🎓 Lesson 19
D5
From Lab Stirred Tank to Full-Scale Bioreactor: Geometric and Dynamic Scaling
Scaling up a lab bioreactor to an industrial one means making it bigger while keeping the same performance—like blowing up a photo without blurring it.
🎯 Learning Objectives
- ✓ Calculate Reynolds, Power, and Oxygen Transfer (kLa) numbers for both lab and industrial bioreactors
- ✓ Design impeller speed and power input for a 50-m³ bioreactor using constant P/V or constant tip speed scaling rules
- ✓ Analyze failure modes in scaled bioreactors caused by violated similarity criteria (e.g., poor oxygen transfer due to low kLa)
- ✓ Explain trade-offs between geometric similarity and practical constraints (e.g., aspect ratio limits, motor availability, heat removal)
📖 Why This Matters
In bioleaching, heap biooxidation, or microbial sulfide ore treatment, lab-scale success rarely translates directly to plant scale—leading to stalled kinetics, oxygen starvation, or thermal runaway. Scaling isn’t just ‘bigger’; it’s about preserving the *physics* that govern microbial activity and reagent transport. A single miscalculated impeller speed can drop dissolved oxygen below 2 mg/L—halting Acidithiobacillus ferrooxidans metabolism and costing $200K/week in lost production.
📘 Core Principles
Geometric scaling requires all linear dimensions (tank diameter D, impeller diameter d, baffle width, liquid height H) to scale by the same factor λ = D_large / D_small. Dynamic scaling demands preservation of dimensionless groups: Reynolds number (Re = ρND²/μ) governs flow regime (laminar/turbulent); Power number (Po = P/(ρN³D⁵)) ensures consistent energy input; Froude number (Fr = N²D/g) matters for gas dispersion; and volumetric mass transfer coefficient (kLa) scaling depends on either constant P/V (for aerobic microbes) or constant tip speed (for shear-sensitive cultures). Real-world scale-up often compromises strict similarity—e.g., fixed H/D ratios (1.0–1.5) or standardized impeller types—requiring correction factors and empirical validation.
📐 Power Input Scaling (Constant P/V Rule)
The constant power-per-volume (P/V) rule preserves oxygen transfer capacity and mixing time in aerobic bioreactors—critical for bioleaching and biooxidation. It assumes turbulent flow (Re > 10⁴) and geometric similarity. Deviations require kLa correlation adjustments using the 0.4 power law: kLa ∝ (P/V)^0.4.
💡 Worked Example
Problem: A 5-L lab bioreactor (D = 0.15 m) operates at N = 300 rpm with P = 15 W. Scale to a 50-m³ production bioreactor (D = 3.2 m) using constant P/V. Assume geometric similarity (H/D = 1.2). What is the required impeller speed and power?
1.
Step 1: Compute lab-scale P/V = 15 W / 0.005 m³ = 3000 W/m³.
2.
Step 2: Required total power = 3000 W/m³ × 50 m³ = 150,000 W (150 kW).
3.
Step 3: Since P ∝ ρ N³ D⁵ and ρ constant, N ∝ (P / D⁵)^(1/3). So N_large = N_small × (D_small/D_large)^(5/3) = 300 × (0.15/3.2)^(5/3). Calculate exponent: (0.0469)^(1.667) ≈ 0.011 → N_large ≈ 300 × 0.011 = 3.3 rpm.
4.
Step 4: Verify Re: Lab Re = (997×300/60×0.15²)/0.00089 ≈ 1.3×10⁵ (turbulent); Plant Re = (997×3.3/60×3.2²)/0.00089 ≈ 6.7×10⁴ — still turbulent, acceptable.
Answer:
Required impeller speed = 3.3 rpm; total power = 150 kW. Note: This ultra-low speed implies large-diameter, slow-turning impellers—common in industrial biooxidation tanks (e.g., Gekko’s Albion Process).
🏗️ Real-World Application
At the Escondida copper mine (Chile), a pilot-scale 200-L biooxidation reactor achieved 92% pyrite dissolution in 72 h. When scaled to 3,000 m³ using constant P/V and geometric similarity (D = 18 m, H = 12 m), initial operation showed <40% dissolution due to oxygen limitation. Investigation revealed kLa dropped 60% vs. prediction—caused by underestimated gas holdup and coalescence in large vessels. The fix: added draft-tube internals and switched to disc turbine + Rushton impellers, restoring kLa via improved gas dispersion—demonstrating that geometric similarity alone is insufficient without validating mass-transfer similarity.