt (inverse of the volumetric mass transfer coefficient), while Lara et al. (19) calculated the time constants for oxygen consumption of different organisms and compared them with reported tmt. Mixing problems will be encountered if tM > trxn, while oxygen limitation will occur if tmt > trxn. Accordingly, it was concluded that even for the long mixing times of the airlift, neither oxygen limitation nor dissolved oxygen gradients will occur at low plant cell concentrations (5 kg/m3, Fig. 7a). Nonetheless, as cell concentration increases to 30 kg/m3, mixing becomes limiting in the airlift reactor at gas velocities below 0.5 m/s and, thus, oxygen gradients will develop (Fig. 7c). Furthermore, for the high cell concentration case, oxygen limitation will occur in the airlift below gas velocities of 0.1 m/s and in the stirred tank below an agitation rate of 6 s−1 (Fig. 7c and d). Note that, due to cell fragility, most bioreactors are operated at a gas velocity and agitation rates well below 0.5 m/s and 6 s−1, respectively.

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Figure 7. Comparison of time constants for 10,000-L hypothetical plant cell bioreactors. (a) External-loop airlift reactor: cell concentration 5 kg/m3 dry weight. (b) Stirred-tank reactor: cell concentration 5 kg/m3 dry weight. (c) External-loop airlift reactor: cell concentration 30 kg/m3 dry weight. (d) Stirred-tank reactor: cell concentration 30 kg/m3 dry weight.

Reprinted with permission from Ref. 15

Mixing problems in airlift vessels have been documented experimentally (46). As for stirred-tank vessels, the fragile nature of most higher eukaryotic cells limits the options for improving homogeneity in airlift and bubble column reactors. Accordingly, some solutions to mixing problems, such as addition of impellers to the draft tube of airlifts, have not been widely applied and appear to contradict the design essence of an airlift. Proper design of reactor geometry can be an efficient alternative to improve homogeneity. For instance, minimal mixing times of internal-loop airlift reactors have been observed for riser-to-column diameter ratios (Tr/Tv) above 0.6 (15). Accordingly, a riser-to-downcomer cross-sectional area equal to unity (Tr/Tv = 0.71) has been proposed as a good design criterion (47). Other geometric characteristics that can considerably affect homogeneity of airlift reactors are the draft tube and sparger positions, the draft tube to liquid height ratio, and the curvature of the bottom sections.

In the case of bubble columns, two types of flow regimes have been described, homogeneous and heterogeneous (48). Homogeneous flow regime, characterized by the absence of a circulatory flow, occurs at low gas superficial velocities (< 0.04 m/s) and when the sparger holes are uniformly distributed on the bottom of the vessel. In typical conditions, mostly all bubble columns operate under heterogeneous flow regimen where circulatory flow is present as a result of uneven distribution of sparger holes or high superficial gas velocities. Mixing time has been correlated with geometric characteristics and operation parameters for bubble columns under heterogeneous flow regime according to (48):

  • mathml alt image(8)

where uGs is the superficial gas velocity corrected for local pressure.

A comparison of calculated mixing times for airlift and bubble column bioreactors has been presented by van't Riet and Tramper (48). Such comparison revealed that for low superficial gas velocities (0.001 m/s), mixing times of bubble columns were shorter than that for airlifts, and the opposite occurs for gas velocities above 0.001 m/s. Nonetheless, for all conditions calculated and an aspect ratio of 10, differences in mixing times between both reactors were small and never exceeded 30%. Furthermore, such differences were even smaller as the reactor volume increased. Accordingly, the behavior of large-scale airlift and bubble column reactors in terms of homogeneity and presence of concentration gradients should be relatively similar.

Although high superficial velocities improve homogeneity and prevent formation of concentration gradients in airlift and bubble column reactors, foaming problems and bubble-associated cell damage limit the use of high aeration rates. Tramper et al. (49) have proposed a killing volume hypothesis, where cells are killed within a hypothetical volume associated with each air bubble. The specific death rate constant, kd, was then correlated with operation and geometric characteristics of bubble columns according to

  • mathml alt image(9)

where Fg is gas flow rate, db is bubble diameter, and Vk is killing volume, which is constant for a particular system and can be experimentally determined. Equation 9 shows that the aspect ratio of bubble column bioreactors can have important consequences on animal cell survival. For instance, a decrease in aspect ratio will result in an increase in the death rate constant for a given reactor volume and superficial gas velocity. Thus, a high aspect ratio should be the design criterion. However, Meier et al. (50) showed that cell damage increases with liquid height. As liquid height is increased, a higher number of cells attach to bubbles, due to their longer ascension time. Cell attachment to bubbles is reduced by the addition of Pluronic F68 or other shear protectants to culture medium.

2.4 Heterogeneous Bioreactors

Heterogeneous systems can be defined as those where cells grow either attached to or entrapped by a solid substratum arranged within a particular device or bioreactor configuration. Many different types of substrata and geometric configurations exist; however, heterogeneous systems can be simply classified according to Table 2 (51). In almost all heterogeneous systems, oxygen transfer will be the limiting factor, and, thus, as discussed below, dissolved oxygen concentration gradients will be present. Accordingly, predicting dissolved oxygen profiles constitutes the basis for a rational design of many heterogeneous systems. The simplest designs include static units, such as dishes, flasks, and trays, where oxygen is transferred through the liquid surface only by diffusional mechanisms. As described by Murdin et al. (52), the dissolved oxygen profile can then be predicted from a steady state mass balance according to:

  • mathml alt image(10)

where c and cm are dissolved oxygen concentration in the liquid and at saturation, respectively, OUR is oxygen uptake rate, y is liquid depth, and Do/w is the diffusion coefficient of oxygen in water (2.6 × 10−5 cm2/s). For a typical maximum cell concentration (3  ×  106 cell/mL) and typical specific oxygen consumption rate (4 × 10−10 mmol/cell h), Equation 10 predicts that medium height must be maintained below 2 mm in order to avoid oxygen limitation. This result indicates that very high superficial area to culture volume ratios (A/V), usually in the range of 2.5–5 cm−1, are required. That is, two to three orders of magnitude higher than that of large-scale homogeneous bioreactors. A modest increase (two- to threefold) in substratum area, without a corresponding increase in A/V ratios, can be achieved by circulating medium through multistacked static units or by rotating vessels and flasks containing multiple internal surfaces. Scalability of high A/V culture units is limited, since their cumbersome configurations require labor-intensive operations; yet, volumes as large as 200 L have been reported (51). Very high substratum areas to culture volume ratios, and concomitantly very high cell concentrations (> 1  ×  108 cell/mL), can be attained in some heterogeneous bioreactors, such as packed beds (4–100 cm−1) and hollow fiber (HF) (30–200 cm−1). High gas/liquid areas needed for oxygen transfer are eliminated by perfusing oxygen-saturated medium. This results in very compact bioreactor designs, as well as in the possibility of culturing anchorage-independent cells in perfusion mode, at very low shear stresses, and close to in vivo cell concentrations.

