What Is the Bioreactor kLa & Oxygen Transfer Rate Calculator?
kLa is the overall volumetric mass transfer coefficient describing how quickly oxygen dissolves across the gas-liquid bubble interface.
It is the single most critical scale-up parameter in industrial aerobic fermentation engineering.
How Does the Bioreactor kLa & Oxygen Transfer Rate Calculator Work?
Dynamic gassing out involves stripping oxygen with nitrogen sparging, followed by switching to air and tracking DO re-saturation.
The slope of ln((C* - C0) / (C* - C)) plotted against time yields kLa in reciprocal seconds or hours.
Multiplying kLa by saturation DO provides the maximum Oxygen Transfer Rate (OTR).
Bioreactor kLa & Oxygen Transfer Rate Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Calculates volumetric oxygen mass transfer coefficient and maximum oxygen dissolution rate.
How to Use the Bioreactor kLa & Oxygen Transfer Rate Calculator
- Enter the broth equilibrium saturation oxygen concentration (approx. 7.5 to 9.0 mg/L at 25-37 C).
- Input measured dissolved oxygen values at two distinct points during re-aeration.
- Enter the elapsed seconds between readings and bioreactor working volume.
Step-by-Step Example Calculation
Bioreactor kLa Standard Case
Input Values:
Understanding Your Result
kLa values in industrial fermenters typically range from 50 to 500 h^-1.
Mammalian cell cultures operate at lower kLa (5-20 h^-1) to minimize impeller shear damage.
High-density bacterial and yeast cultures require kLa > 200 h^-1 to prevent anaerobic fermentative pathways.
Factors That Affect the Result
- Impeller agitation speed (RPM): Increases turbulence, shearing bubbles into smaller diameters and expanding interfacial area 'a'.
- Gas superficial velocity: Higher sparge gas flow (VVM) increases gas holdup.
- Broth viscosity: Filamentous mycelial broths drastically reduce kLa due to bubble coalescence.
When Should You Use This Calculator?
- Characterizing new fermenter vessels, impellers, and micro-spargers.
- Scale-up calculations from bench-scale (5 L) to pilot (500 L) and production (50,000 L) fermenters.
Assumptions & Limitations
- Assumes DO electrode response time is much faster than the re-aeration rate (electrode tau < 1/kLa).
- Assumes well-mixed liquid broth with uniform DO distribution.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard dynamic re-aeration logarithmic slope mass transfer formulation.