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.
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