A Unified Approach for Scaling Bioprocess Unit Operations

Published on: 
BioPharm International, BioPharm International-02-01-2021, Volume 34, Issue 2
Pages: 31–39

A unified scale-up approach, as presented here, can be applied to any unit operation.

Successful scale-up of bioprocess steps is a key activity for any drug, from lab to pilot scale, pilot to clinical manufacturing, clinical to commercial manufacturing, and post-approval technology transfers. Successful scale-up results in timely startup and consistent, uneventful processing. Unsuccessful scale-up can lead to delays in project timelines (e.g., delays in start of clinic trials or inability to meet market demand) and/or intermittent process deviations taxing the manufacturing science and technology (MSAT) quality groups with deviation investigations.

In recent years, the biopharmaceutical industry has trended toward increased outsourcing of drug manufacturing to provide additional manufacturing capacity or to complement existing, internal capacity. Outsourcing adds another dimension to multi-dimensional technology transfer projects, making effective scale-up increasingly important to ensure uneventful and on-time process transfer and manufacture. It should be noted that technology transfer projects will not always require process scale up. It is possible that the receiving facility may operate at a smaller scale. In these cases, the principles introduced here for process scale-up apply equally well to process scale-down.

This article presents a unified scale-up approach that can be applied to any unit operation. Practical scaling techniques are presented for upstream and downstream unit operations commonly found in a typical monoclonal antibody (mAb) process. Finally, a case study is presented.

A unified scale-up approach

The goal of scale up is to produce comparable drug substance (DS) and drug product at the larger scale. One way to achieve this is to employ the Similarity Principle, which states that this equivalence is established by, first, specifying certain levels of similarity for the two systems at different scales and, second, by maintaining certain critical or key process parameters equivalent at corresponding points between the small- and large-scale processes (1). Similarity can be maintained based on geometric, mechanical, thermal, or chemical characteristics.

Geometric similarity refers to linear dimensions. For some processes, maintaining a key linear dimension unchanged, such as the feed channel path length for ultrafiltration/diafiltration (UFDF) devices and bed height for chromatography column steps, will help ensure equivalent process performance. For bioreactor processes, maintaining similar ratios of key linear dimensions refers to spatial dimensions, such as constant aspect ratio (H/T) and impeller-to-tank diameter ratio (D/T) (see Figure 1).

Mechanical similarity refers to process variables normalized for dimension to compare variables independent of scale. One example is similar pressures, such as a process set point in a constant pressure filtration step compared to similar pressure profiles on a constant flow depth filtration step. Another example is the expression of flow rates as velocities, such as a UFDF cross flow (L/m2/min) or a bioreactor gas sparge rate expressed as a superficial velocity. Other similarity levels can be based on thermal similarity, such as a process temperature value for a bioreactor process or a hydrophobic chromatographic column step, or chemical similarity, such as chromatography buffer component concentrations.

Once the similarity levels are specified, a “scaling rule” for the process can be established by expressing the similarity as criteria that are simple ratios of measurements, fluxes, or forces. For example, two criteria for scaling a normal flow filtration step, such as a sterilizing-grade membrane step or a virus filtration step, can be same separation and productivity. Because the separation performance of a membrane step is determined by the membrane characteristics (e.g., pore size, number of membrane layers, pore structure), using the same membrane at both scales will ensure the same performance. Next, using a mathematical model that describes membrane performance will help identify how to scale this process to ensure the same productivity at both scales. Most biopharmaceutical process streams can be described by the gradual pore plugging model (Equation 1):

[Eq. 1]

Because the same membrane will be used at both scales, the membrane permeability (Lm) will remain the same, and, assuming the feedstock plugging profile or filterability remains the same, the maximum filtration volume (Vmax) will also be the same. Therefore, to maintain the same filtration productivity (time), the filtration pressure (∆P) and throughput, or volumetric loading (VB/A) must be maintained at constant. For larger scales and increased process volumes (VB), constant loading is achieved by proportionally increasing filter area. Intuitively, it would make sense to select a filter that is twice as large in filtration area, if the goal is to filter twice as much volume. However, this section shows how one can arrive at rational scaling rules by employing the Similarity Principle. Using this same approach, scaling rules can be developed for other bioprocess unit operations. A summary is provided in Table I. A list of abbreviations used in the table and in this article is provided in Table II.

