You will need this information to work with:
Yearly requirement of product
Fermentation yield Yf
Down stream processing yield Yd/p
Fermentation time
Cleaning and sterilization time
Down time (days when the plant shuts off)
Failure rate
Working bioreactor volume
Start by calculating the working days by subtracting the down time from 365 days.
Calculate 1 cycle duration = cleaning and sterilization time + fermentation time.
Calculate the number of cycles per year (working days)/(cycle duration)
Insert the following values into the equation:
(yearly requirement of product)/( Yf * Yd/p * number of cycles) = fermentation volume for each fermentation
Number of bioreactors = (cycle volume/ bioreactor volume)
To take into account the failure rate
(number of bioreactors)/(1-(failure rate in%/100)