1. The Scale-Up Problem
Here is the fundamental truth of bioreactor scale-up: what works at 2 L does not automatically work at 2000 L. Every bioprocess engineer learns this the hard way. A process that runs beautifully in a bench-top fermenter can fail spectacularly when transferred to a production vessel.
The reason is geometric. When you increase a bioreactor's volume by 100-fold, the diameter increases by only ~4.6-fold (since V scales with D3). But surface-to-volume ratio drops, mixing becomes non-uniform, and the physics of mass transfer, heat transfer, and fluid dynamics shift in ways that are not linear.
The core challenge is that you cannot keep everything constant simultaneously. It is physically impossible. If you maintain constant power per unit volume, tip speed increases. If you hold tip speed constant, power per unit volume drops. The engineer must choose which parameter to conserve—and accept the trade-offs on everything else.
Scale-Up Calculator
Calculate all 5 criteria simultaneously and compare trade-offs side by side. Includes standard vessel geometry presets.
2. The Five Criteria
2a. Constant P/V (Power per Unit Volume)
The most commonly used criterion in industry and the default starting point for most scale-up exercises.
Where:
NP — Power number (dimensionless, depends on impeller type)
ρ — Fluid density (kg/m³)
N — Impeller speed (rev/s)
Di — Impeller diameter (m)
V — Working volume (m³)
Keeping P/V constant preserves the average energy dissipation rate per unit volume. This means similar levels of turbulence and, roughly, similar mass transfer characteristics. For a standard Rushton turbine, NP is approximately 5.0 in turbulent flow.
Worked Example: 10 L to 1000 L, Constant P/V
Small scale: 10 L, Di = 0.06 m, N = 800 RPM (13.3 rev/s), Rushton turbine (NP = 5.0)
P/V = 5.0 × 1000 × 13.3³ × 0.065 / 0.01 = 914 W/m³
Large scale: 1000 L, Di = 0.28 m (geometric similarity, Di/Dt = 1/3)
To maintain P/V = 914 W/m³:
N = (P/V × V / NP × ρ × Di5)1/3
N = (914 × 1.0 / 5.0 × 1000 × 0.285)1/3
N = (914 / 8.58)1/3 = (106.5)1/3 = 4.74 rev/s = 284 RPM
But check the tip speed:
Small: π × 13.3 × 0.06 = 2.51 m/s
Large: π × 4.74 × 0.28 = 4.17 m/s
Tip speed increased from 2.5 to 4.2 m/s. For microbial cultures, this is fine. For shear-sensitive mammalian cells, this could be a problem.
When to use: General fermentation, microbial cultures, most common default. If you are unsure which criterion to choose, start here.
Limitation: At large scale, the same P/V produces much higher tip speed. For shear-sensitive organisms, this can cause cell damage.
2b. Constant Tip Speed (πNDi)
Preserves the maximum shear rate at the impeller tip.
Tip speed determines the maximum shear stress that cells experience as they pass through the impeller zone. For shear-sensitive cells—CHO, hybridoma, insect cells, primary human cells—this is often the critical parameter.
Typical tip speed limits:
- Mammalian cells: < 1.0–1.5 m/s (CHO can tolerate up to ~2 m/s with Pluronic F-68)
- Insect cells: < 1.0 m/s
- Microbial cultures: < 5 m/s (less sensitive)
- Filamentous fungi: < 2–3 m/s (mycelial fragmentation)
The trade-off: at larger scale, maintaining the same tip speed requires a lower impeller speed (since Di is larger). This means P/V drops—potentially below what is needed for adequate mixing and oxygen transfer.
When to use: Shear-sensitive cultures, especially mammalian cells. This is the primary criterion for CHO antibody processes.
CHO viability dropping after scale-up?
Use the CHO Troubleshooter to diagnose whether shear damage from excessive tip speed is the cause.
