This document reviews scale-up techniques for Escherichia coli and yeast fermentation processes. It analyzes the design parameters of a fermentation pilot plant with vessels ranging from 100L to 19,000L. Scale-up estimates were performed based on geometric similarity, agitator tip speed, gassed power per unit volume and mixing time. Generally, scale-up calculations from the 280L scale best matched installed equipment parameters. Maintaining geometric similarity, constant power input per unit volume, or constant agitator tip speed are common scale-up approaches. Analysis of historical process data helped identify key issues for scaling up specific processes in the pilot plant vessels.
This document reviews scale-up techniques for Escherichia coli and yeast fermentation processes. It analyzes the design parameters of a fermentation pilot plant with vessels ranging from 100L to 19,000L. Scale-up estimates were performed based on geometric similarity, agitator tip speed, gassed power per unit volume and mixing time. Generally, scale-up calculations from the 280L scale best matched installed equipment parameters. Maintaining geometric similarity, constant power input per unit volume, or constant agitator tip speed are common scale-up approaches. Analysis of historical process data helped identify key issues for scaling up specific processes in the pilot plant vessels.
This document reviews scale-up techniques for Escherichia coli and yeast fermentation processes. It analyzes the design parameters of a fermentation pilot plant with vessels ranging from 100L to 19,000L. Scale-up estimates were performed based on geometric similarity, agitator tip speed, gassed power per unit volume and mixing time. Generally, scale-up calculations from the 280L scale best matched installed equipment parameters. Maintaining geometric similarity, constant power input per unit volume, or constant agitator tip speed are common scale-up approaches. Analysis of historical process data helped identify key issues for scaling up specific processes in the pilot plant vessels.
This document reviews scale-up techniques for Escherichia coli and yeast fermentation processes. It analyzes the design parameters of a fermentation pilot plant with vessels ranging from 100L to 19,000L. Scale-up estimates were performed based on geometric similarity, agitator tip speed, gassed power per unit volume and mixing time. Generally, scale-up calculations from the 280L scale best matched installed equipment parameters. Maintaining geometric similarity, constant power input per unit volume, or constant agitator tip speed are common scale-up approaches. Analysis of historical process data helped identify key issues for scaling up specific processes in the pilot plant vessels.
Vol. 97, No. 6, 347364. 2004 Scale-Up Methodologies for Escherichia coli and Yeast Fermentation Processes BETH HELENE JUNKER 1 Merck Research Laboratories, Bldg. 810-127, PO Box 2000, Rahway, NJ 07065, USA 1 Received 22 August 2003/Accepted 15 March 2004 Scale-up techniques from the literature have been compiled and reviewed for applicability to Escherichia coli and yeast processes. The consistency of design and operating parameters for the pilot scale vessels in an existing fermentation pilot plant, ranging in nominal volume from 100 l to 19,000 l, was established and compared favorably with approaches found in the literature. Differ- ences were noted as a function of parameters such as fermentor scale, vessel geometry, agitator type/size and ungassed/gassed power input. Further analysis was conducted using actual fermen- tation data for historical and recent development processes collected over a 10-year-period, focus- sing on operating conditions at peak culture oxygen uptake rates. Scale-up estimates were per- formed based on geometric similarity, agitator tip speed, gassed power per unit volume and mix- ing time. Generally, scale-up calculations from the 280 l scale were most similar to the parameters of installed equipment. Scale-up from the 30 l laboratory scale typically underpredicted parame- ters with scale-up from the 280 l scale being most appropriate. The 19,000 l fermentor installation was notably different in geometric similarity from the 280 l1900 l scales since its design was meant to accommodate a wide range of operating volumes. Analysis of historical and recent proc- essing performance was conducted for single cell bacterial or yeast fermentations which chal- lenged peak operating conditions of the fermentors. Identification of key issues associated with scale-up for these specific pilot plant vessels was believed to be critical to efficient process devel- opment, clinical material production, and expected process transfer to a manufacturing facility. [Key words: scale-up, Escherichia coli, yeast, pilot plant, fermentor] General concerns for recombinant DNA scale-up have been addressed by Van Brunt (1). Although the three main scales for bioprocess development are laboratory, pilot plant and production (2), Votruba and Sobotka have added the shake-flask scale to this list (3). The scale-up ratio is typi- cally about 1: 10 for biotechnological processes up to 100,000 l (3), but lower ratios of about 1: 5 often have been used for increased comfort levels (i.e., decreased risk of unexpected performance on scale-up). Production scale for many recombinant DNA products is likely to be about 10,000 l which is more traditionally pilot scale for other types of products (4). The exact methodology used for scale- up is largely dependent on process conditions and whether preliminary data exist to show that the procedure chosen is applicable (5). Some authors maintain that the total environment (Young [6] coined this term to encompass all the chemical and physical variables relating to the fermentor broth) of the cell needs to be considered (6). A complete catalog of factors affected by scale is detailed extensively by Reisman (7) with key items being emphasized by other authors (16) as well. Additionally, the role of scale-down studies can be sig- nificant in identifying and evaluating problems at the large scale (811). Biological factors affected by scale include the number of generations associated with the inoculum development and production phases, mutation probability, contamination vul- nerability, pellet formation and selection pressure (8, 12). Chemical factors affected by scale include (i) pH control agents (i.e., type and concentration of acid and/or base), me- dium quality (i.e., purity of components) and water quality (8); (ii) carbohydrate (e.g., oil), nitrogen (e.g., ammonia), phosphorus and product concentrations (6); (iii) redox po- tential and foam formation due to surface tension changes (3). Physical factors affected by scale include tank configu- ration, aeration, agitation, back-pressure (and hydrostatic pressure), medium sterilization, temperature control/heat transfer and removal, and mixing (3, 8, 12). There is a comprehensive paper outlining general ap- proaches to scale-up (13) and it includes comments from several other authors on the implications of general trends in scale-up. Unless specifically maintained constant with scale-up to the larger fermentor, dissolved carbon dioxide (dCO 2 ) is higher in the larger vessel than the smaller vessel due to the added head pressure, shear force variation is e-mail: Beth_Junker@Merck.com phone: +1-732-594-7010 fax: +1-732-594-7698 JUNKER J. BIOSCI. BIOENG., 348 higher, and bulk mixing is less efficient due to longer circu- lation times and larger stagnant regions (8). In addition, for the larger vessel, the liquid height to tank diameter ratio can be greater, gas moves upwards with more limited backmix- ing, vertical dissolved oxygen (DO) gradients exist if bulk mixing is slower than mass transfer rates, and radial DO gradients emerge since the shear rate declines rapidly with distance from the impeller (14). Other trends in scale-up in- clude decreased heat transfer surface to volume ratio, de- creased quality of mixing, generally higher superficial air velocity, and lower average shear force although peak shear forces are higher (14, 15). Furthermore, if cheaper medium components have been selected with variable composition for different bulk lots, a previously unnoticed auxotrophic growth pattern may appear (15), but this occurrence is mini- mized by the use of defined medium. There are several published descriptions of scale-up stud- ies and a few interesting examples are noteworthy. Oxygen transfer often can be most important upon scale-up due to its low solubility in medium (16). Key to scale-up using constant oxygen transfer rate (OTR) is the ability to mea- sure or estimate the volumetric mass transfer coefficient, K L a, and the gassed power per unit liquid volume, P g /V L . Published correlations can generate significant errors as in the example of K L a factors for a commercial-scale penicillin fermentation (17). The scale-up of bialaphos production by Streptomyces hygroscopicus based on K L a and P g /V L was not successful due to the large DO concentration gradients in the fermentor (18). In this example, the culture was not sensitive to impeller tip speed changes upon scale-up. Scale- up was successful when the target DO in the laboratory fer- mentor was used to control the large scale fermentor DO us- ing a probe located at the bottom of the large scale fermen- tor. Similarly, scale-up deteriorated production syndrome (SUDS) was observed during the scale-up of milbemycin production by S. hygroscopicus when agitation rate was used to control DO as was done at the small scale (19). SUDS syndrome included culture morphological changes which affected packed cell volume and viscosity, carbon source uptake changes, and decreased productivity. An alternative DO control strategy using aeration rate, back-pressure, tem- perature, in addition to agitation rate, was developed to maintain laboratory yields upon scale-up. Additional examples focus on parameters other than oxy- gen transfer. For the scale-up