Table 2. Classification of Heterogeneous Systems
Adapted from Ref. 51.
Plate devices 
 StaticT-flasks, plate units, trays, multiwell plates, petri dishes
 DynamicPlate units, roller bottles
FilmsBags, spiral wound
TubesMacroforms, hollow fibers
Packed bedsCeramic, glass spheres, helixes, springs, diatomeceous earth, polystyrene jacks, sponges
 MonolithicCeramic matrix
MicrocarriersSimple solid, collagen coated, porous
MicroencapsulationAlginate, agarose, polylysine

In spite of the fact that heterogeneous systems are extensively used in lab-scale applications and commercial size operations, a strictly controlled and uniform environment cannot be maintained. Thus, undesirable heterogeneities and existence of concentration gradients will inevitably occur during scale-up. Accordingly, heterogeneous systems are usually scaled up by increasing the number of small-scale units, rather than increasing the size of the equipment. Many disadvantages exist for such an approach, including higher capital and operation costs, poorly controlled and monitored operation, and unit-to-unit variability. Therefore, the challenge is to design heterogeneous bioreactors that approach a more uniform environment. This can be achieved through proper design of geometric characteristics and operation conditions. Since many different types of heterogeneous systems exist, each case deserves a unique analysis. Nonetheless, geometric and homogeneity considerations of microcarrier systems, HF, and packed-bed reactors are analyzed below, since these are among the most important systems for a commercial scale operation.

2.4.1 Hollow Fiber Reactors

Conventional HF reactors are composed by a bundle of HF sealed into an outer casing, forming a shell and tube configuration of 3.2–9 cm in diameter and 6–30 cm in length. HF are anisotropic structures composed of a thin (0.1–2.0 µm) inner or “active” skin and a thick (50–85 µm) spongy support layer. The internal fiber diameter commonly ranges from 40 to 200 µm and the molecular weight (MW) cutoffs (MW of species retained) vary from 300 to 300,000 Da. Medium is perfused from the lumen side and transported through the porous membrane to the shell side, where the cells are immobilized. As illustrated in Fig. 8, there are three common operation modes (open shell, closed shell, and crossflow), each resulting in a different pressure distribution throughout the HF cartridge (53). The axial pressure drop inside the fibers can be expressed, to a good approximation, by Equation 11, obtained from the Hagen–Poiseuille equation for flow in a pipe (54):

  • mathml alt image(11)

where pc, and uc are pressure and average axial velocity inside the capillary, respectively, z is axial position, and rc is the inside capillary radius. The transmembrane flux depends on the pressure difference between the shell and lumen sides of the fiber. For the open and closed shell operation modes, the pressure gradient, and thus medium flux, decreases along the axial direction, causing undesirable concentration gradients. The result is a higher cell concentration at the inlet section and only negligible growth after a certain cartridge length. Most commercial HF devices operate on the closed mode, resulting in a reversed flux at the downstream section of the reactor. Thus, while fresh medium is supplied to the cells in the inlet section, exhausted medium and toxic wastes are removed in the outlet segment, creating severe environmental heterogeneities. Accordingly, scale-up of HF reactors in the axial direction is limited and explains the short length of commercially available devices. In conventional HF reactors, only diffusional transport exists on the shell side. Thus, fibers must be tightly packed to avoid nutrient limitation and/or by-products accumulation at the interstitial zones. Even so, necrosis usually occurs since distance from the interstices to the inner capillary skin is, at best, 150 µm. Necrotic zones will still occur even if convective transport is forced through the shell side, as the tissue-like cell concentrations prevent a uniform flow distribution. Accordingly, severe radial gradients are also present in many HF reactors. Concentration polarization and fouling of the inner lumen surface are additional problems that can lead to reactor heterogeneities. Experimental determinations of axial and radial heterogeneities are well documented (53, 55-57).

thumbnail image

Figure 8. Schematic representation of common operation modes and pressure distribution in hollow fiber reactors. Open arrows indicate feed inlet and closed arrows indicate effluent streams. The tube-side pressure is represented by a solid line and shell-side pressure by a dashed line. (a) Open shell ultrafiltration and transmembrane pressure difference, A1. (b) Closed shell ultrafiltration and transmembrane pressure difference, B1 and B2. (c) Crossflow ultrafiltration and transmembrane pressure difference, C1.

Reprinted with permission from Ref. 53

Many solutions have been proposed for improving homogeneity and preventing nutrient limitation and by-products buildup in HF reactors, most of them on the basis of modifying geometric characteristics and operation conditions (55-57). For instance, combination of fibers and membranes in flat-bed HF arrangements; introduction of porous distribution tubes to perfuse either fresh medium or oxygen; mixing aeration and medium supply fibers; combination of different fiber types; selection of MW cutoffs; flow alternation between shell and lumen sides; and flow reversal at different interval times. Still, scale-up of HF reactors is primarily performed by increasing the number of devices in a modular fashion. Predicting dissolved oxygen profiles in the radial direction can help design more efficient HF reactors (fiber size, distance between fibers, etc.). A simplified approach is to perform a steady state mass balance around a cylindrical capillary where only diffusion is considered. Dissolved oxygen profiles can then be obtained, as detailed by Murdin et al. (52), from the following equation:

  • mathml alt image(12)

where r is radius and r0 is radius at which oxygen concentration falls to zero.

