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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: Y X/S = 0.4 g/g, α = 2.0 g/g, β = 0.2 hr - 1 , μ m = 0.50 hr - 1 , P m = 50 g/L, K m = 1.0 g/L, K i
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