of toyocamycin production by a shear-sensitive mutant of Streptomyces chrestomyceticus, neither the constant P g /V L method nor the constant OTR method could be used, and thus scale-up was done at the lowest possible tip speed for the geometrically similar larger vessel (20). Mixing and circulation times were found to be more important than using constant oxygen uptake rate (OUR) for the scale-up of a 2,3-butanediol fermentation by Enterobacter aerogenes under microaerobic conditions in which homogeneity was important (21). Although, in gen- eral, the scale-up based on dCO 2 would be even more feasi- ble as more reliable dCO 2 sensors become available (16), the specific carbon dioxide evolution rate was currently still felt to be useful for scale-up of secondary metabolite cul- tures (22). The purpose of this paper is to briefly describe and evalu- ate various scale-up methods and approaches which can be applied to example E. coli and yeast processes. The first step involved cataloging characteristic measurements for ex- isting laboratory (30 l scale) and pilot plant (100 l19,000 l scale) fermentors (Tables 1 and 2). Next, relevant parame- ters were calculated and compared as a function of scale based on geometry, power input per unit volume, gas flow rate and mixing time (Tables 35). Various scale-up scenar- ios were explored based on maintaining geometric similar- ity (Table 6), constant impeller speed (Table 7), and con- stant power input per unit liquid volume (Tables 8 and 9). A comparison was also completed based on medium heat stress during sterilization (Table 10). A listing of historical and recent achievable processing conditions was developed (Tables 11 and 12), and the relationship of OUR to K L a and P g /V L to K L a was quantified for various processes (Table 13). For consistency, all volumes quoted in this text are nominal vessel volumes (rather than total or working vol- umes) unless otherwise stated. Units were selected to mini- mize rounding errors where possible. I. SCALE-UP METHODS AND APPROACHES Several scale-up methods are described below, and se- lected scale-up approaches were evaluated using two scales as a basis: the 280 l pilot scale which is a common first step pilot plant fermentor scale and the 30 l laboratory scale which is common to use for pre-pilot plant (laboratory) stud- TABLE 1. Characteristics of laboratory and pilot scale vessels Scale (nominal volume) Working tank volume, V L (l) Installed motor power, P o (hp) Max. agitator speed, N max (rev/min) Vessel tangent/tangent, H TT (m) Vessel total height (with top and bottom dish), H T (m) Vessel width, OD, D T (m) Max. air flow rate, Q max (l/min) 30 l 20 1 875 0.66 0.742 0.31 30 100 l 75 3 400 0.785 0.96 0.41 (ID) 120 280 l 180 7.5 460 1.12 1.34 0.56 300 800 l 600 7.5 330 1.63 2.08 0.81 600 1000 l 750 10 300 1.52 1.88 0.86 (ID) 1200 1200 l 900 15 282 1.83 2.185 0.92 1200 1900 l 1500 15 230 2.13 2.57 1.07 1500 19000 l 15000 60 155 5.87 6.58 1.98 15000 The 280 l scale fermentor was originally designed with a 3 hp motor which was enlarged to 7.5 hp for replacement convenience. OD, Outer di- ameter; ID, inner diameter. SCALE-UP METHODOLOGIES FOR FERMENTATION PROCESSES VOL. 97, 2004 349 ies. Details of some of these vessels and their impellers have been discussed elsewhere (2325). Figure 1 shows a typical fermentor diagram with key locations identified. Geometric similarity of reactor geometry [D T /V T ) 1/3 or (D T /V L ) 1/3 ] Geometric similarity is expressed as follows: D T2 /D T1 =(V T2 /V T1 ) 1/3 (1) TABLE 2. Characteristics of laboratory and pilot-plant scale impellers Scale (nominal volume) Impeller type (upper/lower) Impeller diameter, D I (m) Impeller tip speed, pN max D I (m/s) Number of impellers, N I 30 l Rushton 0.102 4.7 4 100 l Hydrofoil 0.184 3.8 2 A315 280 l Rushton 0.205 4.9 2 Hydrofoil 0.28 6.7 3 Maxflo T 800 l Rushton 0.305 5.4 2 Hydrofoil 0.406 7.2 2 Maxflo T Hydrofoil 0.406 7.2 2 A315 Smith Top, 0.343 Top, 6.1 2 CD-6 Btm, 0.356 Btm, 6.3 Hydrofoil/Smith Top, 0.406 Top, 7.2 2 Maxflo T/CD-6 Btm, 0.394 Btm, 7.0 HE-3/Smith Top, 0.533 Top, 9.4 2 HE-3/CD-6 Btm, 0.394 Btm, 7.0 1000 l Rushton 0.305 4.8 2 Hydrofoil 0.37 5.8 2 A315 1200 l Hydrofoil 0.46 6.8 2 A315 1900 l Rushton 0.42 5.1 3 Hydrofoil 0.535 6.4 3 Maxflo T 19000 l Rushton 0.685 5.6 4 Hydrofoil 0.915 7.4 4 Maxflo T Hydrofoil Top/Mid, 0.94 7.6 3 A315 (Btm, 8.4) (Btm, 8.4) Impeller data for top/bottom impellers. Units of length selected to minimize rounding errors. Top, Top impeller; Mid, middle impeller; Btm, bot- tom impeller. TABLE 3. Geometric comparisons for laboratory and pilot scale fermentors Scale (nominal volume) H T /D T (H TT /D T ) D I /D T D T /(V L ) 1/3 at V L (l), geometric similarity Re10 6 (water) V L /V T 30 l 2.4 0.33 (R) 1.14 at 20 0.48 (R) 0.57 (2.1) 100 l 2.4 0.45 (A) 0.97 at 75 0.71 (A) 0.75 (1.9) 280 l 2.4 0.36 (R) 0.99 at 180 1.0 (R) 0.60 (2.0) 0.5 (M) 1.9 (M) 800 l 2.6 0.38 (R) 0.96 at 600 1.6 (R) 0.704 (2.0) 0.5 (M) 2.9 (M) 0.5 (A) 2.9 (A) 1000 l 2.1 0.35 (R) 0.95 at 750 1.5 (R) 0.75 (1.7) 0.43 (A) 2.2 (A) 1200 l 2.4 0.5 (A) 0.95 at 900 3.1 (A) 0.75 (2.0) 1900 l 2.4 0.39 (R) 0.935 at 1500 2.1 (R) 0.79 (2.0) 0.5 (M) 0.96 at 1400 3.4 (M) 19000 l 3.3 0.346 (R) 0.80 at 15000 3.8 (R) 0.79 (2.9) 0.462 (M) 0.95 at 9000 6.8 (M) 0.47 (A) 7.2 (A) (Btm, 0.56) (Btm, 8.8) V T is total tank capacity not nominal volume. R, Rushton; M, Maxflo T; A, A315; Btm, bottom impeller. JUNKER J. BIOSCI. BIOENG., 350 where D Ti is the tank diameter and V Ti is the total tank vol- ume of vessel, i. Alternatively, the liquid volume, V Li , might be used. It assumes reasonably constant impeller geometry (i.e., impeller diameter, D I , and number of impellers, N I ) as specified below. Based on target working/total volumes ob- tained from geometric similarity (Table 6), the desired work- ing volume in the fermentor may be altered during experi- mentation. Experiments to obtain data for several empirical correla- tions utilized geometrically similar vessels. Although geo- metric similarity is a pre-requisite for applying established scale-up relationships, it is rarely achievable in practice (26, 27). Subsequently, a range of acceptance of equivalency was proposed (26) to include the following: (i) D I /D T =0.3 0.45, where D I /D T is the ratio of the impeller to tank diame- ters; (ii) H L /D T is less than or equal to 2 (no range was given), where H L is the height of the liquid in the vessel; and (iii) either two or three impellers. As shown in Table 3, D I /D T values ranged from 0.330.5 for all vessels in this fa- cility. Specifically, the range was 0.330.39 for vessels with Rushton radial flow impellers (Lightnin, Avon, NY, USA), 0.4620.5 for vessels with Maxflo T axial flow impellers (Chemineer, Dayton, OH, USA), and 0.430.56 for vessels with A315 axial flow impellers (Lightnin). In the case of the vessels studied, H T /D T ratios ranged from 2.13.3 where H T is the total tank height. The range of the tangent-to-tangent tank height to tank diameter ratio, H TT /D T (which was felt to be more useful than H L /D T to compare since fermentor working volumes may be variable), was 1.72.9, with the value of 2.9 for the 19,000 l fermentor being well above the remainder which ranged from 1.72.1. All vessels had two or three impellers except for two of the three 19,000 l ves- sels (those with Rushton and Maxflo T impellers) which had four impellers. Fermentors with a standard geometry are beneficial since several published scale-up correlations assume geometry to be constant (8). However, lab fermentors may have substan- tially lower H T /D T ratios of 1:1 compared to 3: 1 for pilot scale fermentors, so laboratory scale data may be deceiving (8). Larger pilot scale and production fermentors can be de- signed for variable working volumes to accommodate the larger range of batch sizes expected in a multi-use facility. Table 6 shows the scale-up parameters of expected total and working volumes calculated based on geometrical simi- larity. For the 280 l scale-up basis, the calculated numbers differed dramatically from installed equipment for the 30 l and 19,000 l scales, but were reasonably close (within 2 17%) between the 100 l and 1900 l scales. Although the 19,000 l expected values were lower by 3047%, the 30 l value was higher by 4655%. For the 30 l scale-up basis, all the calculated numbers were substantially lower than the in- stalled values by 1945% between the 100 l and 1900 l scales and 5265% for the 19,000 l scale. Reasons for these differences were evident by comparing values of the geo- metric similarity parameter, (D T /V L ) 1/3 , listed in Table 3. Val- ues for the 100 l to 1900 l scale ranged from 0.9350.99 (average of 0.9580.019); values for the 30 l and 19,000 l FIG. 1. Schematic of fermentor showing nomenclature. FIG. 2. Decline of installed, ungassed and gassed power draw per unit working volume as a function of scale for fermentors under study at operating conditions listed in Table 1 and for impeller geometries listed in Table 2. For all scales, 1.7<H TT /D T <2.9 and 1.0<Q max /V L <1.67. (a) For Rushton (R) geometry, 0.33<D I /D T <0.39, 4.7<ITS<5.6. (b) For Maxflo T (M) hydrofoil geometry, 0.462<D I /D T <0.5, 6.4<ITS<7.4. For A315 (A) axial flow geometry, 0.43<D I /D T <0.56, 5.8<ITS<7.6. SCALE-UP METHODOLOGIES FOR FERMENTATION PROCESSES VOL. 97, 2004 351 scales were notably different (greater than 4.59.5 SD from the mean). Operation of the 19,000 l scale fermentor at a lower working volume brings its geometrical similarity closer to the average value of the smaller vessels. Constant impeller tip speed (ITS) or shear ITS is expressed as N 2 /N 1 =D T1 /D T2 =(V T1 /V T2 ) 1/3 (2) which assumes that ITS=pN i D Ii where N i and D Ii are the im- peller speed and impeller diameter for vessel i (8). Table 2 shows that typical installed impeller tip speeds ranged from 3.8 to 7.6 m/s with no clear trend observed with scale, but about a 2537% increase with the hydrofoil (A315 and Maxflo T) impellers than the disk turbine (Rushton) im- pellers for the same fermentor scale primarily due to their larger diameters. Tip speed is used as a rule for scale-up when there is not a good understanding of the relationship between shear and TABLE 4. Mixing time, power input and gas flow comparisons for laboratory and pilot scale fermentors Scale (nominal volume) Mixing time, T mix from Eq. 10h (s) Design P o /V L (hp/1000 l) P o /V L (observed in water) (hp/1000 l at rpm) P g /V L at Q max and N max (observed in water) (hp/1000 l at lpm) Q max /V L (vvm at working V L min 1 ) Superficial gas velocity, V s = 4Q max /(pD T 2 ), (cm/s) Gas flow number, N A = Q max /N max D I 3 30 l 3.4 50.0 NI NI 1.5 0.66 0.032 (R) 100 l 13.4 40.0 NI NI 1.6 1.5 0.050 (A) 280 l 20.1 41.7 23.9 at 450 (R) 18.8 at 300 (R) 1.67 2.0 0.078 (R) 18.9 at 450 (M) 16.7 at 300 (M) 0.030 (M) 800 l 29.2 12.5 15.0 at 335 10 at 600 (R) 1.0 2.0 0.063 (R) 12.5 at 300 (R) 16.3 at 335* 8.8 at 600 (M) 0.027 (M) 12.1 at 300 (M) 11.2 at 335 7.8 at 600 (A) 0.027 (A) 8.7 at 300 (A) 1000 l 30.9 13.3 7.7 at 300 (R) 4.3 at 1200 (R) 1.6 3.4 0.140 (R) 5.1 at 300 (A) 4.9 at 600 0.079 (A) 3.5 at 1200 (A) 4.6 at 600 1200 l 32.3 16.7 10.1 at 282 (A) 6.8 at 1200 (A) 1.33 3.0 0.044 (A) 7.1 at 600 1900 l 36.2 10.0 13.9 at 225 (R) 6.8 at 1500 (R) 1.0 2.8 0.088 (R) 10.0 at 225 (M) 8.0 at 1500 (M) 0.043 (M) 19000 l 53.7 4.0 4.4 at 142 (R) 2.0 at 15000 (R) 1.0 8.1 0.300 (R) 4.4 at 150 (M) 4.1 at 15000 (M) 0.130 (M) 4.4 at 150 (A) 3.2 at 15000 (A) 0.120 (A) Power measurements performed at 25C in water and at ambient pressure. Unaerated conditions not maintainable at top speed for certain fer- mentors marked with an asterisk due to drive overheating. No power measurement devices installed at 30 l or 100 l scales. R, Rushton; M, Maxflo T; A, A315. NI, Power measuring device not installed. TABLE 5. Mass transfer comparisons for laboratory and pilot scale fermentors Scale (nominal volume/designation) V s at Q max (cm/s) Q max /V L (vvm, min 1 ) Measured P g /P o at Q max and N max (P o /V L ) a (V s ) b using Eq. 9a and 9b and design P o (P g /V L ) a (V s ) b using Eq. 9a and 9b and measured P g 30 l 0.66 1.5 NA 31.1 NI 100 l 1.5 1.6 NA 15.5 NI 280 l 2.0 1.67 0.79 (R) 19.4 11.3 (R) 0.88 (M) 10.5 (M) 800 l 2.0 1.0 0.67 (R) 8.6 7.4 (R) 0.54 (M) 6.8 (M) 0.70 (A) 6.3 (A) 1000 l 3.4 1.6 0.55 (R) 12.8 6.0 (R) 0.69 (A) 5.3 (A) 1200 l 3.0 1.33 0.67 (A) 13.8 7.5 (A) 1900 l 2.8 1.0 0.49 (R) 9.3 7.2 (R) 0.80 (M) 8.0 (M) 19000 l 8.1 1.0 0.45 (R) 10.3 6.5 (M) 0.93 (M) 10.4 (M) 0.74 (A) 8.8 (A) The 1000 l scale fermentor was typically run at 600 lpm rather than at 1200 lpm maximum air flow rate which was used to obtain calculated and measured values. Equation 9a used for 30 l scale and Eq. 9b used for 100 l19,000 l scales. Power measurements performed at 25C in water and at ambient pressure. No power measurement devices installed at 30 l or 100 l scales. R, Rushton; M, Maxflo T; A, A315. NI, Power measuring device not installed. NA, Calculation not applicable. JUNKER J. BIOSCI. BIOENG., 352 morphology for mycelial cultures. A rough rule of thumb is that cell damage can occur at tip speeds above 3.2 m/s, but the exact value is influenced by many factors such as broth rheology (28). Calculated tip speeds usually are greater than 3 m/s for production fermentors (29) and ranged from 57 m/s from a survey of industrial fermentors (Einsele, A., Abstr. 5th Intern. Ferment. Symp., p. 69, 1976). A constant tip velocity in the range of 57 m/s was found to be used for scale-up for antibiotic fermentations (Einsele, Abstr. 5th Intern. Ferment. Symp., 1976). Although useful in branched yeast, filamentous bacterial and fungal fermentations for estimating the potential for hyphae breakage and thus alter- ation of broth morphology, tip speed is less useful for single cell bacterial or yeast fermentations. If scale-up is conducted using constant tip speed (with geometric similarity), then often the value of P g /V L is low- ered which can adversely affect aeration efficiency. It is possible to recover from this deficiency using more impel- lers in the larger vessel and in this manner it may be pos- sible to maintain both tip speed and P g /V L constant (30). Tip speed influences impeller shear which is proportional to product of impeller tip speed and impeller diameter, ND I 2 , for turbulent flow conditions (29). As shown in Table 7, for the 280 l scale-up basis, there was reasonable agreement (within 224%) between ex- pected and actual total and working volumes for the 280 l 1900 l scales, but expected values were substantially lower (5869%) at the 19,000 l scale and grossly higher (97 355%) for the 30 l and 100 l scales. For the 30 l scale-up basis, all estimated values were substantially lower (40 85%) than installed values, except for the 100 l vessel which was substantially higher (131175%) due to its higher peak agitation rate. Since geometric similarity was used to calcu- late the values in Table 7, this explains why the 30 l and 19,000 l values were substantially different than installed values and why the values for the 30 l scale-up basis were not in agreement as well. Constant ungassed or (more often) gassed power input per liquid volume (P o /V L or P g /V L ) Scale-up designs may also include the ungassed power input, P o , which is ex- pressed as P o =N P N 3 D I 5 r (3) where N P , the power number, is a proportionality factor based on the impeller design (among other factors) and r is the broth density (8) which is typically considered to be slightly greater than water. The power number generally re- mains constant with scale-up if the same impeller type is used. Constant ungassed power, (P o /V L ) i , for vessel, i, is ex- pressed as (P o /V L ) 2 /(P o /V L ) 1 =(V L1 /V L2 ) c or P o /V L =f 1 V L c (4) where c was found to be -0.37 in practice based on a survey of industrial plants of various scales and processes (Einsele, Abstr. 5th Intern. Ferment. Symp., 1976). A similar rela- tionship can be applied for gassed power inputs. General values of P o /V L are 13 kW/m 3 (1.34 hp/1000 l) for vessels up to 300 m 3 (300,000 l) working volume (Einsele, Abstr. 5th Intern. Ferment. Symp., 1976), and a rule of thumb is that P o /V L is 24 kW/m 3 (2.75.4 hp/1000 l) at the produc- tion scale with no volume range given by Kossen and Oosterhuis (29). If scale-up is conducted using constant P o /V L with geo- metric similarity, then circulation time, mixing time and im- TABLE 6. Scale-up based on geometric similarity a. Base case 280 l (pilot scale) Scale (nominal volume) Total volume, actual, V T (l) Total volume, expected, V T (l) Working volume, actual, V L (l) Working volume, expected, V L (l) 30 l 35 51 20 31 100 l 100 117 75 71 280 l 299 Basis 180 Basis 800 l 852 905 600 545 1000 l 1000 1100 750 661 1200 l 1271 1304 900 785 1900 l 2044 2086 1500 1256 19000 l 18887 13216 15000 7956 b. Base case 30 l (laboratory scale) Scale (nominal volume) Total volume, actual, V T (l) Total volume, expected, V T (l) Working volume, actual, V L (l) Working volume, expected, V L (l) 30 l 35 Basis 20 Basis 100 l 100 81 75 46 280 l 299 206 180 118 800 l 852 624 600 357 1000 l 1000 758 750 433 1200 l 1271 900 900 514 1900 l 2044 1439 1500 822 19000 l 18887 9120 15000 5211 Relationship: D T2 /D T1 =(V T2 /V T1 ) 1/3 =(V L2 /V L1 ) 1/3 . TABLE 7. Scale-up based on constant impeller speed a. Base case 280 l (pilot scale) Scale (nominal volume) Total volume, actual, V T (l) Total volume, expected, V T (l) Working volume, actual, V L (l) Working volume, expected, V L (l) 30 l 35 69 20 42 100 l 100 455 75 274 280 l 299 Basis 180 Basis 800 l 852 754 600 454 1000 l 1000 1078 750 649 1200 l 1271 1298 900 781 1900 l 2044 2392 1500 1440 19000 l 18887 7815 15000 4705 b. Base case 30 l (laboratory scale) Scale (nominal volume) Total volume, actual, V T (l) Total volume, expected, V T (l) Working volume, actual, V L (l) Working volume, expected, V L (l) 30 l 35 Basis 20 Basis 100 l 100 231 75 132 280 l 299 152 180 87 800 l 852 382 600 218 1000 l 1000 547 750 312 1200 l 1271 658 900 376 1900 l 2044 1214 1500 693 19000 l 18887 3965 15000 2266 Relationship: N 2 /N 1 =D T1 /D T2 =(V T1 /V T2 ) 1/3 =(V L2 /V L1 ) 1/3 (assumes geo- metric similarity). SCALE-UP METHODOLOGIES FOR FERMENTATION PROCESSES VOL. 97, 2004 353 peller tip speed increase (30), but the size of eddies does not change (29). The P o /V L required to provide a certain OTR generally decreases with scale (2). Scale-up on the basis of constant P o /V L can result in a larger than necessary motor size. In addition, it is difficult to have high power per unit volume inputs at the large scale (27) due to practical limita- tions in motor size. Assuming geometrically similar vessels in which D T1 /D T2 =(V T1 /V T2 ) 1/3 (5), then scale-up based on constant ungassed or gassed power per unit volume (P o /V L or P g /V L , respec- tively) simplifies to N 2 /N 1 =(V T1 /V T2 ) 2/9 (5) This expression is very similar to N 2 /N 1 =(V T1 /V T2 ) 1/3 used in Table 7 which was derived for scale-up on the basis of con- stant tip speed and geometric similarity (5). Although the gassing rate influence is incorporated into the value of P g based on measurements or expected decreases in power loss upon gassing, it can be challenging to accurately account for the gassing (aeration) efficiency. In addition, this relation- ship is most effective for turbulent flows observed during single cell E. coli and yeast cultures and less effective for high viscosity mycelial cultures (5). As seen in Table 4, measured values of P g /V L at maxi- mum aeration (Q max ) and agitation (N max ) rates for stated working volumes ranged from nearly 19 hp/1000 l down to 2 hp/1000 l as the scale increased from 280 l to 19,000 l. Measured values of P o /V L were higher than those for P g /V L due to power decrease upon gassing, and the ratio of P g /P o varied according to impeller type, fermentor scale and sparger/impeller geometry (Table 5; 24). Tables 8a (for Rushton radial flow impellers) and 9 (for Maxflo T and A315 hydrofoil axial flow