2c. Constant kLa (Volumetric Mass Transfer Coefficient)
For aerobic fermentations, oxygen transfer is often the bottleneck. The kLa describes how efficiently oxygen moves from gas bubbles into the liquid phase. Keeping it constant across scales ensures the same oxygen transfer capability.
kLa depends on both agitation (P/V) and aeration (superficial gas velocity, vs). The classic Van't Riet correlation for stirred tanks is:
Typical values for coalescing media: C = 0.026, a = 0.4, b = 0.5
For non-coalescing media (electrolytes): C = 0.002, a = 0.7, b = 0.2
The challenge: since kLa depends on two independent variables (P/V and vs), matching kLa across scales may require iterating on both impeller speed and gas flow rate. There is no single unique solution.
When to use: High cell density aerobic fermentations where O2 is the limiting factor. High-density E. coli (>30 g/L DCW) and Pichia pastoris methanol-phase cultures are classic examples.
Estimate kLa for Your System
Compare OTR vs. OUR for your culture conditions to predict oxygen limitation before it happens.
2d. Constant Reynolds Number (Re)
Where μfluid is the dynamic viscosity (Pa·s)
The Reynolds number characterises the flow regime—laminar (Re < 10), transitional (10 < Re < 10,000), or turbulent (Re > 10,000). Keeping Re constant preserves the flow pattern.
Why this is rarely used: In most production bioreactors with aqueous media, Re is already in the fully turbulent regime (>50,000). Matching Re across scales would require reducing impeller speed so much that P/V drops to impractical levels. The flow stays turbulent regardless.
When to use: Viscous fermentations—filamentous fungi (e.g., Aspergillus producing citric acid), polysaccharide producers (xanthan gum, gellan), or cultures that become highly viscous as biomass accumulates. In these systems, the broth viscosity can increase 100-fold during fermentation, and maintaining the turbulent regime becomes non-trivial.
2e. Constant Mixing Time
Mixing time (tmix) is the time required to achieve 95% homogeneity after adding a tracer. In a stirred vessel:
Mixing time increases with vessel volume and decreases with agitation intensity.
At lab scale (2–10 L), mixing time is typically 2–5 seconds—essentially instantaneous. At 10,000 L, mixing time can reach 30–120 seconds. At 100,000 L, it can be several minutes.
This has real consequences. In a fed-batch process, the feed enters at a single point. If mixing takes 60 seconds, the cells near the feed inlet experience a glucose concentration 10–100 times higher than cells on the opposite side of the vessel. This creates substrate gradients that cause local overflow metabolism, pH gradients (from local acid production), and heterogeneous cell populations.
When to use: pH-sensitive processes, fed-batch with high feed concentrations (e.g., 700 g/L glucose), large-scale processes where mixing gradients are a known problem.
3. The Comparison Table
This is the table every bioprocess engineer should have pinned to their wall. It shows what happens to the other parameters when you hold one constant during a 100× scale-up (10 L to 1000 L):
| If you keep constant → | P/V | Tip Speed | kLa | Re | Mix Time |
|---|---|---|---|---|---|
| P/V at target scale | = | ↑ 3–4× | ≈ | ↑↑ | ↓ |
| Tip speed | ↓↓ | = | ↓ | ↑ | ↑↑ |
| kLa | varies | ↑ | = | ↑ | ↓ |
| Re | ↓↓↓ | ↓ | ↓↓ | = | ↑↑↑ |
| Mixing time | ↑↑ | ↑↑ | ↑ | ↑↑↑ | = |
Reading this table: when you hold P/V constant during scale-up, tip speed increases 3–4× (potential cell damage), Reynolds number increases dramatically (no problem—stays turbulent), and mixing time gets worse (longer). Conversely, holding tip speed constant means P/V drops significantly (risk of poor mixing and O2 transfer).
The table makes it viscerally clear: there is no free lunch. Every choice involves trade-offs.
Radar chart with five axes: P/V, Tip Speed, kLa, Mixing Time, and Reynolds Number. Each axis is normalized so that a value of 1.0 means the parameter matches the source scale. Five datasets are plotted, one for each scale-up criterion. When P/V is held constant (teal), P/V stays at 1.0, but tip speed rises to about 2.15, kLa stays near 1.0, mixing time increases to about 2.5, and Re increases to about 4.6. When tip speed is held constant (blue), P/V drops to about 0.22, tip speed stays at 1.0, kLa drops to about 0.5, mixing time rises to about 4, and Re increases to about 2.15. When kLa is held constant (coral), P/V is about 1.1, tip speed about 2.2, kLa is 1.0, mixing time about 2.3, and Re about 4.8. When Re is held constant (purple), P/V drops to about 0.05, tip speed drops to about 0.46, kLa drops to about 0.15, mixing time rises to about 10, and Re stays at 1.0. When mixing time is held constant (yellow), P/V rises to about 4.6, tip speed rises to about 3.6, kLa rises to about 2.5, mixing time stays at 1.0, and Re rises to about 16.7. The ideal scenario would keep all parameters at 1.0 but this is physically impossible.