Practical scaling techniques

Several practical techniques can be employed for scaling bioprocess applications: linear, predictive, and hybrid scaling techniques. These are described as follows.

Linear scaling requires the use of representative feed and a “scale-down” element that is used to develop scaling information. The scale-down element is the smallest element available that maintains the appropriate similarity levels with the large- or process-scale unit operation—for example, dimensions (geometry), flow (mechanical), and concentrations (chemical)—to ensure successful scale up. As a simple example, consider scale up of a microfiltration normal flow filtration (NFF) step with a target filtration time of 1.5 hours and filtration pressure of 10 psig.Using representative feed material, a bench-scale trial can be performed with a scale-down element (e.g., Optiscale 3.5cm2 test device, MilliporeSigma). At process time t=1.5 hr, the filtration volume is recorded. This volume corresponds to the throughput (L/m2) for that feed stream and membrane at the target filtration pressure and time. Using this information, the process can be linearly scaled. For example, if 350 mL were processed through the scale-down test device (3.5 cm2) in 1.5 hours (at 10 psig), the throughput is 1000 L/m2 (=0.35 L/0.00035 m2). For a 2000-L process, 2 m2 of filter area would be required to complete filtration in 1.5 hr. at 10 psig. In practice, a safety factor would be applied to the calculated (minimum) membrane area to allow for normal process and filter variability (2).

Predictive scaling uses a well-tested and “trusted” model to estimate critical scaling parameters and to predict large-scale performance behavior. One example is the gel model used for UFDF application, which describes the permeate flux as a function of the bulk protein concentration. Using experimental data that include permeate flux and bulk concentration, the gel model (Equation 2) can be used to predict process-scale performance including the optimum concentration for diafiltration (3).

[Eq. 2]

Another example is the Vmax method used for constant pressure NFF filtration steps. Similar to the gel model used for UFDF applications, the Vmax method uses a set of experimental data (filtrate volume and time) to predict process performance by employing the gradual pore plugging (GPP) model. The experimental data are used to calculate the maximum volume that can be filtered through a membrane on a per unit area basis, the Vmax value (4). Once the Vmax value has been calculated, process-scale performance can be predicted including the required membrane area using Equation 3:

[Eq. 3]

Taking the example presented above (scale up of a microfiltration normal flow filtration step using the linear scaling technique), the predictive scaling technique could be used as an alternative approach. Here, rather than extending the “scale-down” test run to the target 1.5-hr filtration time, the bench-scale test could be run for 10–20 minutes at the same 10 psig filtration pressure. The GPP model could then be used to calculate the Vmax value and predict performance at a 1.5-hr batch time at any scale.

Finally, the hybrid scaling technique takes advantage of the linear scalability of scale-down models and the predictive power of models to successfully scale up processes. Generally, key parameters are maintained constant (e.g., flux, N, or # of plates in a column), while “cautious liberties” are taken with less critical parameters (e.g., process time, loading in UFDF). The following shows an example of a UFDF process that was tested at a feed volume loading of 50 L/m2 at the process development-scale (e.g., to accelerate test time) but scaled up to a 200-L/m2 volume at the process- or manufacturing-scale (see Figure 2).

In this example, the cross flow, transmembrane pressure, and flux are maintained constant, and only the loading (and process time) are varied.Generally, a small-scale verification run at the target manufacturing loading would be recommended.The hybrid scaling technique offers a “best of both worlds” approach and often represents a robust method for scaling.

It should be noted that the success of these scaling techniques depends on the use of time-tested and “trusted” models and appropriate scale-down models that have the appropriate similarity levels.The validity of the scale-down model must be tested, verified, and confirmed.

Bioreactor scale up

As described earlier, the Similarity Principle provides an approach for process scale up that relies on maintaining certain appropriate levels of similarity and critical, or key, process parameters constant across scales.The ideal case is to achieve complete similarity levels.Bioreactor scale up requires special consideration because complete similarity is not possible. Several scaling rules can be applied to bioreactor scale up, but it is not possible to faithfully apply all rules. In this way, bioreactor scale up employs partial similarity.The bioprocess engineer must rely on industry experience and best practices to determine which scaling rules will be used to ensure that partial similarity enables successful scale up.

