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Baker's yeast (S. Cerevisiae) is grown in a large 800 L batch reactor according to the following balanced stoichiometri equation: C6H12O6 + 3 02 + 0.48 NH3 → 0.48 C6H10NO3 + 4.32 H2O + 3.12 CO₂ Glucose yeast cells It is desired to produce new yeast cells so that the yeast cell concentration in the batch reactor increases by 55 gdw/L during batch growth. A. Determine Yx/s for glucose and Yx/o₂ for oxygen. B. Determine the total mass of oxygen required to produce the desired mass of yeast cells. C. If the growth rate in the exponential phase is 0.89 gdw/L-h, what is the corresponding oxygen utilization rate (OUR) in g O₂/L-h in this phase? At what rate would O₂ need to be fed to the reactor (g O₂/h)? (For this part, assume that oxygen mass transfer (OTR) is rapid and does not limit growth)

Baker's yeast (S. Cerevisiae) is grown in a large 800 L batch reactor according to the following balanced stoichiometri equation: C6H12O6 + 3 02 + 0.48 NH3 → 0.48 C6H10NO3 + 4.32 H2O + 3.12 CO₂ Glucose yeast cells It is desired to produce new yeast cells so that the yeast cell concentration in the batch reactor increases by 55 gdw/L during batch growth. A. Determine Yx/s for glucose and Yx/o₂ for oxygen. B. Determine the total mass of oxygen required to produce the desired mass of yeast cells. C. If the growth rate in the exponential phase is 0.89 gdw/L-h, what is the corresponding oxygen utilization rate (OUR) in g O₂/L-h in this phase? At what rate would O₂ need to be fed to the reactor (g O₂/h)? (For this part, assume that oxygen mass transfer (OTR) is rapid and does not limit growth)

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Baker's yeast (S. Cerevisiae) is grown in a large 800 L batch reactor according to the following balanced stoichiometric equation: C6H12O6 + 3 02 + 0.48 NH3 → 0.48 C6H10 NO3 + 4.32 H₂O + 3.12 CO₂ Glucose yeast cells It is desired to produce new yeast cells so that the yeast cell concentration in the batch reactor increases by 55 gdw/L during batch growth. A. Determine Yx/s for glucose and Yx/o2 for oxygen. B. Determine the total mass of oxygen required to produce the desired mass of yeast cells. C. If the growth rate in the exponential phase is 0.89 gdw/L-h, what is the corresponding oxygen utilization rate (OUR) in g O₂/L-h in this phase? At what rate would O₂ need to be fed to the reactor (g O₂/h)? (For this part, assume that oxygen mass transfer (OTR) is rapid and does not limit growth) D. Using an equation in Chapter 6 (and given in the class notes) that relates heat generation to oxygen consumption, estimate the rate of heat removal required to keep the reactor isothermal and match the oxygen consumption rate in part C for exponential growth. Convert your answer to Watts. E. Starting with the equation for oxygen transfer rate (OTR = k₁a (C*-CL), where a is the total bubble surface area divided by the reactor volume), determine the total number of 0.13 mm diameter spherical bubbles that must be in the 800 L fermenter to meet the OUR requirements determined in part C during exponential growth. You may assume that dissolved oxygen saturates the broth as if it is at 30 °C in water at 1 atm (http://antoine.frostburg.edu/chem/senese/101/solutions/faq/predicting-DO.shtml can be used to find the saturation DO level). The oxygen mass transfer coefficient, KL, is 0.87 cm/s. You may assume to get the maximum oxygen transfer rate that C₁ = 0; recall the surface area of a sphere = 4 πr².
Transcribed Image Text:Baker's yeast (S. Cerevisiae) is grown in a large 800 L batch reactor according to the following balanced stoichiometric equation: C6H12O6 + 3 02 + 0.48 NH3 → 0.48 C6H10 NO3 + 4.32 H₂O + 3.12 CO₂ Glucose yeast cells It is desired to produce new yeast cells so that the yeast cell concentration in the batch reactor increases by 55 gdw/L during batch growth. A. Determine Yx/s for glucose and Yx/o2 for oxygen. B. Determine the total mass of oxygen required to produce the desired mass of yeast cells. C. If the growth rate in the exponential phase is 0.89 gdw/L-h, what is the corresponding oxygen utilization rate (OUR) in g O₂/L-h in this phase? At what rate would O₂ need to be fed to the reactor (g O₂/h)? (For this part, assume that oxygen mass transfer (OTR) is rapid and does not limit growth) D. Using an equation in Chapter 6 (and given in the class notes) that relates heat generation to oxygen consumption, estimate the rate of heat removal required to keep the reactor isothermal and match the oxygen consumption rate in part C for exponential growth. Convert your answer to Watts. E. Starting with the equation for oxygen transfer rate (OTR = k₁a (C*-CL), where a is the total bubble surface area divided by the reactor volume), determine the total number of 0.13 mm diameter spherical bubbles that must be in the 800 L fermenter to meet the OUR requirements determined in part C during exponential growth. You may assume that dissolved oxygen saturates the broth as if it is at 30 °C in water at 1 atm (http://antoine.frostburg.edu/chem/senese/101/solutions/faq/predicting-DO.shtml can be used to find the saturation DO level). The oxygen mass transfer coefficient, KL, is 0.87 cm/s. You may assume to get the maximum oxygen transfer rate that C₁ = 0; recall the surface area of a sphere = 4 πr².
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