impellers) show that scale-up based on measured P o /V L and measured P g /V L values agreed reasonably well (within 26%) with expected values for the 800 l, 1900 l and 19,000 l scales. The notable exception was the 19,000 l scale with Rushton impellers for which the ex- pected value was higher than the measured value by 85%. Expected values for the 1000 l and 1200 l scale fermentors were notably higher by about 83180% due to the lower than typical measured P g /V L for this scale vessel (versus installed motor power). Measured values for the 30 l and 100 l scales were not able to be compared since no power measurement device was installed. Table 8b shows the use of installed values for P o /V L for the 30 l fermentor as a basis for scale-up. Agreement of the expected and actual values to within about 30% was evident for all scales except the 1000 l scale which was higher by 70%. Using the 1000 l scale as a basis (data not shown), the expected values were lower for all scales by at least 40%, a trend which is also due to the lower than typical measured P g /V L . Similar impeller Reynolds number (N Re ) Scale-up can be accomplished based on a constant impeller Reynolds number, N Re : N Re =rND I 2 /h (6) where h is the broth viscosity (8, 31). For the same broth, this expression simplifies to N 2 /N 1 =(D I1 /D I2 ) 2 (7) For the maximum operating conditions of agitation (Table 1), impeller Reynolds numbers ranged from 0.488.810 6 for water (or for single cell E. coli and yeast broths with viscosities similar to water), suggesting that for filamentous broths with higher viscosities flow may switch from turbu- lent to laminar. The use of constant Reynolds number gen- erally has not worked well for fermentation scale-up since the effect of aeration on the process was not incorporated (2), and the impeller Reynolds number generally increases for successful scale-up designs (26). Other dimensionless TABLE 8. Scale-up based on constant power per unit volume for Rushton radial flow impellers a. Base case 280 l (pilot scale) Scale (nominal volume) P o /V L measured at N max (hp/1000 l) P o /V L expected at N max (hp/1000 l) P g /V L measured at N max and Q max (hp/1000 l) P g /V L expected at N max and Q max (hp/1000 l) 30 l NI 53.9 NI 42.4 100 l NI 33.0 NI 26 280 l 23.9 Basis 18.8 Basis 800 l 15.0 15.3 10.0 12.0 1000 l 7.7 14.1 4.3 11.1 1200 l NA 13.2 NA 10.4 1900 l 13.9 10.9 6.8 8.6 19000 l 4.4 4.65 2.0 3.7 b. Base case 30 l installed hp (laboratory scale) Scale (nominal volume) P o /V L measured at N max (hp/1000 l) P o /V L expected at N max (hp/1000 l) 30 l NI Basis 100 l NI 30.7 280 l 23.9 22.2 800 l 15.0 14.2 1000 l 7.7 13.1 1200 l NA 12.2 1900 l 13.9 10.1 19000 l 4.4 4.3 Relationship: (V L1 /V L2 ) 0.37 =(P o /V L ) 2 /(P o /V L ) 1 or (P g /V L ) 2 /(P g /V L ) 1 . Mea- sured P o and P g values used in calculations except for 30 l base case where installed value for P o of 1 hp used. NI, Power measuring device not installed. NA, Calculation not applicable. TABLE 9. Scale-up based on constant power per unit volume for hydrofoil axial flow impellers Base case 280 l (pilot scale) Scale (nominal volume) P o /V L measured at N max (hp/1000 l) P o /V L expected at N max (hp/1000 l) P g /V L measured at N max and Q max (hp/1000 l) P g /V L expected at N max and Q max (hp/1000 l) 30 l NI 42.6 NI 37.7 100 l NI 26.1 NI 23.1 280 l 18.9 (M) Basis 16.7 (M) Basis 800 l 16.3 (M) 12.1 8.8 (M) 10.7 11.2 (A) 7.8 (A) 1000 l 5.1 (A) 11.2 3.5 (A) 9.8 1200 l 10.1 (A) 10.4 6.8 (A) 9.2 1900 l 10.0 (M) 8.6 8.0 (M) 7.6 19000 l 4.4 (M) 3.7 4.1 (M) 3.3 4.4 (A) 3.2 (A) Relationship: (V L1 /V L2 ) 0.37 =(P o /V L ) 2 /(P o /V L ) 1 or (P g /V L ) 2 /(P g /V L ) 1 . Mea- sured P o and P g values used in calculations. M, Maxflo T; A, A315. JUNKER J. BIOSCI. BIOENG., 354 groups also have been examined for scale-up with limited success, often resulting in technically unrealistic equipment and operating parameters. As it is difficult to maintain all dimensionless parameters constant upon scale-up, those most important to the process must be identified accurately. Constant oxygen uptake rate (OUR), mass transfer coefficient (K L a) or dissolved oxygen (DO) Scale-up based on constant OUR assumes that the OUR is equal to the OTR: OTR=K L a(C sat -C L ) =OUR=mX/Y X/O2 (8) where C sat is the broth DO concentration at saturation, C L is the measured broth DO concentration, m is the specific growth rate, X is the measured cell density and Y X/O2 is the calculated cell yield per amount of oxygen consumed (32). Changes in back-pressure and hydrostatic pressure with scale-up influence the values of C sat (and subsequently C L ). It is also possible to use the log mean of the DO concentra- tion difference. Since for most aerobic fermentations the critical DO concentration which adversely affects growth rate is very low, C L is assumed to be zero. Several correlations of the general form K L a =f 2 (P g /V L ) a V s b (9) exist to estimate K L a using gassed power per liquid volume, P g /V L , and gas superficial velocity, V s , for fermentations (similar to the Van Riet correlation for mass transfer): K L a =f 2 (P g /V L ) 0.95 V s 0.67 for laboratory scale (8 l) vessels (5) (9a) K L a =f 2 (P g /V L ) 0.67 V s 0.67 for pilot scale (400 l) vessels (5) (9b) K L a =f 2 (P g /V L ) 0.50 V s 0.50 for production (23,000 l46,000 l) vessels (5) (9c) where f 2 is a proportionality constant in all equations whose value varies depending upon the specific process and the units of K L a, P g /V L and V s used in the calculations. All vol- umes cited in Eq. 9ac are operating volumes. For these correlations, the dependence of K L a on P g /V L is lower as the vessel scale increases (i.e., the exponent decreases). Simi- larly, the dependence of K L a on V s also decreases upon scale-up, but mainly between the pilot scale and production stages. Most commonly when the power is changed only by increasing agitation speed, then Eq. 9c simplifies to K L a =f 2 (P g /V L ) 0.50 for production vessels (33) (9d) In laboratory scale fermentors where measurements of P g /V L are difficult to accurately obtain, then the key components of the power number (N, D I ) may be used: K L a =f 2 (N 3 D I 2 ) 0.42 for laboratory vessels (34) (9e) where, although the exponent of 0.42 was established for a 0.6 l working volume, the literature range is 0.160.68. Since they are generally most applicable at or near the con- ditions used to determine the exponents, these correlations might best be used for only qualitative guidance in scale-up calculations (28). As shown in Table 5, calculated values of (P g /V L ) a V s b using measured values of P g /V L and Eq. 9a and 9b are reasonably similar (average [ave]: 7.81.9; relative stan- dard deviation [rsd]: 24%) from the 280 l to 19,000 l (180 l 15,000 l working volume) scales. When design values of P o /V L are used, much higher values of (P g /V L ) a V s b are ob- tained as expected, with the values being reasonably similar (ave: 11.02.2; rsd: 20%) from the 800 l to 19,000 l scales and much higher below the 800 l scale (600 l working vol- ume). Only a fraction of these design values actually can be delivered to the fermentation broth with the amount depen- dent on vessel/agitator geometry, rheology, agitator speed, and superficial velocity (28). From a survey of industrial fermentors up to 100,000 l in volume, K L a values ranged from 400800 h 1 (Einsele, Abstr. 5th Intern. Ferment. Symp., 1976). The K L a values obtained in Tables 11 and 12 are generally within this range assuming a Henrys law constant of 1 mmol/l-atm. The K L a varies roughly with the inverse of the apparent broth viscos- ity (15). Surface aeration can be a substantial contributor for smaller-scale fermentors, specifically about 33% for 5 l ves- sels and about 10% for 50 l vessels (15). Pilot scale fermen- tors below 250 l in volume usually have significant surface aeration compared to larger scale vessels, so it is generally best to scale-up from larger vessels of about 500 l1000 l (8). Surface aeration decreases markedly with scale (27); thus for larger vessels, K L a values can be more easily inter- preted. Scale-up based on K L a is complicated by the fact TABLE 10. Comparison of typical heat up, hold time and cool down times as well as F o and R o values for medium sterilizations as a function of scale Scale (nominal volume/jacket type) Heat up time (min) Heat up (area%) Hold time (min) Hold time (area%) Cool down time (min) Cool down (area%) F o total (min) R o total (min) 100 l (dimple, jacket loop) 29 24.3 40 65.5 18.6 10.2 75.0 61.6 280 l (straight) 15.516.2 1516 40 74.9 2629.4 9.6 74.9 57.0 800 l (dimple) 2021 1315.6 45 74.378.6 17.718.6 8.210.0 73.7 63.6 1000 l (dimple, jacket loop) 3438 1920 45 7071 2727.5 910 108.8 74.1 1200 l (half pipe coil) 2430 1922 45 6566 3335 1214.5 85.4 66.2 1900 l (half pipe coil) 3542 2427 45 61.863.3 3032 1113 86.7 72.8 19000 l (half pipe coil) 8388 37 45 46.4 95110 16.4 91.2 86.6 Medium hold temperature of 123.5C for batch sterilization. Hold temperatures of 124C for 1000 l and 123C for 100 l scale. F o and R o values calculated according to Junker et al. (38). Only temperatures above 60C were included in summation. Heat up and cool down times calculated from 40C. A 19,000 l scale vessel used cooling tower water for cool down and not chilled water. Area% is the area under the temperature versus time curve for the stage divided by the total area. Heat up and cool down area percentages calculated for temperatures above 60C. SCALE-UP METHODOLOGIES FOR FERMENTATION PROCESSES VOL. 97, 2004 355 that it is process-specific and that it changes over the course of the fermentation (35), making it difficult to reliably quan- tify. Alternatively, an optimal value for C L may be determined from laboratory studies and used for scale-up (2). Equation 8 then can be rearranged to calculate K L a values during the fermentation at various ages. Scale-up based on constant DO can be an attractive method. Although K L a and OUR can change