2.4.2 Packed-Bed Reactors

Packed-bed reactors are also widely used for the culture of anchorage-dependent and independent cells (58). In general, an aspect ratio of 3 is suitable for packed beds. As shown in Table 2, many different materials have been used as packing matrix. The diameter of the various matrix particles commonly range from 0.1 to 5 mm, resulting in typical void fractions of 0.3–0.6. Depending on the packing material used, very high substratum area to culture volume ratios can be reached (see above), which approximate those of HF reactors. However, in contrast to HF, properly designed packed-bed reactors should not present radial gradients, and, thus, a straightforward scale-up in this direction is possible. Still, axial concentration gradients are inherently present and will limit reactor length. Again, dissolved oxygen is almost always the limiting substrate and its concentration profile along the axial direction can be determined using a macroscopic mass balance (59):

  • mathml alt image(13)

where c0 is inlet dissolved oxygen concentration and uL is superficial liquid velocity based on empty bed. Concentration gradients will decrease as uL increases (Eq. 13). Nonetheless, maximum uL will be limited by permissible maximum pressure drop, which can be determined from the Ergun equation (60):

  • mathml alt image(14)

where ɛ is void fraction, Tp is particle diameter, and μb is culture medium viscosity. Maximum shear stresses in the bed must also be considered for determining the maximum allowable uL.

2.4.3 Microcarriers

Stirred vessels and airlifts are the reactor configurations used for cultivation of cells attached to microcarriers. Furthermore, the density of microcarriers is only slightly above that of culture medium (1.03–1.05 g/mL). Thus, geometric considerations and homogeneity characteristics of the bulk liquid phase will be the same as for homogeneous systems. Nonetheless, concentration gradients within porous microcarriers (typical diameter range between 100 and 500 µm) can still exist. Dissolved oxygen profiles within porous microcarriers can be modeled from a steady state mass balance of oxygen diffusion into a sphere, as has been described by Murdin et al. (52). Alternatively, mass transfer limitations, and, thus, formation of undesirable gradients within a porous microcarrier can be determined from plots of the observable module (obtained from the Thiele modulus), Φ, versus the effectiveness factor, η, shown in Fig. 9 (61). For spherical particles and OUR being the rate of interest, Φ and η are defined as

  • mathml alt image(15)
  • mathml alt image(16)

where Ap and Vp are the external surface area and volume of a microcarrier, respectively, and OURo is the observed OUR. De is effective diffusion coefficient, which in turn is a function of the microcarrier porosity and tortuosity factor. From Fig. 9 and Equations 15 and 16, it can be seen that oxygen limitation will occur at an observable module above 0.3. Accordingly, oxygen limitation can be avoided (Φ < 0.3) through proper design of microcarrier geometry (Fig. 9 and Eqs 15 and 16). This approach can also be applied to other immobilized systems such as HF and microencapsulation.

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Figure 9. Effectiveness factor as a function of the observable modulus. Michaelis–Menten kinetics. Continuous line, spherical geometry and dashed line, slab geometry.

Reprinted with permission from Ref. 61

3 Heating and Cooling

  1. Top of page
  2. Introduction
  3. Aspect Ratio, Homogeneity, and Gradients
  4. Heating and Cooling
  5. Nomenclature
  6. References

Maintenance of a constant and homogeneous temperature is an essential requirement in cell culture. Temperature variations of 1°C can reduce cell growth, viability, and/or product production (62). Temperature has also been reported to affect cell cycle phases, metabolism, and cell resistance to shear (63), while its control is particularly relevant when temperature inducible genes are used for recombinant protein production (64). High temperatures may also increase proteolytic activity and alter protein posttranslational modifications (63). Moreover, culture susceptibility to viral infection can be modified by temperature (65). Although for some processes, viral infection is an undesirable event, in others, such as virus production for vaccines or bioinsecticides, viral progeny is the desired product. As shown in Table 3, there exists a wide range of optimum temperatures for tissue culture. Mammalian cell lines are usually cultured at or near 37°C, while cells from other origins, such as insect, amphibian, fish, or plant, require lower temperatures, usually between 10 and 30°C. Optimum temperature for growth is not always the best for product production. In an attempt to provide the most favorable conditions for growth and product production, several groups have proposed production strategies that demand a fine control of temperature (63, 66). Moreover, temperature monitoring has been proposed as a tool for designing control strategies (63, 67). Altogether, it is clear that optimum temperature control and monitoring are imperative, especially when applications of cell culture are scaled up to a commercial level.

Table 3. Optimum Temperatures for Cell Culture
Cell lineOptimum Temperature (°C)Parameter (Maximum Value)Reference
  1. a

    Optimum temperature should be determined for each recombinant protein produced.

Murine hybridoma HB-3233Viability index66
Murine hybridoma HB-3239qMab66
Rat–mouse–mouse trioma37Xt and qMab68
CHO cells37Growth rate62
Insect cells27–29Xt69
Insect cell—baculovirus expression system22–29Recombinant protein productiona69
Catharantus roseus plant cells30Xt70
 21.5Product synthesis70
Perilla frutescens plant cells28Xt71
 25Anthocyanin productivity71
Chlorella vulgaris SO-26 green alga cells20Specific growth rate72
 14Cellular sugar content72
Salmonid fish cell lines15–20Xt73
Non-salmonid fish cell lines20–30Xt73

For fermentations of lower eukaryotes or prokaryotes, heat transfer becomes increasingly problematic as the fermenter is scaled up. This is due to the high cell concentrations reached, the high heat generated from metabolic activity, and the very large volumes of fermenters employed. The importance of heat transfer in such processes can be illustrated by the production of single-cell protein, where operating costs from heat removal can be higher, or at least equal, than that from oxygen transfer (14). A particular problem that occurs at very large scales is that heat transfer from the vessel walls is severely limited since reactor volume increases to the cube while reactor area increases only to the square. A contrasting situation exists for cell culture, where heat transfer is not considered an important problem and has been widely overlooked, while other aspects such as oxygen transfer have received much more attention. The reasons for this are the lower cell concentrations, smaller power inputs, lower size of commercial reactors, and lower generation of metabolic heat of animal and plant cell culture compared to microbial fermentations. Nonetheless, careful attention must still be placed on the design of the heat transfer and temperature control systems of large-scale cell cultures, particularly if temperatures near ambient are required. Heat transfer can become an important issue as higher cell density cultures are developed and larger reactor volumes are needed. Also, particular operation strategies can result in temperature gradients. Druoin et al. (74) observed transient temperature increases when CHO cells were circulated through a sonic separator in perfusion cultures. Temperature increases in animal and microbial cell cultures trigger heat shock responses, which have various effects on metabolism and productivity (75, 76). Moreover, the fragile nature of most animal cells limits the use of highly turbulent mixing, necessary if high heat transfer rates are needed. Accordingly, heat transfer phenomena must be considered during the design of a large-scale cell culture and microbial process.

