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To calculate the minimum feed stock concentration use the following formula:
Cnc = (SI * Mrc * Vol) / (.8 * SI)
Dlv
Where:
SI = 2700 Sampling Interval in minutes.
Mrc = Maximum rate of change of the analyte concentration in the analyte’s
unit of measure per minute per liter of volume (e.g. g/min/L).
Vol
(Average controlled volume of reactor in Liters)
= (largest smallest volume)
2
Dlv = feed pump rate of delivery in liters/min.
NOTE: Cnc = correction feed stock concentration in the analyte’s unit of measure.
To calculate TPU use the following formula:
TPU = (1 / Cpdlv) * Vol
Where:
Cpdlv = Correction pump delivery rate in the analyte’s unit of measure per second
(e.g. mg/second, g/second, etc).
Vol
(Average controlled volume of reactor in Liters)
= (largest smallest volume)
2
NOTE: Time-Per-Unit error in seconds per unit of measure liter (e.g. 50 seconds/gram
liter).
Example:
You are trying to regulate a 5.0 Liter bioreactor at 1.00 g/L glucose concentration. The actual volume of
broth in the reactor is maintained at 3.5 Liters. You know from previous fermentations of that the
maximum consumption rate of glucose is approximately 28.5 g/L/hr. The feed pump delivery rate is 0.1
L/min. The 2700 sampling interval is 5 minutes.
The lowest acceptable concentration of glucose feedstock (Cnc) is calculated as follows:
Sampling Interval = SI = 5 minutes
Maximum rate of change = Mrc = 28.5 g/L/hr = 0.475 g/L/min.
Reaction Volume = Vol = 3.5 Liters
Feed pump delivery rate = Dlv = 0.1 L/min.
Minimum Glucose feedstock concentration = (Cnc)
Cnc = (SI * Mrc * Vol) / (.8 * SI)
Dlv
Cnc = (5 * 0.475 * 3.5) / (0.8 * 5)
0.1
Cnc = 8.3125 / 4.0 = 20.78 g/L glucose
0.1
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