che446_10_hw3 - Homework #3 ChE 446 Fall 2010 Consider a...

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Homework #3 ChE 446 Fall 2010 Consider a continuous biochemical reactor in which two cell populations compete for a common rate limiting substrate. Let X , Y , and S denote the mass concentrations of the first cell population, the second cell population, and the substrate, respectively. The specific growth rates of the first cell population ( μ X ) and the second cell population ( μ Y ) are assumed to follow Michaelis–Menten kinetics: μ X ( S ) = μ max X S K X + S μ Y ( S ) = μ max Y S K Y + S The yield parameters ( Y X , Y Y ) associated with cell growth are assumed to be constant. The feed stream to the reactor has volumetric flow rate F and substrate mass concentration S i . The reactor has constant volume V and density ρ . The dynamic model equations are: dX dt = - DX + μ X ( S ) X dY dt = - DY + μ Y ( S ) Y dS dt = D ( S i - S ) - μ X ( S ) X Y X - μ Y ( S ) Y Y Y where the dilution rate is D = F/V . Define the cell concentration ratio as r = X X + Y . Consider the following model parameters:
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che446_10_hw3 - Homework #3 ChE 446 Fall 2010 Consider a...

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