Effective heat transfer is required not only for maintaining a constant temperature in the bioreactor, but also for sterilizing and cooling the vessel, the latter being important for assuring product stability at the end of the culture. In this section, a general introduction to heat transfer in bioreactors is given, with special emphasis to cell culture. Only the maintenance of a desired temperature during the culture phase is discussed, as sterilization and product recovery are discussed elsewhere. Finally, the relevance of heat transfer is evaluated from calculations for hypothetical large-scale cultures.

3.1 Heat Transfer in Bioreactors: The Basics

The main heat flows in a stirred-tank bioreactor are shown in Fig. 10. The heat accumulation rate in such a reactor, for constant pressure, is given as follows:

  • mathml alt image(17)

where Qmet is heat produced by metabolism of the cells, Qsen is sensible enthalpy gain by flow streams (outlet–inlet), Qag is heat generated by power input from agitation, Qsp is heat generated by sparging, Qevap is heat removed by evaporation, and Qex is heat transferred by the heat exchanger. Heat transferred between the environment and the reactor can be important for small-scale vessels, but becomes negligible as volume increases. Heat transferred from the environment can be included in Qex. If temperature of the reactor is maintained constant, then

  • mathml alt image(18)
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Figure 10. Main heat flows in a stirred-tank bioreactor.

Each of the terms in Equation 17 is individually analyzed below.

3.1.1 Metabolic Activity

Heat generated by metabolic activity depends, among other things, on the type of cell, growth phase, type and concentration of substrates, concentration of by-products, shear and osmotic stresses, and physicochemical properties of the culture medium (77). This has been extensively analyzed for cultures of prokaryotes or lower eukaryotes, but only very scarce information exists for animal and plant cell cultures. Heat generated from aerobic growth can be calculated from the oxygen consumption using the oxycaloric equivalent, which is defined as the heat yield from oxygen consumed. For any cell type, fully aerobic metabolism, and all biologically useful organic substrates, the oxycaloric equivalent has been determined to be –450 (±5%) kJ/mol O2 (77). However, compared to in vivo, the oxycaloric equivalent is always more negative for cells grown in vitro. This is caused by nutritional deficiencies present in the in vitro environment, which must be fulfilled by rapidly growing cells through anaerobic processes (77). Under such conditions, use of the oxycaloric equivalent to calculate the heat produced from cell metabolism can lead to an underestimation of almost 40%. Heat flow rates for several biological models have been determined under controlled pH and dissolved oxygen using microcalorimeters or bench-scale calorimeters (67, 77, 78). Heat fluxes (heat flow rate per cell) for some mammalian cell lines are shown in Table 4. However, caution should be taken when using such values, as the heat generated by metabolism is affected by the various parameters mentioned above.

Table 4. Specific Heat Flux for Some Cell Types
Cell TypeHeat flux (pW/cell)
  1. a

    In grams per liter, calculated from data of Ref. 78.

Reprinted with permission from Ref. 77.
Human erythrocytes0.01
Human platelets0.06
Bovine sperm1.3 ± 0.1
Human neutrophils2.5 ± 0.3
Human lymphocytes5
Horse lymphocytes8
Human T-lymphoma8 ± 1
3T3 mouse fibroblasts17
Chinese hamster ovary 320 (recombinant)∼23
kB25
Vero27 ± 2
Mouse lymphocyte hybridoma30–50
HeLa-53G31.2
Mouse macrophage hybridoma, 2C11-1232 ± 2
Chinese hamster ovary K138
Human foreskin fibroblast40 ± 10
Rat white adipocytes40
Human white adipocytes49 ± 15
Human melanoma, H147780
Human keratinocytes83 ± 12
Hamster brown adipocytes110
SV-K14 (transformed) keratinocytes134 ± 35
Rat hepatocytes329 ± 13
Kluyveromyces fragilis1.2a

If metabolic pathways are lumped into one global reaction, then heat produced by cellular metabolism can also be calculated from the standard enthalpies of substrates, biomass, and products. Again, caution should be taken as metabolic reactions are very variable, and depend on the particular system studied, including substrate availability, physicochemical conditions, and toxicity of by-products. Even when catabolism of higher eukaryotic cells is very complex, Kemp and Guan (77) have concluded that, for heat balance considerations, the metabolic processes of animal cells can be described essentially by glycolysis, oxidative phosphorylation, the pentose phosphate pathway, and glutaminolysis. Accordingly, they summarized animal cell growth and product production as follows:

  • mathml alt image(19)

Qmet can then be calculated from the standard enthalpies of formation of each compound, if reaction stoichiometry is known, according to (14)

  • mathml alt image(20)

where m and n are the number of products and substrates, respectively; bi and aj are the stoichiometric coefficients of product i and substrate j, respectively; and Hp, i and Hs, j are the enthalpies of product i and substrate j, respectively. It should be noted that the contribution of anabolism to heat generation is generally negligible (67). Some standard enthalpies of formation for common cell culture substrates and by-products are shown in Table 5. von Stockar and Marison (78) have determined that neither temperature nor the thermodynamic state of compounds is significant for energy balance calculations of aerobic (or mainly aerobic) cell growth. Therefore, values shown in Table 5 can be utilized for energy balances for culture temperatures different at 25°C without any further corrections.