4. Decision Framework
When you are staring at a new scale-up project and wondering which criterion to choose, work through these questions:
Quick Decision Guide
Calculate All 5 Simultaneously
Our Scale-Up Calculator computes all five criteria and shows the trade-offs side by side, so you can make an informed decision.
Flowchart diagram with five sequential decision diamonds. First diamond asks if cells are shear-sensitive, leading to Constant Tip Speed if yes. Second asks if the process is oxygen-limited, leading to Constant kLa. Third asks if the broth is viscous, leading to Constant Reynolds Number. Fourth asks if there are pH or gradient issues, leading to Constant Mixing Time. If none apply, the default recommendation is Constant P/V as the industry standard starting point.
5. Real-World Case Studies
Case 1: E. coli at 10 L to 1000 L — Constant P/V (Success)
Case Study: Success
A recombinant E. coli process producing an industrial enzyme was scaled from 10 L to 1000 L using constant P/V = 2.5 kW/m³.
- 10 L: N = 900 RPM, Di = 0.06 m, tip speed = 2.8 m/s
- 1000 L: N = 310 RPM, Di = 0.28 m, tip speed = 4.6 m/s
Tip speed increased from 2.8 to 4.6 m/s, but E. coli is a robust rod-shaped bacterium with a rigid cell wall. No impact on viability. kLa was sufficient at both scales (supplemented by increased aeration at 1000 L). Mixing time increased from 3 s to 25 s, but the fed-batch process tolerated the modest substrate gradient.
Result: Final DCW within 5% of lab scale. Product titre matched. Successful tech transfer.
Case 2: CHO at 3 L to 200 L — Constant P/V (Failure), then Tip Speed (Success)
Case Study: Initial Failure
A CHO DG44 cell line producing an IgG1 monoclonal antibody was scaled from 3 L to 200 L using constant P/V = 50 W/m³.
- 3 L: N = 150 RPM, Di = 0.045 m, tip speed = 0.35 m/s
- 200 L: N = 120 RPM, Di = 0.18 m, tip speed = 1.13 m/s (calculated for constant P/V)
At 200 L, the tip speed of 1.13 m/s was acceptable, but the actual P/V calculation required N = 180 RPM to truly match, giving a tip speed of 1.70 m/s. Cell viability dropped from 95% to 78% by day 10. LDH release increased 3-fold. Antibody titre dropped 40%.
Root cause: Excessive shear at the impeller tip caused membrane damage to the CHO cells.
Case Study: Corrected Approach
The team switched to constant tip speed as the scale-up criterion, capping vtip at 0.35 m/s (matching the 3 L scale).
- 200 L: N = 0.35 / (π × 0.18) = 37 RPM
P/V dropped significantly, so they compensated by:
- Switching from a Rushton to a pitched-blade impeller (better axial flow at low RPM)
- Adding a second impeller on the shaft
- Increasing sparge rate to maintain kLa
Result: Viability restored to 94% by day 10. Titre matched lab scale within 10%. Process validated.
Case 3: Pichia pastoris at 5 L to 500 L — Constant kLa (Success)
Case Study: Success
A Pichia pastoris process expressing a lipase during methanol induction was scaled from 5 L to 500 L. The team identified O2 transfer as the bottleneck: at 5 L, the culture reached 120 g/L DCW with an OUR of 250 mmol/L/h.
They matched kLa = 400 h-1 across scales by adjusting both impeller speed and gas flow:
- 5 L: N = 1000 RPM, 1 vvm air + O2 enrichment to 40%
- 500 L: N = 350 RPM, 1.5 vvm air + O2 enrichment to 50%, using dual Rushton impellers
Result: DO maintained above 20% throughout methanol phase. Final DCW of 115 g/L (within 5% of lab scale). Product activity matched.
