Bioreactor Oxygen Transfer Rate, OUR and kLa Capacity Calculator

Related Calculators

Table of contents

• How to use
• Common mistakes
• Definitions
• Methodology
• Limitations & assumptions
• Sources

kLa: Volumetric mass transfer coefficient. It describes how quickly oxygen moves from gas to liquid under stated reactor conditions; its unit is inverse time, such as 1/h.

OTR: Oxygen transfer rate, the modeled oxygen supplied to liquid per volume per time. This calculator reports mg/L/h.

OUR: Oxygen uptake rate, the oxygen demand of the culture per volume per time. At steady oxygen balance, OTR equals OUR. [1]

C*: Saturation dissolved oxygen, the dissolved-oxygen concentration the liquid approaches under the entered conditions.

Target dissolved oxygen: The controller setpoint or chosen liquid oxygen concentration, expressed as mg/L or as a percent of C*.

Oxygen capacity margin: OTR minus OUR at the target dissolved oxygen. A positive margin is modeled surplus; a negative margin is modeled shortfall.

Mistake: Treating Volumetric mass transfer coefficient, kLa as if it were already an oxygen rate.
Fix: Enter kLa with its actual time basis in kLa time unit; the calculator combines it with the dissolved-oxygen driving force to calculate OTR at target dissolved oxygen.

Mistake: Using a clean-water or different-vessel value for Volumetric mass transfer coefficient, kLa without checking conditions.
Fix: Use a kLa measured or estimated for the applicable liquid, aeration, agitation, pressure, and gas composition.

Mistake: Entering a percent setpoint as mg/L in Target dissolved oxygen.
Fix: Set Target dissolved-oxygen unit to Percent of saturation (%) before entering a percentage, or choose mg/L for an absolute concentration.

Mistake: Comparing mmol/L/h directly with mg/L/h by choosing the wrong OUR unit.
Fix: Choose the unit printed with Oxygen uptake rate, OUR. The calculator converts mmol/L/h to mg/L/h before finding Oxygen capacity margin.

Mistake: Setting Target dissolved oxygen equal to or above Saturation dissolved oxygen, C* (mg/L).
Fix: Enter a target below C*. The model needs a positive concentration difference for oxygen transfer.

• The calculation uses a fixed kLa and a fixed C*. In a real reactor, both can change with agitation, gas flow, vessel geometry, pressure, gas composition, temperature, broth viscosity, cells, and antifoam.
• Use a kLa that applies to the actual process broth and operating conditions. A clean-water, vendor-estimated, or different-scale value can overstate or understate capacity.
• The model reports volumetric rates in mg/L/h. It does not calculate total oxygen transfer for the vessel because working volume is not entered.
• OUR must describe the same culture condition and time basis as the capacity check. A current OUR may be lower than a later peak OUR.
• If Calculated steady-state dissolved oxygen is shown as N/A, entered OUR exceeds Maximum modeled OTR at zero dissolved oxygen. There is no nonnegative steady-state dissolved-oxygen value in this model.
• This is a capacity estimate, not a replacement for dissolved-oxygen control data, off-gas analysis, or a validated process model.

Calculation method

The calculator first converts kLa to 1/h, converts a percent dissolved-oxygen target to mg/L using C*, and converts mmol/L/h OUR to mg/L/h using 31.9988 mg per mmol O2.

kLa_per_h = kLa_value, kLa_value * 60, or kLa_value * 3600

target_DO_mg_L = target_DO_value or C* * target_DO_value / 100

OUR_mg_L_h = OUR_value or OUR_value * 31.9988

The oxygen-transfer model uses the difference between saturation dissolved oxygen and target dissolved oxygen as the driving force.

OTR = kLa_per_h * (C* - target_DO_mg_L)

oxygen_capacity_margin = OTR - OUR_mg_L_h

required_kLa = OUR_mg_L_h / (C* - target_DO_mg_L)

steady_state_DO = C* - OUR_mg_L_h / kLa_per_h

maximum_OTR_at_zero_DO = kLa_per_h * C*

Worked example

With kLa = 100 1/h, C* = 8 mg/L, target dissolved oxygen = 2 mg/L, and OUR = 500 mg/L/h, the driving force is 6 mg/L. OTR is 600 mg/L/h, so the oxygen capacity margin is +100 mg/L/h. The kLa needed at that target is about 83.3 1/h, and the calculated steady-state dissolved oxygen is 3 mg/L.

The calculator blocks targets at or above C* because the driving force would be zero or negative. It also shows no physical steady-state dissolved-oxygen value when demand is greater than the modeled maximum OTR.