Table 5. Standard Formation Enthalpies of Various Compounds (25°C, 1 atm)
CompoundFormulaΔH0f (kcal/mol)
Adapted from Refs 14, 79, 80. (s), (l), (g), and (aq) refer to the thermodynamic state of compounds.
Acetic acidC2H4O2(aq)−94.5
Acetate ionC2H3O2 − (aq)−116.1
AlanineC3H7O2N(s)−88.9
AmmoniaNH3(g)−41.4
 NH3(aq)−19.4
Ammonium chlorideNH4Cl(s)−75.4
Ammonium ionNH4 +(aq)−31.8
Bicarbonate ionHCO3 +(aq)−165.5
BiomassCH1.8O0.5N0.2(aq)−21.9
Carbon dioxideCO2(g)−94.0
 CO2(l)−98.9
Carbonic acidH2CO3−167.2
EthanolC2H5OH(l)−66.3
Formic acidCH2O2(aq)−85.1
α − β-d-GlucoseC6H12O6(aq)−302.0
Glutamic acidC5H8O4N(s)−170.4
Hydrochloric acidHCl(g)−22.1
 HCl(aq)−18.0
Hydrogen ionH+(aq)0
Lactic acidC3H6O3(l)−124
MethaneCH4(g)−17.9
MethanolCH3OH(l)−57.0
OxygenO2(g)0
 O2(aq)−2.9
Potassium chlorideKCl(s)−104.2
Pyruvic acidC3H3O3(s)−114.1
Sodium chlorideNaCl(s)−98.2
Sodium hidroxideNaOH(s)−102.0
Succinic acidC4H6O4(l)−178.8
SucroseC12H24O12(s)−371.6
Sulfuric acidH2SO4(l)−193.9
WaterH2O(g)−57.8
 H2O(l)−68.3
3.1.2 Inlet and Outlet Flows

The heat flow contributed by substances fed to or eliminated from the reactor, Qsen, if no phase change occurs and if inlet and outlet flows are equal, is given as follows:

  • mathml alt image(21)

where Ffd is flow rate, Cp the heat capacity of the stream, and Tout and Tin are the temperature of the outlet and inlet flows, respectively. Heat generation can also originate from the temperature difference between the gas and the culture broth. For instance, if gases are compressed adiabatically, their temperature can be higher than the liquid, particularly for cultures controlled at low temperatures (48). Accordingly, the sensible enthalpy gain by the gaseous stream is given as

  • mathml alt image(22)

where Tb is the temperature of the culture broth, ρg is gas density, and the subindex g refers to the gas phase.

Other reactions occurring in the system simultaneously to cell growth, such as neutralization of buffers in culture media, also contribute to the energy balance (80). The enthalpies of neutralization of physiological buffers are shown in Table 6, which are usually exothermic in culture conditions (80).

Table 6. Enthalpies of Neutralization of Physiological Buffer Systems for the Reaction A + H+ [RIGHTWARDS ARROW] AH
Buffer SystemT(°C)ΔbHH+ (kcal/mol) H+pka
Adapted from Ref. 80.
Bicarbonate25−2 to −1.86.4
 HCO3/CO2(aq)37−1.26.3
Carboxyl groups   
 Succinate25−0.075.6
Citrate25+0.86.4
 Phosphate25−16.9
 HPO42−/H2PO437−0.86pH 6.6
3.1.3 Power Input by Agitation and Sparging

An important source of heat in a bioreactor is the power input from agitation and sparging. The power transferred to the reactor from sparging, Pg, can be calculated from the following equation (14, 81):

  • mathml alt image(23)

where R is the gas constant, MW is the gas molecular weight, p1 is pressure at the sparger, p2 is pressure at the top of the vessel, α is the fraction of gas kinetic energy transferred to the liquid (typically 0.06) and inline image is the gas velocity at the sparger orifice. For well-designed spargers, the term inline image, which represents the jet kinetic energy developed at the sparger holes, is small and can be neglected (14). Equation 23 can be used to calculate power dissipation due to sparging into stirred tanks, bubble columns, and airlift bioreactors. Notice that, Equation 23, neglecting the jet kinetic energy at the sparger holes, corresponds to the term of energy dissipation rate from aeration of Equation 2. This is obtained by substituting in Equation 23 the molar gas flow rate and pressure difference between the sparger and top of the vessel, given by Equations 24 and 25, respectively:

  • mathml alt image(24)
  • mathml alt image(25)

where inline image is the molar gas flow rate.

The power, P, transferred to a Newtonian fluid by agitation depends on the fluid density, viscosity, agitation speed, impeller type, impeller diameter, vessel diameter, liquid height, and other geometric characteristics and parameters of the system (18). Then, using dimensional analysis, the energy dissipated to the liquid by agitation is a function of

  • mathml alt image(26)

where W is impeller width. P0, Re, and Fr are the power, Reynolds, and Froude numbers, respectively, defined as

  • mathml alt image(27)
  • mathml alt image(28)
  • mathml alt image(29)

Fr is important only if gross vortexing exists in the reactor. If vortexing is prevented by baffling or off-center stirring, then the power number will be only a function of Re and geometrical ratios (18). As shown in Fig. 11, this is true for the laminar flow regime (Re < 3 × 105), where P0 is related to Re through the proportionality constant, Kp, which only depends on the system geometry:

  • mathml alt image(30)
thumbnail image

Figure 11. Power number as a function of Reynolds number. (1) Turbine stirrer, Tv/D = 3.33, Hb/D = 1, wb = without baffles, b = with baffles. (2) Marine propeller, angle 25°, Tv/D = 3.33, Hb/D = 1.5. (3) Anchor impeller, Tv/D = 1.02, Hb/D = 0.01, W/D = 0.1. (4) Helical ribbon impeller, Tv/D = 1.02, Hb/D = 0.1, W/D = 0.1.

Reprinted with permission from Ref. 48

In turbulent flow regime the power input is independent of Re. Figure 11 can be used to predict P0 for various system geometries. For other geometries, P0 must be determined experimentally. For vessels equipped with multiple impellers, the interaction between them is not significant if the distance between impellers exceeds their diameter (48). Power consumed will then be the addition of the power consumed by each impeller. Furthermore, if an agitated vessel is also aerated, then power input from agitation will decrease with respect to the unaerated case. van't Riet and Tramper (48) recommend the correlation by Hughmark for turbine stirrers in water for calculating aerated power inputs Pa:

  • mathml alt image(31)
3.1.4 Evaporation

If the inlet gas is at a lower temperature than the bioreactor, heat loss due to evaporation can be significant. Furthermore, evaporation can contribute to substantial water loss in the fermenter, which has to be replaced or avoided through the use of effective condensers. As the gas temperature increases, the water content of saturated air increases. The latent heat of evaporation for water,λ, is 41 kJ/mol, and the heat loss due to evaporation can be calculated as (14)

  • mathml alt image(32)

where Fg is dry air flow and wout and win are the water contents of the inlet and outlet flows, respectively. Water contents can be calculated from psychrometric charts.