In this section, the various scaling rules available for bioreactor scale up are described. Examples are discussed, which illustrate that it is not possible to maintain a constant for all scale-up criteria constant.Finally, a best-practice approach for bioreactor scale up is described.

At a high level, for mammalian cell culture processes, bioreactor scaling concerns two critical bioreactor performance characteristics: mixing (solution homogeneity) and mass transfer (oxygenation, and carbon dioxide [CO2] stripping).Along with geometric similarity, bioreactors can be scaled by maintaining some, but not all, of the following engineering parameters constant:

Geometric similarity: there are two geometric similarities that are ideally held constant across scales—first, the bioreactor aspect ratio (H/T), which is the ratio of the full volume liquid (H) to the tank diameter (T) and, second, the ratio of the impeller diameter (D) to the tank diameter (T) or D/T. For mammalian cell culture processes, bioreactor H/T is typically in the range of 1.5–2.0 and D/T is typically in the range of 1/3–1/2. Manufacturers will commonly have many production bioreactors distributed across multiple manufacturing sites that may also include contract manufacturing partners. The bioreactors may have different designs (i.e., H/T and D/T) and even include different sparger types as well as different impeller types and placement. In these instances, geometric similarity is not possible. For single-use production, several single-use bioreactor suppliers provide a family of bioreactors that are geometrically similar over a 40x production scale.

Mixing time: good mixing is required to ensure even distribution of dissolved gases, nutrients, and cells, and to enable effective process control (e.g., pH, dissolved oxygen [DO], and temperature). Appropriate mixing will minimize the likelihood that cells are exposed to localized areas of low DO and minimize the time that cells are exposed to high pH due to bolus titrant addition. Mixing can be accelerated by increasing the impeller agitation rate; however, increased agitation rates will also increase impeller tip speed, which can result in cell damage. Therefore, mixing must be balanced with the need to provide a healthy environment for the cells (i.e., low shear). Generally, mixing times are not held constant and increase with scale. Scaling at constant mixing time would result in increased P/V values that can be excessively high at larger scales (5).

It should be noted that, beyond bioreactor systems, tank mixing in general is an important scale-up activity, and this includes buffer tanks, process pooltanks, and process pool conditioning tanks. Mixing should be confirmed for each tank with a relevant solution; although, a matrix/family approach may be used with appropriate justification as follows:

Tip speed: as the impeller(s) rotates to provide mixing, the outer edge of the impeller blades create shear as they rotate through the liquid, which, at sufficiently high agitation rates, could damage cells. Historically, tip speed, Vtip = πDN (Equation 4), has been used as an indicator of the shear potential near the impeller blade edge. Scaling with constant tip speed would ensure that cells will not be subjected to increased shear at larger scales. It should be noted that the equation for tip speed does not take into consideration the impeller type/design, which may also contribute to the levels of shear produced. Typically, tip speeds <2 m/s are considered appropriate for mammalian cells (6).

Power per unit volume (P/V): P/V is a measure of the power imparted by the impellers to the solution volume, calculated by Equation 5:


[Eq. 5]

For a given bioreactor system, the agitation rate N is varied to maintain P/V constant across scales. P/V can be expressed in units of W/m3 or W/kg (energy dissipation rate). It has been shown to affect the mass transfer coefficient and is often used to create predictive modeling correlations (5).

Oxygen mass transfer coefficient (kLa): one of the critical functions of a bioreactor system is to supply oxygen to the cells. kLa is a key parameter that characterizes the rate at which a bioreactor system is able to supply dissolved oxygen. Often the kLa is characterized as a function of P/V and the superficial gas velocity (m/s) of the sparged gas (e.g., air, O2) as shown in Equation 6:

[Eq. 6]

Selecting scale-up parameter

As noted earlier, it is not possible to maintain all scaling parameters constant for bioreactor operations. The bioprocess engineer must select which critical engineering parameters to maintain constant to ensure performance equivalency and which parameters can be allowed to vary with scale.

