HW3_2011 - BME 339/ CHE 339/BIO 335 Fall 2011 Homework #3...

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Unformatted text preview: BME 339/ CHE 339/BIO 335 Fall 2011 Homework #3 Assigned: September 15, 2011 Due: Thursday, September 22, 2011 1. A value of kLa = 30 h‐1 has been determined for a fermenter at its maximum practical agitator rotational speed and with air being sparged at 0.5 L gas/1 reactor volume‐min. E. coli with a qO2 of 10 mmol O2/g‐dry wt‐h are to be cultured. The critical dissolved oxygen concentration is 0.2 mg/L. The solubility of oxygen from air in the fermentation broth is 7.3 mg/L at 30°C. a. What is the maximum concentration of E. coli that can be sustained in this fermenter under aerobic conditions? b. What concentration could be maintained if pure oxygen was used to sparge the reactor? (mole fraction of oxygen in air=0.21) 2. Consider a culture of bacteria making a valuable product in a chemostat operated at steady state. The liquid feed is sterile and contains 50 mM glucose (the limiting growth substrate S). In a series of steady state runs, the dilution rate D is increased incrementally, and the cell density exiting the chemostat is measured for each: D (h‐1) X (g/L) 0.05 1.58 0.10 2.17 0.15 2.47 0.20 2.65 0.25 2.76 0.30 2.83 0.35 2.86 0.40 2.84 0.45 2.74 0.50 2.25 0.52 1.32 0.53 0 a. Explain why the cell density can increase as the flow rate is increased, as shown here with D < 0.35 h‐1. b. Calculate the true yield coefficient, YTrue. c. At what dilution rate should you operate the chemostat to optimize productivity of a strictly growth‐associated product? Explain the basis for your answer. 3. A 10 liter jar contains 105 contaminating organisms/ml. The jar is to be sterilized by heating but unfortunately, the medium contains a limiting nutrient which is susceptible to thermal destruction. It is desired to carry out sterilization so that Nf=10‐3 (i.e. probability of contamination is 1:1,000). If sterilization is carried out at 140 °C, what fraction of the limiting nutrient will have been destroyed? Assume no destruction of spores and nutrients during heating or cooling. Activation energy for thermal death, Esterilization =67,700 cal/mole Arrhenius constant for thermal death, Asterilization= 1×1036 min‐1 Activation energy for nutrient decomposition, Enutrient=22,000 cal/mole Arrhemius constant for decomposition, Anutrient=2×1010 min‐1 R=1.987 cal/mole °K 4. An agitated batch bioreactor is aerated with O2‐containing gas (C in the gas phase = 10 mM). The equilibrium concentration of oxygen in the liquid is given by C ∗ = C /40. At a certain point during exponential phase, the dissolved oxygen concentration is C = 0.2 mM; when the sparging is turned off briefly, CL drops to 0.1 mM in 30 seconds. Estimate the value of kLa (s‐1). ...
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