dramatically over the course of the fermenta- tion, the minimum acceptable value of C L is usually known from laboratory studies. A C L above 3070% saturation usually assures adequate DO in less mixed regions of a vis- cous mycelial fermentation; for a less viscous E. coli or yeast fermentation, a C L above a lower limit of 1030% sat- uration can be adequate. Scale-up based on constant DO must consider the scale-up of methods to control DO such as agitation, pressure and air flow rate (19). Cascade control of DO by agitation, pressure and air flow rate can be effec- tive in maintaining DO above critical values (35). Constant gas flow number (N A ), volumetric gas flow rate per unit volume of liquid (vvm or Q/V L ), or superfi- cial velocity (V s ) Scale-up also can be performed based on the flow (aeration) number, N A =Q/ND I 3 , where Q is the volumetric flow rate. A typical range for the flow number for production fermentors is 0.10.15 (29) which compares favorably with the values of 0.120.13 for the 19,000 l fer- mentors with hydrofoil impellers and is much lower than the value of 0.3 obtained for the 19,000 l fermentor with a Rushton impeller (Table 4). Aeration numbers for other pilot scale vessels (100 l1900 l) ranged from 0.0270.14 with an aeration number of 0.032 obtained for the 30 l labo- ratory vessel (Table 4). Scale-up based on the volumetric gas flow rate per unit volume of liquid (Q/V L or vvm) also should be examined to ensure that resulting values of superficial velocity are rea- sonable. For a specific process, a balance must be achieved. If the volumetric gas flow rate per unit volume of liquid, Q/V L , remains constant upon scale-up, then V s may increase to the point of flooding in production-scale tanks (2). Simi- TABLE 11a. Representative historical (1992 through mid-2001) comparison of achievable processing conditions as a function of scale for E. coli cultivations Cultivation/Scale (nominal volume) Fermentation volume (l) (impeller type) Peak oxygen uptake rate (mmol/l-h) Air flow rate, Q (l/min) Pressure (kg/cm 2 ) Impeller speed, N (rpm) Gassed power, P g (hp) P g /V L (hp/1000 l) Calculated K L a at peak OUR (mmol/l-h-atm) Value of f 2 using Eq. 9b K L a/[(P g /V L ) 0.67 (V s ) 0.67 ] E. coli DH5/280 l 180 (R) 260 300 1.8 400 NI NI 685 NA E. coli DH5/280 l 150 (M) 172 190 1.25 400 NI NI 624 NA E. coli PF436/280 l 175 (M) 65 80 0.6 383 NI NI 346 NA E. coli RR1/280 l 160 (M) 77 80 0.3 409 NI NI 472 NA E. coli OP50/280 l 175 (R) 39 100 0.5 213 NI NI 186 NA E coli K12/800 l 605 (M) 94 400 0.7 287 6.3 10.4 434 76 E. coli DH5/1000 l 600 (M) 141 600 1.0 300 4.1 6.8 738 143 E. coli PF436/1900 l 800 (M) 38 400 0.7 178 5.6 7.0 167 55 E. coli RR1/1900 l 760 (M) 95 450 0.3 229 11.2 14.7 596 111 E. coli OP50/1900 l 810 (R) 49 500 0.7 125 2.7 3.3 303 143 E. coli Polym./1900 l 1080 (M) 101 600 1.2 225 9.0 8.3 486 110 P. aeruginosa/1900 l 1200 (M) 47 510 0.3 132 7.4 6.2 186 57 Values bolded are at/near (within 20%) of maximum conditions for that particular scale. R, Rushton; M, Maxflo T; A, A315. NI, Power measure- ment device was not installed. NA, Calculation not applicable. TABLE 11b. Representative historical (1992 through mid-2001) comparison of achievable processing conditions as a function of scale for yeast cultivations Cultivation/Scale (nominal volume) Fermentation volume (l) (impeller type) Peak oxygen uptake rate (mmol/l-h) Air flow rate, Q (l/min) Pressure (kg/cm 2 ) Impeller speed, N (rpm) Gassed power, P g (hp) P g /V L (hp/1000 l) Calculated K L a at peak OUR (mmol/l-h-atm) Value of f 2 using Eq. 9b K L a/[(P g /V L ) 0.67 (V s ) 0.67 ] C. sorbophila/280 l 150 (R) 54 100 0.7 223 NI NI 226 NA C. chilensis/280 l 180 (R) 141 180 1.5 400 NI NI 297 NA S. cerevisiae QC2B/280 l 180 (R) 74 80 0.7 354 NI NI 350 NA S. cerevisiae 1375/280 l 180 (R) 64 90 0.5 315 NI NI 324 NA C. sorbophila/800 l 475 (R) 105 505 0.7 320 >7.5* >15.8 465 NA 475 (M) 90 475 0.7 286 >7.5* >15.8 386 NA C. chilensis/800 l 600 (R) 106 335 1.2 245 4.2 7.7 325 77 500 (M) 117 490 1.7 220 3.2 7.0 318 62 S. cerevisiae QC2B/800 l 570 (M) 93 220 0.7 265 2.4 4.2 463 218 S. cerevisiae 1375/800 l 530 (R) 63 250 0.5 266 5.2 9.8 344 84 S. cerevisiae 1375/1000 l 600 (M) 60 400 0.34 308 4.2 7.0 844 211 C. chilensis/1900 l 1500 (M) 49 530 0.83 175 3.1 2.1 252 155 S. cerevisiae 1375/1900 l 1400 (M) 53 700 0.5 173 5.5 3.9 264 89 Values bolded are at/near (within 20%) of maximum conditions. Values marked with an asterisk denote saturated power measurement readings. R, Rushton; M, Maxflo T; A, A315. NI, Power measurement device was not installed. NA, Calculation not applicable. JUNKER J. BIOSCI. BIOENG., 356 larly, if it is desired to maintain V s constant upon scale-up, then larger values of Q/V L must be implemented at the smaller scale (36). Typical values of Q/V L range from 1.67 down to 1.0, with the values generally decreasing at the larger scale (Table 4). Although the volumetric air flow rate has relatively little effect on the K L a value, higher air flow rates can cause dramatic foaming (27) and higher gas holdup in the fermentor. If the superficial velocity, V s , and P g /V L are constant, the gas holdup does not change with scale-up (29). Flooding happens when the superficial air velocity, V s , approaches 2550% of the bubble rise velocity since the fermentor gas holdup volume only can be about 20% or less (15). In the case of water with an average bubble rise ve- locity of 22 cm/s, flooding occurs at 510 cm/s (15). When flooding occurs, the impeller cannot disperse all the sup- plied gas, the gas rises as big bubbles to the liquid surface and the impeller pumping action diminishes (2). As shown in Table 5, V s ranges from 0.663.4 cm/s for vessels be- tween 30 l and 1900 l in total volume, jumping to 8.1 cm/s for the 19,000 l scale. Based on these guidelines, possibly the 19,000 l scale Q max conditions may be prone to flooding. Note that flooding also may occur at low agitation speeds with too high of an air flow rate for all scales. Constant mixing time Alternatively, scale-up can be accomplished by maintaining estimated mixing times con- stant. Several relationships have been derived or empirically developed T mix =f 3 V L 0.3 (10a) from a survey of industrial fermentors from 50 l to 100,000 l in volume (26; Einsele, Abstr. 5th Intern. Ferment. Symp., 1976) and T mix =f 3 (P g /V L ) 0.37 (10b) for a tetracycline process up to 52,000 l in volume (Einsele, Abstr. 5th Intern. Ferment. Symp., 1976), where k is a pro- portionality constant in both equations. For geometrically similar vessels in the region of turbulent flow: T mix N 2/3 D I 1/6 =constant (5) (10c) Thus, solving Eq. 10c assuming equal mixing times gives Eq. 10d (5): N 2 /N 1 =(D I2 /D I1 ) 1/4 (10d) and the corresponding power inputs are given by Eq. 10e (5): (P o /V L ) 2 /(P o /V L ) 1 =(N 2 3 D I2 2 )/(N 1 3 D I1 2 ) (10e) TABLE 12a. Comparison of recent (mid-2001 to 2002) typical achievable processing conditions as a function of scale for E. coli cultivations Scale (nominal volume) Fermentation volume (l) (impeller type) Peak OUR (mmol/l-h) Air flow rate, Q (l/min) Pressure (kg/cm 2 ) Impeller speed, N (rpm) Gassed power P g (hp) P g /V L (hp/1000 l) Calculated K L a at peak OUR (mmol/l-h-atm) Value of f 2 using Eq. 9b K L a/[(P g /V L ) 0.67 (V s ) 0.67 ] 280 l 180 (R) 155 300 1.2 460 3.25 18.1 572 51 180 (M) 158 300 1.2 460 3.4 18.9 475 41 800 l 600 (R) 142 500 1.4 330 9.2 15.3 391 46 600 (M) 115 500 1.5 330 9.2 15.3 354 42 600 (A) 126 470 1.5 330 6.2 10.3 330 40 600 (HE) 127 500 1.2 338 8.6 14.3 393 48 600 (MC) 124 500 1.2 338 9.0 15.0 364 40 600 (CC) 136 500 1.25 330 7.2 12.0 527 70 1200 l 900 (A) 116 1200 1.3 280 5.5 6.1 296 42 1900 l 1500 (R) 96 1500 1.0 230 11.4 7.6 354 46 1500 (A) 116 1500 0.9 230 13.2 8.8 465 55 Values bolded are at/near (within 20%) of maximum conditions for that scale. R, Rushton; M, Maxflo T; A, A315; HE, HE-3/Maxflo T; MC, Maxflo T/CD-6; CC, CD-6/CD-6. TABLE 12b. Comparison of recent (mid-2001 to 2002) typical achievable processing conditions as a function of scale for yeast cultivations Scale (nominal volume) Fermentation volume (l) (Impeller type) Peak oxygen uptake rate (mmol/l-h) Air flow rate, Q (l/min) Pressure (kg/cm 2 ) Impeller speed, N (rpm) Gassed power, P g (hp) P g /V L (hp/1000 l) Calculated K L a at peak OUR (mmol/l-h-atm) Value of f 2 using Eq. 9b K L a/[(P g /V L ) 0.67 (V s ) 0.67 ] 280 l 180 (M) 98 235 1.0 338 1.7 9.6 430 69 800 l 600 (R) 93 500 0.7 325 7.7 12.8 453 60 500 (M) 97 268 1.1 276 5.0 9.9 490 114 600 (A) 82 500 0.7 327 5.0 8.3 577 101 600 (MC) 92 500 0.7 271 4.6 7.7 461 85 1200 l 900 (A) 94 1000 1.1 226 2.8 3.1 390 99 1900 l 1500 (R) 79 925 0.97 172 5.0 3.3 385 120 1500 (M) 88 980 0.97 170 6.0 4.0 450 119 19000 l 14600 (M) 78 7800 0.89 96 16.2 1.1 380 136 14600 (A) 82 9300 0.95 106 16.2 1.1 343 109 14600 (R) 74 8400 0.90 115 29.5 2.0 343 78 Values bolded are at/near (within 20%) of maximum conditions for that scale. R, Rushton; M, Maxflo T; A, A315; HE, HE-3/Maxflo T; MC, Maxflo T/CD-6; CC, CD-6/CD-6. SCALE-UP METHODOLOGIES FOR FERMENTATION PROCESSES VOL. 97, 2004 357 For geometrically similar vessels in the region of turbulent flow where both P o /V L and mixing time are constant, Eq. 10e becomes (12) N 1 /N 2 =(D I2 /D I1 ) 2/3 (10f) The volumetric power input required to maintain equal mix- ing time increases as V L 2/3 . Thus, using the relationship of Eq. 10f, P g /V L can become prohibitively high upon scale-up and is usually overestimated. This technique generally has not worked well for fermentations (2). A mixedness index, I m , also has been proposed (7) which does not assume geometric similarity: I m =f 3 (ITS)(D T /H T )(D T ) 2/3 (10g) This expression may be particularly useful for scale-up for vessels already constructed in which geometric similarity may not have been maintained. Mixing times need to be evaluated relative to nutrient mass transfer rates for fed- batch cultures in the presence of cellular nutrient uptake. For a culture (not specified but likely to be a yeast) with