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Unformatted text preview: Homework 5: Due Wednesday, Oct. 20th Chemical Engineering 170A: Biochemical Engineering Question 1. Bacterial Growth A simple, batch fermentation of an aerobic bacterium growing on methanol gave the results shown in the table: Time (h) 0 1 2 4 6 8 9 10 11 12 13 14 16 18 Plot the biomass concentration and label the phases of growth in the plot Find the maximum specific growth rate, μmax. Find the yield on substrate, YX/S and YP/S. Find the saturation constant KS. Find the specific growth rate at t = 10 hr. What maximum cell concentration would one expect in 20 g of methanol were used with the same size inoculum? How much product would be produced? Question 2. Hydrolysis of BAEE by Ficin Blanch and Clark Ch 4 Problem 6. Question 3. Consider the following experimental setup for biomass production in a chemostat, in which a fraction of the exit stream, α, is recycled to the (sterile) feed stream. The consumption of substrate follows Monod kinetics, and there is no extracellular product. a) b) c) d) e) f) X (g/l) 0.2 0.205 0.222 0.335 0.55 0.92 1.33 1.9 2.6 3.55 4.7 5.6 6.15 6.2 S (g/l) 9.23 9.22 9.21 9.07 8.75 8.03 7.64 6.8 5.7 4.6 2.5 0.92 0.077 0 P 0.00 0.00 0.01 0.04 0.12 0.27 0.51 0.87 1.36 1.99 2.57 2.89 2.92 2.92 Write the steady state mass balances for X and S in the reactor, making no assumptions about the composition of the recycle stream. b) Using the S balance from part (a), derive an expression for X at steady state. c) Using the X balance from part (a) derive an expression for μ/D at steady state. d) Show that, in the absence of a recycle stream, these expressions reduce to those we derived in class for Xss and Sss for a single chemostat. Question 4. One method to model the production of secondary metabolites is to incorporate the concept of cell age into the model. We can consider two age groups of cells: “mature” cells capable of product synthesis and “immature” cells unable to form product. The growth rate of a mature cell into two immature cells is described by Monod type kinetics. Immature cells age at a first order rate (with first order rate constant a12) to form mature cells.
a) Maturation Rate a12, constant Immature Cells Mature Cells Cell Doubling Immature Cells Product Assume that the rate of product formation is first order with respect to the concentration of mature cells. Denoting the immature cell concentration as Xi,the concentration of mature cells as Xm, and the product as P write, mass balances for the unsteady state concentration of Xi, Xm, and P in a constant volume, batch culture. b) Is this model structured or unstructured? Is the model segregated or unsegregated?
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This note was uploaded on 01/28/2011 for the course CHE 170A taught by Professor Blanche during the Spring '10 term at Berkeley.
 Spring '10
 BLANCHE
 Biochemical Engineering

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