Estimate Growth and Yield Parameters from Batch Fermentation Data

Biochemical Engineering

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