Homework+6 - Homework 6: Due Wednesday, Nov. 3rd ...

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Unformatted text preview: Homework 6: Due Wednesday, Nov. 3rd Chemical Engineering 170A: Biochemical Engineering Question 1. A pharmaceutical company is having problems with the production of its new drug “Remembrex”. Over the last several weeks there has been consistent contamination in the batch tank. a) Calculate the time required to obtain a concentration of “Remembrex” of 10mg/mL in batch fermentation. Assume the product is growth associated. μ= 0.6 hr ­1; YP/X = 0.001 g “Remembrex” per g of cell. Initial cell concentration is 0.05 g cell/mL. b) Now derive an expression for P(t) assuming the kinetics of product formation depend on both the growth rate and biomass concentration (i.e., mixed product formation). Otherwise use the same assumptions as in part a. Question 2. Opps! Aerobic microbial cells are growing in a 600 L batch reactor. The air is accidentally shut off. At the time of the air going off, the cell density was 80 gdw/L and CO2 was 7 mg/L. If the critical CO2 (below which the cells die) is 1 mg/L, how long can the cells survive? Additional Data: € kLa = 10 hr ­1 qO2 = 1 mg O2 / gdw ­hr * = 10 mg/L CO2 € Question 3. Flocculent Fungi Fun € We wish to culture the filamentous Arthrographis cuboidea, a mold that produces the cotton ­candy pink stain 5,8 ­dihydroxy ­2,7 ­dimethoxy ­1,4 ­naphthalenedione. Like many molds, A. cuboidea grows in spherical pellets called flocs. In such a case, the growth ­limiting substrate must diffuse into the pellet before A. cuboidea can consume it. In this problem we will analyze the consumption of substrate and the effectiveness factor of the pellet for a spherical floc. Assume that a dimensionless material balance can be written in the following form: d2 S 2 d S φ2 S + = 2 d r r d r 1 + β⋅ S S r So S = r = β = Ro KS So € (a) Assuming the Monod model applies, what is the mathematical definition of ϕ in the equation above? (b) In many cases, substrate consumption can be assumed to be zero ­order in substrate, S (i.e., at values of S >> KS). Under these circumstances, the solution to the above mass balance is: µX S = So − max R 2 − r 2 6Deff YX / S ( ) Furthermore, the substrate concentration S is often zero at a certain radial distance from the center of the floc. We will call this distance the critical radius, rcr. In this € case, the limiting substrate is consumed only in an outer shell of the floc. Given the assumption of zero ­order kinetics, write an expression for the rate of substrate consumption by a single floc (the units of this rate are mols of S per unit time). Your expression should include the radius of the floc, R, and rcr, among other parameters. (c) Now write an expression for the effectiveness factor, η, in terms of the critical radius rcr and the radius of the floc, R. (The actual value of the critical radius can be determined by setting r = 0 in the equation for S above, but we are not asking you to do this.) Question 4. Methane Production in Continuous Culture (Blanch and Clark Ch. 5 Prob. 5) Consider the thermophilic methanogen, Methanococcus jannaschii, grown in continuous culture at steady state. M. jannaschii produces methane according to the overall stoichiometric equation: 4H2 + CO2 CH4 + 2H2O The gaseous substrates, H2 and CO2 are supplied in the entering gas streams, and the product methane is removed in the exiting gas stream. a) Write unsteady state mass balances for hydrogen and methane in both the gas and liquid phases. Write an unsteady state mass balance for biomass. b) In practice, a readily measurable parameter is pCH 4 , the partial pressure of CH4 in the exiting gas stream. Assuming steady state and neglecting the loss of methane in the exiting liquid phase, derive an expression for the specific methane production rate [  ­1 qCH 4 , in moles CH4 (cell ­hr) ] in terms of pCH 4 , Q (the volumetric gas flow rate), VL € (the liquid volume), and X (the steady state biomass concentration). € € ...
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