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A 20 L chemostat at 40 °C is used to grow bacterial cells that have the following parameters for the Monod equation: Hmax = 0.42 h¹ and Ks = 0.97 g S/L. The sterile feed has a concentration of 27.2 g/L of the limiting substrate, S, and the exit concentration of this substrate is 1.54 g/L. (Note: 1 L = 1000 cm³ and recall the assumption used when working with a CSTR or chemostat reactor that the concentrations inside the reactor are equal to the concentrations in the exit stream) Yields are known for the cells growing on the limiting substrate and oxygen are: Yx/s 0.43 g cells/g S (limiting substrate), and Yx/02 = 1.67 g cells/g 02 A. What is the specific growth rate, μ, for the cells in the reactor? B. Assuming the chemostat is operating at steady state such that D = μ, determine the flowrate, F, entering (and leaving) the reactor. C. What is the cell production rate, qx (g cells/h)? D. What is the oxygen utilization rate (OUR) in g 0₂/L-h?

A 20 L chemostat at 40 °C is used to grow bacterial cells that have the following parameters for the Monod equation: Hmax = 0.42 h¹ and Ks = 0.97 g S/L. The sterile feed has a concentration of 27.2 g/L of the limiting substrate, S, and the exit concentration of this substrate is 1.54 g/L. (Note: 1 L = 1000 cm³ and recall the assumption used when working with a CSTR or chemostat reactor that the concentrations inside the reactor are equal to the concentrations in the exit stream) Yields are known for the cells growing on the limiting substrate and oxygen are: Yx/s 0.43 g cells/g S (limiting substrate), and Yx/02 = 1.67 g cells/g 02 A. What is the specific growth rate, μ, for the cells in the reactor? B. Assuming the chemostat is operating at steady state such that D = μ, determine the flowrate, F, entering (and leaving) the reactor. C. What is the cell production rate, qx (g cells/h)? D. What is the oxygen utilization rate (OUR) in g 0₂/L-h?

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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8. A 20 L chemostat at 40 °C is used to grow bacterial cells that have the following parameters for the Monod equation: Hmax = 0.42 h¹ and Ks = 0.97 g S/L. The sterile feed has a concentration of 27.2 g/L of the limiting substrate, S, and the exit concentration of this substrate is 1.54 g/L. (Note: 1 L = 1000 cm³ and recall the assumption used when working with a CSTR or chemostat reactor that the concentrations inside the reactor are equal to the concentrations in the exit stream) Yields are known for the cells growing on the limiting substrate and oxygen are: Yx/s = 0.43 g cells/g S (limiting substrate), and Yx/02 = 1.67 g cells/g O₂ A. What is the specific growth rate, μ, for the cells in the reactor? B. Assuming the chemostat is operating at steady state such that D = μ, determine the flowrate, F, entering (and leaving) the reactor. C. What is the cell production rate, qx (g cells/h)? D. What is the oxygen utilization rate (OUR) in g O₂/L-h? E. Given the following data for oxygen transfer rate at 40 °C, will O₂ limit the cell production rate? Determine the saturation DO content, C* using the same website in problem 7: https://antoine.frostburg.edu/chem/senese/101/solutions/faq/predicting-DO.shtml) Minimum oxygen concentration (CL) for cell growth = 0.15 mg 02/L Oxygen mass transfer coefficient, k₁ = 3.85 cm/s There are 107 bubbles in the 20 L reactor at any time with a total surface area of 275 cm².
Transcribed Image Text:8. A 20 L chemostat at 40 °C is used to grow bacterial cells that have the following parameters for the Monod equation: Hmax = 0.42 h¹ and Ks = 0.97 g S/L. The sterile feed has a concentration of 27.2 g/L of the limiting substrate, S, and the exit concentration of this substrate is 1.54 g/L. (Note: 1 L = 1000 cm³ and recall the assumption used when working with a CSTR or chemostat reactor that the concentrations inside the reactor are equal to the concentrations in the exit stream) Yields are known for the cells growing on the limiting substrate and oxygen are: Yx/s = 0.43 g cells/g S (limiting substrate), and Yx/02 = 1.67 g cells/g O₂ A. What is the specific growth rate, μ, for the cells in the reactor? B. Assuming the chemostat is operating at steady state such that D = μ, determine the flowrate, F, entering (and leaving) the reactor. C. What is the cell production rate, qx (g cells/h)? D. What is the oxygen utilization rate (OUR) in g O₂/L-h? E. Given the following data for oxygen transfer rate at 40 °C, will O₂ limit the cell production rate? Determine the saturation DO content, C* using the same website in problem 7: https://antoine.frostburg.edu/chem/senese/101/solutions/faq/predicting-DO.shtml) Minimum oxygen concentration (CL) for cell growth = 0.15 mg 02/L Oxygen mass transfer coefficient, k₁ = 3.85 cm/s There are 107 bubbles in the 20 L reactor at any time with a total surface area of 275 cm².
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