a cell density of 20 g/l growing at a rate of 0.2 h 1 (doubling time of 3.5 h), if the DO (C L ) is at 20% saturation, oxygen in the broth would be depleted in 2.5 s (32). In the case where glucose was the limiting nutrient, glucose could be depleted as fast as 4.5 s (32). Longer mixing times can cause locally high glucose rates which in turn can cause locally low DO levels owing to higher cell metabolism. As a consequence, local areas of mixed acid E. coli fermentations can result, producing overall lower biomass yields upon scale-up (9). Thus, scale-up based on mixing time can be relevant for fed-batch E. coli and yeast cultures, especially at high cell densities. The characteristic time analysis above can be extended further and divided into characteristic times for transport phenomena (transfer or supply) and characteristic times for conversion (consumption or reaction) rates (11). Transport phenomena include oxygen transfer (including oxygen trans- fer from the gas bubble to the liquid), liquid circulation, gas residence, and heat transfer. Conversion rates include the zero and first order rates for oxygen and substrate consump- tion, cell growth and heat production. It can be important to compare nutrient consumption and transfer rates with each other as well as with circulation times to establish whether gradients are likely to exist (11). Specifically, for gluconic acid fermentation in a stirred tank by a fungal culture, oxygen limitation can occur if con- sumption and transfer rates are similar in magnitude. If liq- uid circulation times also are this same order of magnitude, then oxygen gradients are favored. In contrast, temperature gradients are less likely to occur since, although heat pro- duction and transfer rates are similar, they often are substan- tially greater than liquid circulation times. This analysis is applicable to high cell density fed-batch E. coli and yeast cultures. Observed mixing times of several seconds exist for labo- ratory fermentors, 2030 s for 10002000 l pilot scale fer- mentors and 70140 s for 60,000 l120,000 l production fer- mentors (4). Specific mixing times for these scales of 5 s for 10 l, 20 s for 1000 l, 29 s for 1800 l, 67 s for 60,000 l, 100 s for 100,000 l and 140 s for 120,000 l vessels have been re- ported (14). Finally, mixing times of 15 s for 120 l, 40 s for 1200 l and 60 s for 12,000 l vessels have been reported (20). These mixing times were reported for both Newtonian and non-Newtonian fluids/broths. These mixing time estimates may be graphed (Fig. 3). Linear regression of these available data points from the lit- erature yields the equation T mix =17.5log 10 (V L ) -19.4 (10 l to 60,000 l, r 2 =0.876) (10h) T mix =223.5log 10 (V L ) -1004.6 (60,000 l to 120,000 l, r 2 =0.902) (10i) where T mix is the mixing time in seconds and V L is the liquid working volume in liters. Clearly the mixing time increase with volume is steeper once the working volume is above 60,000 l. Equation 10 h was used to estimate mixing times for each existing fermentor scale (Table 4). The relative magnitudes of these times can be compared with those ob- tained from the times estimated using Eq. 10a and 10b as- suming the proportionality constant, f 3 , remains constant with scale. Other influences After the initial strategies outlined above are implemented, the resulting vessel design needs to consider other influences to assure optimal performance. Heat transfer rates Heat evolution is the combination of mechanical heat from the agitator and metabolic heat from the culture. The ratio of metabolic heat evolution to oxygen consumption is approximately 115 kcal heat evolved per mole of oxygen consumed for selected E. coli, yeast and fungal cultures (32, 37). The total amount of oxygen con- sumed by the culture can be estimated by integration of the OUR value versus time curve then multiplication by the tank working volume. The desired heat transfer coefficient and jacket area then can be evaluated using expected cool- ing fluid flow rates and inlet/outlet temperatures. Require- ments for the jacket type (e.g., dimple, half-coil) and jacket area then are established. For large fermentors over 5000 l, it can be difficult to sustain OURs above 300 mmol/l-h since heat transfer problems arise. Medium sterilization effects As the fermentor scale in- creases, the heat up and cool down times become a larger FIG. 3. Linear regression of literature mixing times (Eq. 10h) re- ported for laboratory, pilot scale and production processes (4, 14, 20). JUNKER J. BIOSCI. BIOENG., 358 proportion of the overall sterilization time cycle as shown in Table 10. The heat up time portion increases from about 15% to about 37%, and the cool down portion increases from 10% to 16% as the scale rises from 280 l to 19,000 l. The 100 l and 1000 l scales are exceptions to this trend as they required slightly longer than the expected ranges be- cause they are equipped with a recirculating jacket loop with indirect heating and cooling via heat exchangers. The values of F o increased from about 75 to about 91 min and the values of R o increased from about 57 to about 87 min over this same range of scales (Table 10; 38). These in- creases in F o and R o directly translate to a rise in the level of sterilization overkill and medium heat stress respectively as scale increases. The adverse impact of medium heat stress is process dependent and can be minimized with the use of continuous (high temperature, short time) media steriliza- tion. Biological factors Biological factors, such as the num- ber of generations through which the organism will progress over the course of the seed and production fermentations, need to be considered in the selection of the final production scale. Assuming exponential growth, the number of genera- tions, N g , can be expressed as (12) N g =1.44(lnV L +ln X N -ln X No ) (11) where X N is the final cell number (or mass) and X No is the initial inoculum cell number (or mass). The stability of the recombinant DNA insert and the requirement for an agent to exert selective pressure need to be evaluated for the number of expected generations in the process plus a comfortable safety margin. Generalized approaches to scale-up Several authors have recommended approaches or combinations of ap- proaches to scale-up based on the equations and principals described above. No single method appears to be suitable for all fermentations with a high probability of success (5), and the applicability of one method over another is process- specific. Success often depends on the reliability of empiri- cal scale-up correlations and the integrity of small-scale data. A few examples are highlighted below. Method of Hubbard This method (39) was developed as a combination of approaches from other authors. During the laboratory scale fermentation, air flow rate, impeller speed, yield, and fermentor geometric dimensions are mea- sured. Basic broth properties such as density, viscosity, sur- face tension, and oxygen diffusion coefficient are deter- mined. (Of these broth properties, it is probably most im- portant to understand the broth rheological behavior for mycelial cultures.) Several quantities, such as Q/V L , N Re , ITS, and N A , are calculated from the laboratory scale fer- mentor conditions based on measured quantities. For the plant scale fermentor, a volume is selected based on product yield and plant capacity. Geometric similarity then is used to calculate vessel dimensions. Scale-up is based on matching K L a values and then proceeding in either one of two ways. The first way is to calculate the flow rate, Q, by either holding Q/V L or superficial velocity, V s , con- stant, then to calculate the impeller speed, N, based on P g /V L versus K L a correlations (Eq. 9ac). The second way is to set N using constant impeller tip speed, then to calculate Q from P g /V L and K L a correlations. An application of this method is the use of K L a for scal- ing-up a Bacillus thuringiensis fermentation. This scale-up was accomplished using the equation, K L a=constant N a V s b (obtained by combining Eq. 9, the expected ratio of P g /V L , and Eq. 3) with scale-up on the basis of K L aP T where P T is the total pressure in the vessel including head pressure (40). Another application is to use an iterative strategy based on incremental air flow rates to calculate resulting scale-up pa- rameters and then to examine each set of parameters for a particular flow rate to further optimize compressor and agi- tator power requirements (36). Method of Ju and Chase/Diaz and Acedevo This method (2, 41) focuses on scaling-up based on equivalent OTR not K L a. First, the scale-up volume is selected, then geometric similarity is used to obtain D T . Constant impeller tip speed is assumed to obtain N. Using the relationship, P g /V L =f 1 V L c (Eq. 4), P g /V L then is estimated and, using em- pirical relationships between P g /V L and K L a (Eq. 9ac), the K L a values for the scale-up fermentor are determined. Final- ly, the OTR rate for the large fermentor is matched with that of the small scale fermentor and the back-pressure for the large fermentor is calculated assuming C L is 0 mmol/l. The key element of this method is that there are three de- grees of freedom for scale-up. These are commonly N, Q and D I /D T (i.e., reactor geometry). Thus, only three items may be specified to be constant for scale-up. If another de- gree of freedom is added such as the gas phase partial pres- sure, then this value also can be specified to maintain the maximum OTR constant. To determine the effect on the cul- tivation, it is generally useful to run small scale fermenta- tions using gas blending to vary this inlet oxygen partial pressure. Method of Wang et al. In this method (42), two key values are maintained constant on scale-up: K L a (calculated by Eq. 9ac) and ITS. The ratio of D I /D T then is adjusted to within reasonable limits to complete the design. Although geometric similarity is not maintained, the resulting varia- tion