3.1.5 Heat Exchangers

Heat exchangers have to be included in vessels for controlling the culture temperature. Vessels can be jacketed, have internal or external coils, and even an external heat exchanger can be used. Jacketed vessels are used in low-scale reactors, but as scale increases, the heat transfer area per unit volume decreases, and internal or external coils may be required for efficient control of temperatures. As illustrated in the practical cases shown below, a jacket is more than enough for transferring the necessary heat in typical large-scale cell cultures. Furthermore, shear damage of cells in pumps and risk of contamination limit the use of external heat exchangers.

In order to maintain a constant culture temperature, the heat generated (or removed) by all the processes analyzed previously must equal the heat transferred by the exchanger. Heat transfer depends on the overall heat flow resistance, R′, and the temperature gradient, ΔT, between the exchanger and the culture broth:

  • mathml alt image(33)

Calculation of ΔT depends on the system geometry and on the direction of motion of the fluids. For heat transfer from jackets in agitated-tank reactors, ΔT is given by the log-mean temperature difference (LMTD):

  • mathml alt image(34)

where Ti and To are the temperatures of the coolant entering and leaving the reactor, respectively. Tb is constant if a perfectly mixed vessel is assumed. In turn, R′ is defined as

  • mathml alt image(35)

where A is the area for heat transfer and U is the overall heat transfer coefficient. U depends on the nature of the material across which heat is transferred, the system geometry, and the nature of the fluid flows involved. As a rule of thumb, U for a clean vessel usually ranges between 280 and 1137 W/m2°C (13). However, a wider range exists for various practical situations (82). Lower values correspond to very viscous non-Newtonian fluids, while larger values correspond to nonviscous Newtonian fluids. The overall heat transfer resistance is the sum of the individual resistances in series in the path of heat transfer. Therefore, for the jacket of thin-walled vessels, where the area normal to the direction of heat transfer can be considered constant, U is given by the following expression:

  • mathml alt image(36)

where hi and ho are the broth and coolant side heat transfer coefficients, respectively; t is vessel wall thickness; km is the metal thermal conductivity; and inline image and inline image are the inside and outside fouling heat transfer coefficients, respectively. Fouling factors are caused by deposits (microbial film, scale, dirt, etc.), which depend on operating conditions and should be kept to a minimum by maintaining vessels and jackets or coils clean. Fouling resistances for various systems can be found elsewhere (82). Individual heat transfer coefficients depend on the fluid properties, geometric characteristics, and operation conditions of the system through complex relations. Thus, from a practical standpoint, individual heat transfer coefficients are obtained from empirical correlations, some provided by vessel vendors, relating the Nusselt number, Nu, with the Reynolds and Prandtl, Pr, numbers. For instance, hi for stirred vessels can be determined as:

  • mathml alt image(37)

where a, b, c, and d are constants (listed in Table 7 for various reactor configuration), μw is broth viscosity at the wall temperature, and Nu and Pr are defined as

  • mathml alt image(38)
  • mathml alt image(39)

where k is broth thermal conductivity. Equation 37 is acceptable for unaerated fluids; however, no correlations have been published for aerated conditions (13). Depending on stirring speed and flooding phenomena, aeration can improve or deteriorate hi. Nonetheless, the influence of gassing is minor in relation to other variables (48).

Table 7. Values of Constants in Equation 37 for Jacketed Vessels
ImpellerabcdRe
Adapted from Ref. 82.
Jacketed vessels     
 Paddle0.360.660.330.21300 to 3 × 105
 Pitched-blade turbine0.530.660.330.2480–200
 Disk flat-blade turbine0.540.660.330.1440 to 3 × 105
 Propeller0.540.660.330.142 × 103
 Anchor10.50.330.1810–300
 Anchor0.360.660.330.18300–40,000
 Helical ribbon0.630.50.330.188–105
Helical coils     
 Paddle0.870.620.330.14300 to 4 × 105

Liquid circulation in bubble columns is determined by the gas flow rate, and, thus, hi can be determined as (48)

  • mathml alt image(40)

where μwt is the water viscosity and μb is broth viscosity. Equation 40 is applicable for vessels with diameters ranging from 0.1 to 1 m and for broths viscosities between 10−3 and 5 × 10−2 N s/m2.

The liquid velocity has to be known in order to perform heat transfer calculations in airlift bioreactors. This is rather complex and, as exemplified by van't Riet and Tramper (48), an average liquid velocity can be estimated only from numerical simulations. Alternatively, simplified correlations, such as the one shown in Equation 7, exist. However, liquid velocity gradients are present, and, thus, a single value for heat transfer cannot be given. Flow in the downcomer can be considered as a single phase. Thus, hi can be determined from correlations of turbulent flow in pipes (48):

  • mathml alt image(41)

where inline image is average superficial liquid velocity in the downcomer and Td is diameter of the downcomer. The flow regime in the riser can be described in the same manner as in a bubble column; that is, either homogeneous or heterogeneous flow (see previous section) (48). The flow regime is determined mainly by the total hydrodynamic resistance of the bioreactor. If the riser acts as a bubble column in the heterogeneous flow regime, Equation 40 can be used for calculating the heat transfer coefficient. For a “true” airlift flow (homogeneous flow), Equation 41 can be used.

For packed-bed reactors, the heat transfer coefficient between the inner container surface and the fluid stream can be calculated from the following correlation (82):

  • mathml alt image(42)

where Tp is particle diameter, G is superficial mass velocity, k and Cp are used to calculate Pr (refer to the liquid phase), b is a coefficient dependent on Tp/Tv (Fig. 12), and b1 is equal to 1.22 (SI) or 1 (US customary).

thumbnail image

Figure 12. Coefficient b of Equation 42, Tp/Tv in inches per foot.

