Problem Statement: A batch fermentation generated the following data.
------------------------ Time biomass Substrate (hr) (g/L) (g/L) ------------------------ 0 0.1 10.0 1 0.15 9.9 2 0.2 9.8 3 0.25 9.7 4 0.68 8.8 5 1.8 6.5 5.5 3.0 4.1 6 5.0 0.2 7 5.3 0 8 5.3 0 ------------------------Estimate the length of the lag phase, specific growth rate, doubling time, and substrate-to-cell yield coefficient. What about the saturation constant (Ks) in the Monod model?
Solution:
The first four points have a linear, rather than exponential,
increase in the biomass concentration; therefore, the lag phase
lasted for the first three hours. We can draw a line through the
semilog plot of biomass versus time to find the specific growth
rate. Alternatively it is:
ln(x/x0)=μ*(t-t0)
ln(5.0/0.25)=μ*(6-3)
Thus, μ=1 hr-1
Doubling time = ln(2)/μ = 0.69 hr
Yield = (5.3-0.1 g biomass)/(10g substrate) = 0.52 g biomass/g substrate
The saturation constant (Ks) in the Monod model cannot
be reliably determined from batch data.
Estimate Growth and Yield Parameters from Batch Fermentation Data
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