of the D I /D T ratio with scale often can still provide ade- quate gas dispersion. This technique adds flexibility for in- stallations of existing fermentors. Proposals for improved scale-up calculations This simplified method (27) evaluates key quantities of scale-up interest based on two variables: N and D I . The impeller Reynolds number is represented by ND I 2 , the Froude num- ber by N 2 D I , the Weber number by N 2 D I 3 , the gassed power per unit liquid volume by N 3 D I 2 , the impeller tip speed by ND I , and Q/H T by D I /N (where H T is specifically the height of the fermentor and not the height of the liquid volume). It combines relevant dimensionless group analysis with other empirically applicable parameters. Scale-up analysis using one or more of these above meth- ods has suggested methods for operating laboratory fermen- tors for the best scale-down performance. For example, nitrogen-diluted air is recommended to be used at the 10 l scale to appropriately mimic scale-up to the 10,000 l scale (2). Scale-down studies designed to simulate large-scale operating conditions have been highly successful in some cases in predicting behavior and identifying causes for sub- optimal large-scale performance (4346). SCALE-UP METHODOLOGIES FOR FERMENTATION PROCESSES VOL. 97, 2004 359 Current scale-up practices for E. coli and yeast cultures are largely based on maintaining equivalent C L , K L a or OTR performance as a first pass. In these fermentations, oxygen supply is limiting upon scale-up due to high cellular oxygen demand and not due to high broth viscosity as in the case of fungal cultures. Subsequently an evaluation of the impact of mixing time as it affects DO and nutrient distribution can be conducted, which is especially recommended for high cell density fed-batch cultures. II. FERMENTATION PROCESS CONDITIONS To evaluate the operating performance of existing pilot scale vessels, fermentor conditions (working volume, air flow rate, pressure, impeller speed, gassed power draw, mass transfer coefficient, OUR) were compiled based on historical records for several E. coli (Table 11a) and yeast cultures (Table 11b). OUR was calculated based on mea- surements of off-gas composition by a mass spectrometer (47). Data was taken at the time of peak OUR which did not necessarily correspond to the time of peak mass transfer co- efficient. Cultivations were conducted at the 280 l to 1900 l scales over the past decade. In addition, specific recent stud- ies were performed at the various scales (280 l19,000 l) for one example E. coli (E. coli DH5, Table 12a) and one ex- ample yeast process (Candida chilensis, Table 12b) using fermentation media designed to promote high-peak OTR. Tabulated data are representative of typical fermentations of that specific process at that selected scale. Control parameters for each fermentation varied accord- ing to development objectives. After its initial decline from pre-inoculation levels, DO was generally controlled be- tween 30% and 80% of saturation, calibrated to air at am- bient pressure, using various strategies. In some cases, the fermentation was initiated with the agitation, back-pressure and/or air flow rates in cascade control with DO. In other cases, when the need to control DO at its set point resulted in the agitation and air flow rates reaching maximum set- tings, these two parameters were placed in automatic mode at their maximum set points and then back-pressure was placed in cascade control. Other strategies were utilized de- pending on the specific process requirements. For example, if foaming occurred in the fermentation or a higher dCO 2 concentration was desired, the back-pressure was typically raised to 11.5 kg/cm 2 earlier in the process. Specific process descriptions have been published for some of the processes described (E. coli RR1 [48, 49], E. coli OP-50 [50], E. coli PF436 [51], Saccharomyces cere- visiae QC2B [52], S. cerevisiae 1375 [53], Pseudomonas aeruginosa MB5001 [54], and Candida sorbophila [5557]). Other process descriptions are not published (E. coli DNA polymerase, E. coli K12, E. coli DH5, C. chilensis), but are consistent with current state-of-the-art procedures. Exact processes run were based on these descriptions, but they de- viated significantly in many cases to achieve process devel- opment goals. III. SCALE-UP RESULTS FOR PRIOR FERMENTATIONS (1992 THROUGH MID-2001) A survey of processing was conducted in this fermenta- tion pilot plant from 1992 through mid-2001 to obtain in- formation about achievable process conditions for E. coli (Table 11a) and yeast (Table 11b) fermentations. Bolded values represent operation within 20% of maximum condi- tions for agitation and aeration for the pilot plant fermentors shown in Table 1. In the case of fermentor back-pressure, the desired maximum value was fixed at 1.5 kg/cm 2 , although during this period of operation (early 1990s) some fermen- tations were conducted at pressures as high as 1.8 kg/cm 2 , a back-pressure subsequently found to adversely affect the agitator double mechanical seal longevity. Also during this period, power draw readings were not available at 280 l scale and the watt transducers installed at 800 l scale, which were not corrected for gearbox losses (24), became satu- rated at higher power draws. Table 11a illustrates that historical E. coli cultivations predominantly challenged the maximum impeller speed pri- marily at the 280 l and 1000 l scales. Only a few 280 l cul- tivations simultaneously approached peak conditions of air flow rate, agitation and pressure. Peak OURs ranged from 38 to 260 mmol/l-h with OURs above 90 mmol/l-h reached for each of the four scales tested. P g /V L and K L a values cal- culated at peak OUR ranged from 3.314.7 hp/1000 l and 167738 mmol/l-h-atm, respectively. Although there was extensive experience at the 280 l and 1000 l scales with high OUR fermentations, the degree of challenge to the operating capacity of the vessels at the other scales was limited. K L a values achieved at the smaller 280 l scale were generally achievable upon scale-up to the 1000 l or 1900 l scales for those processes for which this was a development goal (E. coli DH5, E. coli RR1). Values of the proportionality con- stant, f 2 , from Eq. 9b ranged from 55 to 143, indicating an expected variability in performance of any empirical scale- up correlation due to the specific process, scale-up and op- erating parameters. Table 11b summarizes comparable historical data for yeast cultivations. As noted in the case of the E. coli processing, few challenges to peak operating conditions were made ex- cept at the 280 l and 1000 l scales. Peak OURs were notably lower than in the case of the E. coli fermentations, ranging from 49 to 141 mmol/l-h with OURs above 50 mmol/l-h reached for each of the four scales tested. P g /V L and K L a values calculated at peak OUR ranged from 2.1 hp/1000 l to over 15 hp/1000 l and 226844 mmol/l-h-atm, respective- ly. These ranges were similar to those noted for E. coli proc- esses. Again the extensive experience at the 280 l and 1000 l scales was not matched at the other scales. In the case of these yeast processes (C. sorbophila, C. chilensis, and S. cerevisiae 1375), the K L a values achieved at the 280 l scale were generally able to be obtained at the larger 800 l, 1000 l and 1900 l scales. Values of the proportionality constant, f 2 , from Eq. 9b generally ranged from 62 to 218, again indicat- ing expected variability in performance due to the process, scale-up and operating parameters. For a specific process at a specific scale, the range was substantially smaller. JUNKER J. BIOSCI. BIOENG., 360 IV. SCALE-UP RESULTS FOR CURRENT STUDIES Based on this historical analysis of process performance, recent studies (mid-2001 to present) were conducted to im- prove the challenge to fermentor peak operating conditions for E. coli and yeast fermentations. In the case of E. coli fermentations, initial carbon and nitrogen concentrations were raised to increase the peak OUR beyond that which might normally be observed with this process. It was de- sired to conduct specific studies at the 800 l, 1200 l, 1900 l and 19,000 l scales to obtain more complete information about the capabilities of the installed pilot scale equipment. Upgraded variable frequency drives (VFDs) were installed on all, but the 19,000 l scale vessels (which retained their watt transducers) in which the power draw was monitored directly from the VFD electrical current (Altivair 66; Schneider Electric, Palatine, IL, USA) This resulted in the new capability to measure power draw at the 280 l scale and an expanded measurement range for the 800 l scale. Table 12a summarizes the achievable processing condi- tions for the E. coli DH5 process for a process scaled-up based on maintaining similar minimum DO levels. For these aerobic processes, DO was required to be above its critical value to maximize growth and productivity. Peak OURs de- creased slightly from about 155158 mmol/l-h to about 96 116 mmol/l-h upon scale-up from the 280 l to 1900 l scales. P g /V L decreased with scale as expected ranging from about 1819 hp/1000 l at the 280 l scale to 6.18.8 hp/1000 l at the 1200 l and 1900 l scales. Calculated K L a values declined only slightly with scale, decreasing from 475572 mmol/l- h-atm at the 280 l scale to 354465 mmol/l-h-atm at the 1900 l scale. Values of f 2 in Eq. 9b were substantially more uniform than found with the historical data, ranging from 40 to 70, matching the lower range found with the historical E. coli process data. Values were relatively consistent with scale and operating conditions, suggesting a reliable empiri- cal relationship may be obtainable. Achievable processing conditions for the yeast C. chilen- sis process are summarized in Table 12b, again based on scaling-up using similar minimum DO levels. Upon scale- up from the 280 l to 19,000 l scale, peak OURs decreased slightly from about 98 mmol/l-h to about 7482 mmol/l-h. As expected, P g /V L decreased