Reprinted with permission from Ref. 82

Heat transfer coefficients for other heterogeneous systems, such as HF and fluidized beds, have to be evaluated for each individual case, as the packing, liquid velocity, and the aspect ratio have to be considered. Various correlations for such systems can be found elsewhere (82). Finally, once all the terms of Equation 36 are known, the heat transferred by the exchanger can be calculated by combining Equations 33, 34 and 35:

  • mathml alt image(43)

and the cooling water flow rate, Fw, can be calculated from

  • mathml alt image(44)

Many industrial operations still rely on simply multiplying the number of small-scale units (such as T-flasks or roller bottles) and placing them in contained suites. For such cases, a very different approach for solving heat transfer problems must be taken. These are usually solved through proper design of the HVAC (heating, ventilation, and air conditioning) systems. A “mega roll” industrial unit has been described by Panina (83). This unit has a capacity of 7200 roller bottles of 1 L in cylindrical wire racks. Racks are positioned in an incubator of 269.8 m3 heated with electric heaters that generate 14 kW. Heat is uniformly distributed by forced air circulation and temperature is controlled by a heat exchanger fed with cold water.

3.2 Practical Cases

In order to assess the magnitude of the various heat flows, and thereby the importance of heat transfer in a cell culture process, heat balances for a hybridoma culture in a hypothetical 10,000-L water-jacketed stirred-tank reactor are presented. Comparison is made with a hypothetical baculovirus-infected insect cell culture in the same vessel. The behavior of the large-scale hybridoma culture is assumed to follow real kinetic data obtained from a 1-L agitated batch reactor under the experimental conditions described by Higareda et al. (84). Such an assumption is valid since the data at the 1-L scale, shown in Fig. 13, are very similar to data reported by Backer et al. (9) at the 1000-L scale. The calculations are performed for a hypothetical vessel, detailed in Table 8, which closely resembles the reactor used for CHO cell culture at Glaxo Wellcome and described by Nienow et al. (85).

thumbnail image

Figure 13. Kinetic data of a hybridoma batch culture in a 1-L stirred-tank reactor. (a) Oxygen uptake rate (–) and viable cell concentration (closed squares). (b) Heat flow (closed circles) and heat accumulation (open diamonds). (c) Monoclonal antibody. Dotted-line represents the time of Gln depletion.

Table 8. Details of the Hypothetical 10,000-L Bioreactor
Some values are based on Ref. 85.
Working volume8000 L
Aspect ratio1.3
Liquid height2.54 m
Tank diameter2 m
Vessel wall thickness6 × 10−3 m
Baffles4
Turbine1 Rushton
Turbine diameter0.44 m
Distance of turbine from vessel bottom2/9 Tv
Heat exchangerWater jacket
Area of water jacket12 m2
AerationSuperficial and submerged
Superficial gas velocity2 × 10−4 m/s
Temperature37°C
Dissolved oxygen concentration20% wrt air saturation
Metal conductivity80 W/m2°C

Viable cell concentration and OUR are shown in Fig. 13a. The horizontal line represents the time of glutamine depletion that corresponds to the onset of respiration cessation and the end of exponential growth. A similar behavior has been described by Higareda et al. (84). Heat flow during the lag and exponential growth phases was calculated using 50 pW/cell, which corresponds to the highest heat flux reported for a mouse hybridoma (Table 4). By choosing such a high value, the calculated results should yield the worst case scenario in terms of heat generation. Guan et al. (67) showed that as metabolic activity of a culture decreases, the heat generated approaches the oxycaloric equivalent. Accordingly, during the stationary and death phases, the heat flow was calculated using the oxycaloric equivalent, 450 J/mmol O2. The calculated profiles of volumetric heat flow and accumulated heat (integral of heat flow with time) are shown in Fig. 13b. It can be seen that volumetric heat flow and accumulated heat will have a maximum of 0.17 W/L and 20 J/mL. Thus, for the 10,000-L reactor (8000 L working volume), a maximum heat flow of 1.36 kW will be expected. In comparison, maximum heat flows of 7.4 W/L and 26 W/L have been reported for typical aerobic growth of yeast (at a relatively low maximum biomass concentration of 6.2 g/L) and unicellular protein production in a 2.3  ×  106-L reactor, respectively (78). That is, heat generated from metabolism of the hypothetical hybridoma culture will be between 1 and 2 orders of magnitude lower than that for other microbial fermentations.

To satisfy the oxygen requirements of the culture shown in Fig. 13, OTR must equal OUR. In this example, maximum OUR was 0.8 mmol/L h. Thus, an oxygen transfer coefficient, kLa, of at least 5.47 h−1 is required. As determined by Nienow et al. (85), such a kLa can be obtained if 50 W/m3 are supplied to the reactor by agitation and sparging. Total heat dissipated by the reactor would then be 1.76 kW. Interestingly, under such situations, 80% of the heat flux will originate from cellular metabolism, whereas only 23% from aeration and agitation. For a superficial gas velocity of 2 × 10−4 m/s (Table 8) and using Equations 23 or 2, the power supplied by sparging will be 1.96 W/m3. Thus, 48.04 W/m3 is needed for agitation. An impeller speed of 1.67 s−1 can be calculated from Equation 27 if a power number of 5 is assumed for the reactor (85). This results in a fully turbulent flow regime with a Reynolds number of 323,312 (assuming that culture broth behaves like water), but where shear damage is not expected. A broth side heat transfer coefficient of 1694 W/m2°C can then be calculated using Equation 37. Finally, if no fouling layers in the tank or jacket are formed, and if the heat transfer coefficient on the coolant side is negligible, an overall heat transfer coefficient of 1503 W/m2°C results from Equation 36 and data from Table 8 (vessel wall thickness and metal thermal conductivity). This value agrees with overall heat transfer coefficients of jacketed vessels using brine as coolant and water as fluid in vessel, which range from 230 to 2625 W/m2°C (82).

