Problem Statement: Find the steady-state dilution rate for a continuous bioreactor that maximizes cell productivity for the kinetic and operating parameters given below.

  dx
  -- = (μ-D)*x
  dt

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

  where   μ(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)

Solution:

• PDF Version (max-dx.pdf)
• Mathcad File (max-dx.mcd) -- d?/d?=0 terms not converging in v6.0.

However, dynamic simulation of this system shows that the bioreactor does not operate at a steady-state, rendering this steady-state calculation academic. We reach the same conclusion based on linearized stability analysis.

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Biochemical Engineering -- Optimial Dilution Rate for Maximum Cell Productivity
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Nam Sun Wang Department of Chemical & Biomolecular Engineering University of Maryland College Park, MD 20742-2111 301-405-1910 (voice) 301-314-9126 (FAX) e-mail: nsw@umd.edu ©1996-2007 by Nam Sun Wang