Fermentation Respiration

Calculate OUR, CER, and RQ

Calculator

The global mass balance calculation requires a air flowmeter and an exit gas analyzer. The measurement can be performined online and continuously trended over the course of fermentation.

Gas In
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Exit Gas Analyzer
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Answer

This calculator find the oxygen uptake rate (OUR), carbion dioxide evolution rate (CER), and the repiratory quotent (RQ).


mmoles/hr
mmoles/hr
mmoles/L/hr
mmoles/L/hr
mmoles/L/hr

Example

Use a global mass balance to determine the respiration parameters (OUR, CER, RQ) of the organism in a bioreactor with an air flowrate of 60 nlph entering into a 1L working volume bioreactor with an exit gas analzyer displaying the following readings: O2: 18%, CO2: 2%.

Step 1: Calculate the molar air flowrate into the vessel

Use the ideal gas law. Normal flow is assumed to be 1 atm and 0°C. Standard flow is assumed to be 14.696 psia and 60°F.

PV˙=n˙RTP\dot{V} = \dot{n}RT
n˙=PV˙RT\dot{n} = \frac{P\dot{V}}{RT}
n˙=1atm⋅60nlph8.2∗10−5L⋅atmK⋅mmol⋅273.15K=2,677mmol/hr\dot{n} = \frac{1 atm ⋅ 60 nlph}{8.2*10^{-5} \frac{L⋅atm}{K⋅mmol} ⋅ 273.15K} = 2,677 mmol/hr

Step 2: Calculate oxygen uptake rate

Assume all nitrogen which enters the vessel exits through the vent. Use a nitrogen balance to determine the exit gas rate.

OUR=n˙⋅CinCO2−n˙out⋅CoutCO2VlOUR = \frac{\dot{n} ⋅ C_{in CO_{2}} - \dot{n}_{out} ⋅ C_{out CO_{2}}}{V_l}
n˙out=n˙⋅1−CinO2−CinCO21−CoutO2−CoutCO2\dot{n}_{out} = \dot{n} ⋅ \frac{1 - C_{in O_{2}}- C_{in CO_{2}}}{1 - C_{out O_{2}}- C_{out CO_{2}}}
OUR=n˙Vl(CinO2−1−CinO2−CinCO21−CoutO2−CoutCO2⋅CoutO2)OUR = \frac{\dot{n}}{V_l} (C_{in O_{2}} - \frac{1 - C_{in O_{2}}- C_{in CO_{2}}}{1 - C_{out O_{2}}- C_{out CO_{2}}} ⋅ C_{out O_{2}})
OUR=2,677mmol/hr1L(21%−1−0%−21%1−18%−2%⋅18%)OUR = \frac{2,677 mmol/hr}{1 L} (21\% - \frac{1 - 0\% - 21\%}{1 - 18\% - 2\%} ⋅ 18\% )
OUR=84.8mmol/L/hrOUR = 84.8 mmol/L/hr

Step 3: Calculate carbon dioxide evolution rate

CER=n˙outVl⋅(CoutCO2−CinCO2)CER = \frac{\dot{n}_{out}}{V_l} ⋅ (C_{out CO_{2}} - C_{in CO_{2}})
n˙out=n˙⋅1−CinO2−CinCO21−CoutO2−CoutCO2\dot{n}_{out} = \dot{n} ⋅ \frac{1 - C_{in O_{2}}- C_{in CO_{2}}}{1 - C_{out O_{2}}- C_{out CO_{2}}}
CER=n˙Vl⋅1−CinO2−CinCO21−CoutO2−CoutCO2⋅(CoutCO2−CinCO2)CER = \frac{\dot{n}}{V_l} ⋅ \frac{1 - C_{in O_{2}}- C_{in CO_{2}}}{1 - C_{out O_{2}}- C_{out CO_{2}}} ⋅ (C_{out CO_{2}} - C_{in CO_{2}})
CER=2,677mmol/hr1L⋅1−0%−21%1−18%−2%⋅(2%−0%)CER = \frac{2,677 mmol/hr}{1 L} ⋅ \frac{1 - 0\% - 21\%}{1 - 18\% - 2\%} ⋅ (2\% - 0\%)
CER=52.9mmol/L/hrCER = 52.9 mmol/L/hr

Step 4: Calculate respiratory quotent

RQ=CER/OURRQ = CER/OUR
RQ=52.9mmol/L/hr84.8mmol/L/hrRQ = \frac{52.9 mmol/L/hr}{84.8 mmol/L/hr}
RQ=0.62RQ = 0.62

Definitions

V˙=\dot{V} =
Volumetric air flowrate
C=C =
Volumetric concentration
P=P =
Pressure at standard conditions
T=T =
Temperature at standard conditions
R=R =
Ideal gas constant
n˙=\dot{n} =
Molar air flowrate in
n˙out=\dot{n}_{out} =
Molar air flowrate out
OUR=OUR =
Oxygen uptake rate
CER=CER =
Carbon dioxide evolution rate
OUR=OUR =
respiratory quotient