Dynamic Simulation of Continuous Fermentor

Biochemical Engineering

Problem Statement: The following equations describe a continuous bioreactor. 

  dx
  -- = (μ-D)*x
  dt

  ds              μ*x
  -- = D*(sf-s) - ---
  dt               Y

  where   u(s)=0.3*s/(50+s+0.01*s2)    Y(s)=0.004+0.001*s    sf=200
          s in (g/liter)  and  μ in (h-1)
Dynamically simulate the continuous fermentor at several operating conditions:

CaseDilution Rate
D (h-1) 		Substrate Feed
sf (g/L) 		Initial Conditions Comments
BiomassSubstrate
b 0.05 100 5 30 Reference
a 0.10 100 5 30 Increase D
c 0.01 100 5 30 Decrease D
d 0.05 200 5 30 Increase sf
e 0.05 50 5 30 Decrease sf
f 0.10 200 5 30 Increase both D & sf
g 0.05 200 3 30 Change I.C.
This problem tries to demonstrate several points. First, from Cases b and f, we see that steady-state is not always achieved; thus, the preceeding problem, which asks the maximum cell productivity with sf=200 g/L, is just an academic excercise. Second, from Cases f and g, we see that the bioreactor approaches different operating points depending on the initial condition; thus, how we start up a bioreactor may be important. Third, from Cases a and b, we see that high values of D tend to make this system oscillate more. Predicting the dynamic microbial behavior is not always intuitive even for a simple system. We see different behaviors from computer-aided dynamic simulation, and a mathematical package like Mathcad makes it easy for us to explore.

Solution:

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Biochemical Engineering -- Dynamic Simulation of Continuous Fermentor
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Nam Sun Wang
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