In order to maintain the temperature of the reactor constant, heat generated from cellular metabolism, agitation, and sparging has to be removed by the water jacket, dissipating to the environment, and evaporation. Again, for the worst case scenario, maximum heat removal from the exchanger can be determined if heat losses to the environment and from evaporation are neglected. This is possible if the reactor is well insulated and a water saturated gas stream at the culture temperature is used for aeration. Accordingly, solving Equation 43 for a jacket area of 12 m2 yields an LMTD of 0.09°C. Multiple combinations of inlet and outlet water temperatures below 37°C, but above 36°C, can satisfy the calculated LMTD. For instance, water entering the jacket at a temperature of 36°C and a flow rate of 22 L/min (Eq. 44) would be necessary for maintaining the culture temperature at 37°C. Interestingly, such a result indicates that for the hypothetical hybridoma culture, the heat transfer problem actually becomes a heating task, as jacket inlet water is required at a temperature above ambient.

A different situation will result for another model culture, for instance, protein production by the insect cell baculovirus expression vector system (69, 86, 87). An insect cell culture, typically maintained at 27°C, can reach a concentration of 8  ×  106 cell/mL and an OUR of 17 mmol/L h during infection with a baculovirus. Using the oxycaloric equivalent, a heat flow from metabolic activity of 17.2 kW will result for the same hypothetical vessel described above, that is, about 13 times higher than that for the hybridoma culture. For comparison purposes, the same agitation and aeration rates used for the hybridoma culture are also used in this case. Since OUR is several-fold higher, it is assumed that OTR can be increased by oxygen enrichment, additional membrane aeration and/or pressure increase, or other means. It should be cautioned that for a real situation, the practical utility of such alternatives must be carefully evaluated. The fragile nature of insect cells also rules out the use of higher agitation and aeration rates. Accordingly, the total heat generated will be 17.6 kW. Following the same procedure as before, an LMTD of 0.98°C can be calculated. Such an LMTD could be satisfied, at least theoretically, for inlet water temperatures ranging from 6 to 26°C. Thus, more options exist than that for the hybridoma culture, for designing the heat transfer system. In conclusion, the cases illustrated show that jacketed vessels are more than enough to satisfy heat transfer requirements for cell culture at the typical largest scales performed to date. Moreover, compared to microbial systems or oxygen transfer requirements in cell culture, the heat transfer problem is not a major challenge, but cannot be overlooked.

3.3 Acknowledgment

Financial support by grant CONACYT 46408-Z and Conacyt-Salud 69911 is acknowledged. Technical assistance by R. Pastor.

4 Nomenclature

  1. Top of page
  2. Introduction
  3. Aspect Ratio, Homogeneity, and Gradients
  4. Heating and Cooling
  5. Nomenclature
  6. References
Aarea
Addowncomer cross-sectional area
ajstoichiometric coefficient of substrate j
Aparea of microcarrier
Arriser cross-sectional area
bistoichiometric coefficient of product i
cdissolved oxygen concentration
cmdissolved oxygen concentration at saturation
c0inlet dissolved oxygen concentration
Cpheat capacity
Dimpeller diameter
dbbubble diameter
Deeffective diffusion coefficient
Do/wdiffusion coefficient of oxygen in water
Fggas flow rate
Fgdry gas flow rate
Ffdflow rate (feed)
FrFroude number
Fwcooling water flow rate
ggravitational acceleration
Gsuperficial mass velocity
Hliquid height
Hbheight of stirrer above vessel bottom
Hddowncomer height
inline imageinside fouling heat transfer coefficient
inline imageoutside fouling heat transfer coefficient
hibroth side heat transfer coefficient
hocoolant side heat transfer coefficient
Hp,ienthalpy of product i
Hrriser height
Hs,jenthalpy of substrate j
kthermal conductivity
kdspecific death rate constant
kmmetal thermal conductivity
Kpproportionality constant
LMTDlog-mean temperature difference
mnumber of products
Mabmonoclonal antibody
MWmolecular weight
nnumber of substrates
inline imagemolar gas flow rate
Nimpeller speed
N*dimensionless mixing time
NuNusselt number
OURoxygen uptake rate
Ppower
p1pressure at the sparger
p2pressure at top of vessel
Paaerated power input
pcpressure in capillary
Pgpower transferred to liquid from sparging
Popower number
PrPrandtl number
qspecific production rate
Qaccheat accumulation rate
Qagheat produced by agitation
Qevapheat removed by evaporation
Qexheat transferred by the heat exchangers
Qmetheat produced by metabolism
Qsensensible enthalpy gain by flow streams
Qsengsensible enthalpy gain by gas stream
Qspheat produced by sparging
Rgas constant
Rresistance to heat flow
Rradius
r0radius at which oxygen concentration falls to zero
rccapillary radius
ReReynolds number
tvessel wall thickness or time
Ttemperature
Tbbroth temperature
tccirculation time
Tddowncomer diameter
Tgtemperature of gas
Tijacket fluid inlet temperature
Tintemperature of the inlet flow
tMmixing time
tmttime constant for mass transfer
Tojacket fluid outlet temperature
Touttemperature of the outlet flow
Tpdiameter of particle
Trriser diameter
trxntime constant for oxygen consumption
Tvvessel diameter
Uoverall heat transfer coefficient
inline imageaverage axial velocity inside capillary
uGsuperficial gas velocity
inline imagegas velocity at the sparger orifice
inline imagesuperficial gas velocity in the riser
inline imagepressure corrected gas velocity
uLsuperficial liquid velocity
uLrsuperficial liquid velocity in the riser
inline imageaverage superficial liquid velocity in downcomer
Vliquid volume
Vkkilling volume
Vpvolume of a microcarrier
VVMvolume of air per volume of liquid per minute
Wwidth of impeller
winwater content of inlet gas stream
woutwater content of outlet gas stream
Xttotal cell concentration
yliquid depth
zaxial position
αfraction of gas kinetic energy transferred to the liquid
Δppressure drop
ɛvoid fraction
ɛ Ttotal energy dissipation rate
Φobservable module
ηeffectiveness factor
λlatent heat of evaporation of water
μviscosity
μappapparent viscosity
μ bbroth viscosity
μwbroth viscosity at the wall temperature
μwtwater viscosity
ρliquid density
ρ ggas density
End Notes
  • *

    This contribution is an update of the following chapter:L. A. Palomares, O. T. Ramírez; “Bioreactor Scale-Up”; in: The Encyclopedia of Cell Technology; Spier, R.E. (ed) The Wiley Biotechnology Series, John Wiley and Sons; Vol 1, 183–201 (2000). ISBN 0-471-16643-x.

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