Engineering & Science
Bioreactor Volumetric Oxygen Transfer (kLa), OTR & Minimum kLa_min
Calculate aerobic fermenter Oxygen Transfer Rate OTR = k_L*a * (C_star - C_L) (mmol O2/(L*h)), cellular Oxygen Uptake Rate OUR = q_O2 * X, and minimum required k_L*a to prevent dissolved oxygen starvation below C_crit.
Prevent dissolved-oxygen crashes during peak aerobic cell density!
Oxygen is sparingly soluble in warm aqueous fermentation broth (air-saturated C* ~ 0.24 mmol O2/L at 37°C, 1 atm), meaning high-density microbial or CHO cultures would strip every dissolved oxygen molecule out of solution in under 30 seconds without continuous sparging and impeller agitation!
Bioprocess scale-up balances gas-liquid Oxygen Transfer Rate OTR = k_L*a * (C* - C_L) against cellular Oxygen Uptake Rate OUR = q_O2 * X! At volumetric mass-transfer coefficient k_L*a = 180 h^-1, C* = 0.24 mmol/L, and operating dissolved oxygen C_L = 0.06 mmol/L (25% air saturation), OTR = 32.40 mmol/(L*h). Against a culture with specific respiration q_O2 = 4.5 mmol/(g*h) at biomass X = 6.0 g/L (OUR = 27.0 mmol/(L*h)), minimum required mass-transfer capacity to stay above critical C_crit = 0.05 mmol/L is k_L*a_min = (q_O2 * X) / (C* - C_crit) = 142.1 h^-1 (leaving +5.40 mmol/(L*h) headroom)!
| Aerobic Bioreactor Metric (C* = 0.24, CL = 0.06, Ccrit = 0.05 mmol/L) | Formula Expression | Calculated Value |
|---|---|---|
| Gas-Liquid Oxygen Transfer Rate (kLa = 180 h^-1) | kLa * (C* - CL) | 32.40 mmol O2/(L*h) |
| Minimum Required kLa_min (qO2 = 4.5, X = 6 g/L) | (qO2 * X) / (C* - Ccrit) | 142.1 h^-1 |
| Net Oxygen Transfer Headroom (OTR - OUR) | kLa*(C* - CL) - qO2*X | +5.40 mmol O2/(L*h) (Safe Aerobic) |
Volumetric Oxygen Transfer Rate OTR = k_L*a * (C* - C_L) (mmol/(L*h))
Validates C* > C_L >= 0 and positive k_L*a (B2) before computing gas-liquid mass transfer.
=IF(OR(B2 <= 0, B3 <= 0, B4 < 0, B4 >= B3), "Invalid DO Parameters", ROUND(B2 * (B3 - B4), 2))Minimum Required k_L*a_min (h^-1) Above Critical Dissolved Oxygen C_crit
Divides cellular oxygen uptake OUR = q_O2 * X (B6 * B7) by maximum safe concentration driving force (C* - C_crit).
=IF(OR(B3 <= B5, B5 < 0, B6 <= 0, B7 <= 0), "Invalid DO Parameters", ROUND((B6 * B7) / (B3 - B5), 1))Try the example
Use the original values or change them to test your understanding.