In order to maintain P/V constant, Equation 5 must be equal at both scales (e.g., “pilot scale” and large scale) (see Equation 7).

[Eq. 7]

The liquid density (rL) can be taken to be constant. Keeping geometric similarity, bioreactor volume (V) can be expressed in terms of impeller diameter (D). And using the same impeller type, configuration, and spacing in geometrically similar reactors with fully developed turbulent flow (Re > 10,000), NP can be taken to be constant. Equation 7 can be simplified to Equation 8:

[Eq. 8]

Re-arranging to place in terms of agitation rate at the large scale (NLS) gives Equation 9:

[Eq. 9]

Equation 8 shows that the agitation rate must be deceased proportionally to the impeller diameter ratio to the 2/3 power. Similarly, maintaining tip speed constant would require the use of Equation 10,

[Eq. 10]

which can be re-arranged in terms of large-scale agitation rate to Equation 11:

[Eq. 11]

Equation 11 shows that agitation rate must again be decreased proportional to the impeller diameter ratio.

Finally, for mixing time, the observation was made by Sieblist et al. (7) that, for geometrically similar tanks with fully developed turbulent flow (Re > 10,000) and same impeller type, configuration, and spacing, the number of times the impellers must turn to achieve homogeneity (the mixing number) was constant. This relationship was demonstrated for bioreactors ranging from 100 L to 12,000L. This relationship can be expressed in Equation 12:

[Eq. 12]

Here, in order to maintain mixing time (Qm) constant at the large scale, the agitation rate (N) should also be kept constant.

From this analysis, it is clear that only one of these engineering parameters can be maintained constant. Maintaining mixing time constant would result in an increase in both P/V and tip speed. Maintaining tip speed constant would result in an increase in mixing time and a decrease in P/V. Table III summarizes the impact of scaling based on one engineering parameter on the other parameters.

This analysis of bioreactor scaling parameters shows that it is not possible to keep all scaling parameters constant. The process engineer, based on industry experience, knowledge gained during process development, and, when possible, familiarity with the historical performance of the target large-scale bioreactor, must select which scaling parameters to employ for scaling. Because solution homogeneity is important to ensure comparable cell culture performance across scales, P/V is often used as a scaling rule. Additionally, adequate oxygenation is also required.

By keeping P/V and the superficial velocity of the sparged gas constant (per Equation 5), kLa is maintained constant. This simple scaling strategy has proven to be effective in many instances. However, due to the diverse bioreactor characteristics noted previously (geometry, mixing, sparge element type and size[s]) and unique cell line characteristics, alternate scaling approaches may be required.

One example of an alternative scaling approach is the use of single-use bioreactors, which are often designed with a single, unique, bottom-mounted impeller installed at an offset to improve mixing. In some cases, it may not be possible to maintain P/V constant. In these instances, empirical bioreactor kLa performance data are used to identify P/V and gas flow rate values that will meet the target kLa value and ensure solution homogeneity (8).

It should also be noted that, in addition to oxygenation, gas sparging must also facilitate CO2 removal from the culture volume, and, while oxygen transfer is dependent on the superficial gas velocity, CO2 removal has been shown to be dependent on gas volume expressed as vessel volumes per minute (VVM). Therefore, scaling based on superficial velocity alone could result in inadequate CO2 removal. This is generally a concern for scales larger than 2000 L. Strategies for ensuring proper culture oxygenation and CO2 removal are discussed in Xu et al. (9).

Case study

The previous sections described how a unified scaling approached based on the Similarity Principle can be used to develop scaling rules for any bioprocess unit of operation. These scaling rules, especially for linearly scalable processes such as downstream unit operations, are well understood and have proven to reliably scale up processes. Often, when a scale-up issue presents itself, it is not a failure of the scaling rule but a failure or limitation beyond the process, per se. These issues are often related to system or facility constraints—the ancillary dimension.

The case study below illustrates an example where a proven scaling rule was used to scale up a UFDF process. During processing, however, a performance issue was observed. An investigation showed that the root cause was associated with a system issue.