with scale ranging from about 9.6 hp/1000 l at the 280 l scale to 1.12.0 hp/1000 l at the 19,000 l scales. Both peak OUR and P g /V L values were no- tably lower for the yeast process than for the E. coli process. Calculated K L a values declined only slightly with scale, de- creasing from about 430 mmol/l-h-atm at the 280 l scale to 343380 mmol/l-h-atm at the 19,000 l scale. Values of f 2 in Eq. 9b ranged from 60 to 136 and were less uniform with scale and operating conditions than found with current E. coli process data. This difference may have been due to the tendency of this culture to clump and even branch during growth. The range of f 2 values also was lower than that found with the yeast historical data. V. TRENDS AND IMPLICATIONS FOR SCALE-UP Established relationships for scale-up can be difficult to use due to lack of sufficient data over a range of processing conditions from typical process development data sets. Often the range of process conditions that is needed conflicts with how to optimally execute the processes, making data diffi- cult to obtain and back-calculate. It can be difficult to vary conditions within a single cultivation as was done previous- ly (58) without adversely affecting subsequent data. Conse- quently, not all processes/scales were able to be analyzed if the operating conditions at peak OUR values for individual cultivations did not vary sufficiently. Table 13a summarizes the relationship between peak OUR and K L a: OUR=A 1 K L a +B 1 (12a) for selected historical and current processes at various scales for which the broth DO levels were similar. The slope, A 1 , varies from 0.075 to 0.46, indicating a large dependence on process and operating conditions on mass transfer. For a specific process, however, the values when attainable were reasonably constant upon scale-up. Prior scale-up studies in pilot scale vessels have been based on secondary metabolite fermentations in which gen- eral agreement was found with established K L a and P g /V L trends (58). Since the more recent focus of pilot plant stud- ies has been on scale-up of E. coli and yeast cultures, peak data from recent scale-up studies have been analyzed and results presented in Table 13b. The exponent of P g /V L in Eq. 9b, A 2 , was calculated for selected historical and current processes at various scales according to log K L a =A 2 log(P g /V L ) +B 2 (12b) The values obtained appear to be consistent for both E. coli and yeast processes and are about 0.960.98, compared with 0.580.8 found previously for a filamentous bacterial and a fungal cultivation (23, 58). The higher values reflect the greater impact of a K L a change with OUR for these E. coli and yeast cultures, most likely due to their lower broth vis- cosity and largely single cell morphology. Interestingly, the higher value of the exponent appears to be more consistent with the laboratory scale correlation (Eq. 9a) than the pilot scale correlation (Eq. 9b). For mycelial broths, rheological characteristics influence scale-up performance. Heat and oxygen transfer rates are 550% of bacterial fermentations and bulk mixing is poorer leading to lower broth homogeneity (28). As a consequence, ITS often has been a useful rule of thumb for scale-up (27). Rheology is less important for single cell bacterial and yeast fermentations compared with the relative magnitudes of nu- trient uptake and supply rates. Thus, scale-up based on DO, OUR or K L a often has been more useful for these cultiva- tions. For facilities with existing installed equipment, relia- ble scale-up is most readily achieved based on selecting op- erating conditions such that the minimum DO remains simi- lar between the two scales. Implications for other key pa- rameters such as OUR and K L a then can be easily evaluated. Owing to the availability of recombinant E. coli and yeast cultures with high specific productivities, typical production volumes for recombinant proteins often do not range above 5000 l and/or may not require high cell density processes. As demand for capacity increases, additional efforts may be made to improve volumetric productivity and thus push the SCALE-UP METHODOLOGIES FOR FERMENTATION PROCESSES VOL. 97, 2004 361 limits of existing and future fermentor design capacity. When more scale-up experience is gained over a broad range of volumes, the utility of various scale-up methodologies can better be evaluated. Throughout these evaluations, an effec- tive scale-down model is key to effective trouble shooting at the large scale, and its development should be a priority. NOMENCLATURE a : exponent (Eq. 9) b : exponent (Eq. 9) A 1 , B 1 : slope and intercept constants (Eq. 12a) A 2 , B 2 : slope and intercept constants (Eq. 12b) A : Lightnin A315 impeller (pumping downwards) configuration c : exponent (Eq. 4) CC : Chemineer CD-6 top/CD-6 bottom impeller con- figuration C L : measured concentration of dissolved oxygen in broth, mmol/l or %saturation C sat : concentration of dissolved oxygen in broth at sat- uration, mmol/l or % saturation dCO 2 : dissolved carbon dioxide D I : diameter of impeller, m DO : dissolved oxygen D T : diameter of vessel, OD, m D Ti : diameter of vessel, i, OD, m f 1 : proportionality constant (Eq. 4) f 2 : proportionality constant (Eqs. 9, 9ae) f 3 : proportionality constant (Eqs. 10ag) TABLE 13a. Comparison of relationship between OUR and K L a for selected historical and current cultivations Cultivation Scale (nominal volume) A 1 (atm) Regression coefficient, r 2 OUR range used for regression (mmol/l-h) K L a range used for regression (mmol/l-h-atm) Number of cultivations Historical (1992 to mid-2001) C. sorbophila 280 l 0.22 0.97 3053 120230 11 800 l 0.22 0.94 50105 230470 11 C. chilensis 280 l 0.46 0.99 75140 160300 4 800 l 0.32 0.99 65118 155320 3 S. cerevisiae QC2B 800 l 0.19 0.98 4092 180460 22 S. cerevisiae 1375 280 l 0.19 0.91 2566 140340 33 800 l 0.17 0.84 5367 285370 11 1900 l 0.17 0.99 5160 258308 4 E. coli RR1 280 l 0.16 0.90 3186 190500 20 1900 l 0.18 0.88 2597 151596 5 E. coli DH5 1000 l 0.17 0.99 80150 412780 16 E. coli OP50-1 1900 l 0.075 0.95 3949 177303 3 Recent (mid-2001 to 2002) C. chilensis 280 l 0.31 0.97 71158 230535 7 1200 l 0.18 0.92 7395 296445 5 E. coli DH5 280 l 0.39 0.96 5098 250373 4 Equation 12a: OUR=A 1 K L a+B 1 . Based on peak OUR measured during fermentation (not necessarily peak OUR capacity of equipment). TABLE 13b. Relationship between K L a (mmol/l-h-atm) and P g /V L (hp/1000 l) for historical and current results Cultivation Scale (nominal volume) (impeller type) Superficial velocity, V s (cm/s) A 2 B 2 Regression coefficient, r 2 P g /V L range used for regression (hp/1000 l) K L a range used for regression (mmol/l-h-atm) Number of cultivations Single scale results S. avermitilis a (converted to hp/1000 l from kw/1000 l) 800 l (R) 0.667 0.58 1.8 NA 0.678.0 3590 1 800 l (M) 0.667 0.59 2.2 NA 0.332.0 50180 1 A. terreus b (converted to hp/1000 l from kw/1000 l) 800 l (R) 0.51.0 0.6 1.9 NA 0.385.6 30200 1 0.8 1.2 NA 0.314.4 445 1 S. cerevisiae 1375 1000 l (R) 1.131.7 0.96 0.97 0.92 3.77 485897 6 E. coli RR1 1900 l (M) 0.750.84 0.96 1.6 0.81 4.114.7 150600 5 E. coli DH5 280 l (M) 2.0 0.98 1.5 0.89 8.318.9 230535 7 Multi-scale equation Equation 9b as applied to facility vessels 100 l19000 l 1.58.1 0.67 NA NA 120 NA NA Equation 12b: logK L a=A 2 log(P g /V L )+B 2 . Range of superficial velocities assumed constant for calculated values. Common (base 10) logarithm utilized. R, Rushton; M, Maxflo T; A, A315. NA, Calculation not applicable. a See Ref. 58. b See Ref. 23. JUNKER J. BIOSCI. BIOENG., 362 F o : equivalent kill for observed sterilization tempera- ture relative to that at 121C, min g c : gravitational acceleration conversion factor, 1 kg m/Ns 2 HE : Chemineer HE-3 top/CD-6 bottom impeller con- figuration H L : height of liquid in tank (including bottom dish), m H T : total height of tank (including top and bottom dishes), m H TT : tangent to tangent height of tank (excluding top and bottom dishes), m I m : mixedness index ITS : impeller tip speed, pND I , m/s K L a : volumetric mass transfer coefficient, mmol/l-atm-h, or K L a/H, h 1 , where H is Henrys law coefficient (assumed to be about 1 mmol/l-atm for fermenta- tion broth) M : Chemineer Maxflo T impeller (pumping down- wards) configuration MC : Chemineer Maxflo T top/CD-6 bottom impeller configuration N : impeller speed, rev/min (rpm) N A : flow (aeration) number, Q/ND I 3 N B : number of baffles N g : number of generations N I : number of impellers N max : maximum impeller speed, rev/min (rpm) N P : power number, external/inertial, (1/N 3 D I 5 ) (P o g c /r) N Re : impeller-based Reynolds number, inertial/viscous, rND I 2 /h OTR : oxygen transfer rate, mmol/l-h OUR: oxygen uptake rate, mmol/l-h P g : aerated power input, watts or hp P g /V L : gassed power input per unit volume, hp/1000 l P o : unaerated power input, watts or hp P o /V L : ungassed power input per unit volume, hp/1000 l P T : total pressure in vessel including head pressure, kg/cm 2 Q : volumetric air flow rate, l/min (lpm) Q max : maximum volumetric air flow rate, l/min (lpm) Q/V L : volumetric air flow rate per unit vessel liquid vol- ume, 1/min (vvm) R : Lightnin Rushton impeller configuration R o : equivalent nutrient degradation for observed ster- ilization temperature relative to that at 121C, min r 2 : linear regression coefficient T mix : mixing time, s V L : working volume of vessel, l or m 3 V Li : working volume of vessel, i, l V s : superficial velocity, cm/s V T : total (not nominal) volume of vessel, l V Ti : total volume of vessel, i, l VFD : variable frequency drive vvm : vessel volume per minute of air flow rate (Q/V L ), 1/min X : cell density, g dcw/l X N : cell number (or mass) in culture after a time inter- val, # or g X No : initial cell number or mass in inoculum, # or g Y X/O2 : cell yield on oxygen, g dcw/mmol/l m : growth rate, h 1 r : density, g/cm 3 h : viscosity, g/cm-s (poise) REFERENCES 1. 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