## Biomass Estimation from OUR Measurement

### Biochemical Engineering

Problem Statement: Oxygen utilization rate (OUR) is measured on-line with an oxygen analyzer. Find the equation(s) you might use to estimate biomass concentration from OUR data in a batch bioreactor. Given 1) the following OUR data, 2) that the oxygen-to-biomass yield coefficient is 3 g biomass/g O2, and 3) that the maintenance coefficient is 0.1 g O2/g biomass; calculate the biomass concentration with time.

```   Time     OUR          Biomass Conc.
(h)   (g oxygen/L-h)  (g biomass/L)
-----------------------------------
0       0.01             0.1
1       0.02              ?
2       0.10              ?
3       0.20              ?
:        :                :
```

Solution:

```  OUR(t) = (1/Y)*dx(t)/dt + m*x(t)
which is rearranged to: dx(t)/dt = Y*(-m*x(t)+OUR(t))
Euler's approximation of dx/dt: (xi+1-xi)/(ti+1-ti)
Thus,
xi+1=xi+Y*(-m*xi+OURi)*(ti+1-ti)

Time     OUR          Biomass Conc.
(h)   (g oxygen/L-h)  (g biomass/L)
-----------------------------------
0       0.01             0.1
1       0.02             0.1 +3*(-0.1*0.1 +0.01)*(1-0)=0.1
2       0.10             0.1 +3*(-0.1*0.1 +0.02)*(2-1)=0.13
3       0.20             0.13+3*(-0.1*0.13+0.10)*(3-2)=0.39
:        :                :
```
This problem is similar to the following file.