Grouped bar chart with four groups on the x-axis representing bioreactor scales of 10 litres, 100 litres, 1000 litres, and 10000 litres. Within each group are five bars, one for each scale-up criterion. At 10L (source scale), all criteria give 300 RPM. At 100L, constant P/V gives about 172 RPM, constant tip speed gives 90 RPM, constant kLa gives about 180 RPM, constant Re gives about 27 RPM, and constant mixing time gives about 557 RPM. At 1000L, constant P/V gives about 98 RPM, tip speed gives 27 RPM, kLa gives about 108 RPM, Re gives about 2.7 RPM, and mixing time gives about 1034 RPM. At 10000L, P/V gives about 56 RPM, tip speed gives about 8 RPM, kLa gives about 65 RPM, Re gives about 0.27 RPM, and mixing time gives about 1920 RPM. This demonstrates how constant Re gives impractically low RPM at large scale while constant mixing time gives impractically high RPM.
6. The Ugly Truth About Scale-Up
Academic textbooks present scale-up criteria as clean, deterministic calculations. Reality is messier.
Iteration is the norm
In practice, most companies use P/V as a starting point, then iterate. The first large-scale run rarely matches lab performance. Engineers adjust impeller speed, gas flow, feed strategy, and baffle configuration over 3–5 campaigns to optimise the process. Scale-up is empirical, not purely theoretical.
CFD is changing the game
Computational fluid dynamics (CFD) simulations are increasingly used alongside traditional correlations. CFD can predict local shear fields, dead zones, gas hold-up distribution, and mixing time with reasonable accuracy. It is particularly valuable for non-standard geometries (single-use bioreactors, wave-mixed systems) where the classic correlations were never validated.
Single-use bioreactors are different
Single-use bioreactors (SUBs) from Cytiva, Sartorius, and Pall have different impeller geometries (axial flow, magnetically driven) and aspect ratios compared to traditional glass or stainless steel vessels. The Rushton-based correlations that underpin most scale-up calculations may not apply directly. Vendor-provided characterisation data (kLa vs. power, mixing time curves) is essential.
The best approach
Calculate all five criteria. Compare the results. Identify which parameter is most critical for your specific process. Then use that as the primary criterion while monitoring the others to ensure they remain within acceptable ranges.
Calculate All 5 Criteria
Input your small-scale and large-scale vessel dimensions. Get RPM, P/V, tip speed, Re, and mixing time for each criterion.
7. Try It Yourself
Our Scale-Up Calculator lets you:
- Select from standard vessel geometries (1 L to 10,000 L) or enter custom dimensions
- Choose your impeller type (Rushton, pitched-blade, marine propeller, Intermig)
- Calculate the required impeller speed for all five criteria simultaneously
- See what happens to every other parameter when you hold one constant
- Compare the results in a single summary table
Related tools:
- OTR & kLa Estimator — estimate kLa for stirred tanks and shake flasks
- Fed-Batch Calculator — design your feeding profile
- Heat Transfer Calculator — check cooling capacity at production scale
- Fermentation Economics — estimate cost of goods at different scales
References
- Ju, L.K. & Chase, G.G. (1992). "Improved scale-up strategies of bioreactors." Bioprocess Engineering, 8(1–2), 49–53. doi:10.1007/BF00369263
- Xing, Z. et al. (2009). "Scale-up analysis for a CHO cell culture process in large-scale bioreactors." Biotechnology and Bioengineering, 103(4), 733–746. doi:10.1002/bit.22287
- Nienow, A.W. (2006). "Reactor engineering in large scale animal cell culture." Cytotechnology, 50(1–3), 9–33. doi:10.1007/s10616-006-9005-8
- Garcia-Ochoa, F. & Gomez, E. (2009). "Bioreactor scale-up and oxygen transfer rate in microbial processes: an overview." Biotechnology Advances, 27(2), 153–176. doi:10.1016/j.biotechadv.2008.10.006
- Van't Riet, K. (1979). "Review of measuring methods and results in nonviscous gas-liquid mass transfer in stirred vessels." Industrial & Engineering Chemistry Process Design and Development, 18(3), 357–364.