UFDF background

Final UFDF is the final step in a downstream purification process and is designed to ensure the product is at the target DS concentration and in the formulation buffer. After an equilibration step, the product is brought to an intermediate concentration, which is optimized for diafiltration. The diafiltration step is performed typically to 10 diavolumes to ensure removal of starting buffer excipients, at the end of which the product is in the formulation buffer matrix. A final over-concentration step ensures that the product can be recovered from the system at the target DS concentration.

Scale up performance

The UFDF step was scaled with a proven scaling rule. The feed flow rate on a per unit area and the transmembrane pressurewere maintained constant. Additionally, the number of diavolumes was also maintained constant to ensure same buffer exchange efficiency. The starting product pool pH (pre-diafiltration) was 6.0, and the formulation (diafiltration) buffer pH was 5.0. The final pH target was pH 5.0 +/- 0.2. During the first scale-up process batch, the pH of the product pool after the diafiltration was 5.7. An investigation was undertaken to identify the root cause of this process difference.


An informal causal factor analysis was performed to identify the root cause. This analysis is summarized in Table IV.

Root cause and corrective action

Inadequate mixing in the retentate tank was identified as the cause of the inefficient diafiltration step. Here, the scaling rule did not fail, but, rather, the cause was as an artifact of the scale-up system. Mixing in the retentate tank is provided by the tank agitator and by the return of retentate into the retentate tank volume. Previous UFDF processes had a feedside flow rate of 300 L/m2/hr (LMH); however, this process had a feed flow rate of 70 LMH due to the molecule being prone to shear damage. The lower feed flow rate resulted in a reduced mixing in the retentate tank, which in turn resulted in the inefficient diafiltration step and the high pH.

After identifying the root cause and analyzing associated risks, a decision was made to reprocess the pool with another 10 diavolumes at an increased agitator speed, with the intent to compensate for the reduced mixing as a result of the lower feedside flow rate. The agitator speed was determined visually by observing and confirming liquid surface movement during processing. After the reprocessed diafiltration step, the pool pH was confirmed to be 5.0—equal to the target pH value. This result confirmed that the process issue observed was caused by inadequate mixing in the retentate tank based on the lower feedside flow rate. To ensure a similar mixing issue would not impact a future process, agitator speed requirements were determined for several processing conditions, including a range of retentate flow rates, solution viscosities, and retentate tank level, using computational fluid dynamics (CFD). Subsequent wet testing using a 12% sucrose model solution confirmed the CFD-predicted minimum mixing times at various tank levels and mixing speeds by monitoring pH stabilization time post bolus titration.

In summary, this case study shows how a process step, which was scaled via a proven scaling rule, failed to meet target performance because of a system contributing factor—in this case, inadequate mixing in the retentate tank. This case study also showed that tank mixing is an important scale-up activity, as noted earlier in this paper.


Bioprocess scale up is often treated as two separate parallel activities—upstream process and downstream process scale up. By employing the Similarity Principle, however, a unified scaling approach can be used for both upstream and downstream processes. Practical scaling techniques available for scale up are linear, predictive, and hybrid scaling techniques, where the linear technique relies solely on experimental data generated using a scalable test element; the predictive technique utilizes a smaller data set and relies on the predictive power of a process model; and the hybrid technique provides a best-of-both worlds solution. Unlike downstream processes, it is not possible to linearly scale bioreactors and maintain key engineering parameters constant. Here, the process engineer must rely on industry experience, process development data, and historical performance of the large-scale system to determine the best scaling approach. Finally, the scaling rules commonly employed to scale up bioprocesses have proven to be reliable. Often, scale-up “failures” are found to be associated with the “ancillary dimension” (e.g., facility constraints or system limits) and not with the scale up, as illustrated in the case study example.


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About the authors

Joshua Arias*, joshua.arias@milliporesigma.com, is technical leader, BioReliance End to End Solutions, MilliporeSigma, and Mani Vinay Kumar Kotipalli is process engineer, Drug Substance Technology & Engineering, Amgen.

*To whom all correspondence should be addressed.

Article Details

BioPharm International
Vol. 34, No. 2
February 2021
Pages: 31–39


When referring to this article, please cite it as J. Arias and M.V.K. Kotipalli, “A Unified Approach for Scaling Bioprocess Unit Operations,” BioPharm International 34 (2) 2021.