che361_hw6 - Homework #6 ChE 361 Fall 2010 Consider a...

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Homework #6 ChE 361 Fall 2010 Consider a biochemical reactor where biomass and a desired product are produced by microbial growth from a single, rate limiting substrate. Denote the biomass concentration as X , the sub- strate concentration as S , and the product concentration as P . The substrate is continuously supplied to the bioreactor at volumetric flow rate F and concentration S i . A liquid stream is continuously removed from the bioreactor at volumetric flow rate F such that the liquid volume V remains constant. The specific growth rate has the form: μ ( S,P ) = μ m 1 - P P m · S K m + S + S 2 K i where the constants K i and P m reflect growth inhibition by high concentrations of substrate and product, respectively. The bioreactor is described by the following mass balance equations: dX dt = - DX + μ ( S,P ) X = f 1 ( X,S,P ) dS dt = D ( S f - S ) - 1 Y X/S μ ( S,P ) X = f 2 ( X,S,P ) dP dt = - DP + ( αμ ( S,P ) + β ) X = f 3 ( X,S,P ) where D = F/V . Consider the following parameter values:
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che361_hw6 - Homework #6 ChE 361 Fall 2010 Consider a...

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