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A chemostat is a continuous stirred tank bioreactor that can carry out fermentation of a plant cell culture. Its dynamic behavior can be described by the following equations: dX -= μX-DX dt ds dt ux YX/S -D(S-S,). X and S are the cell and substrate concentrations, respectively., and S, is the substrate feed concentration. The dilution rate D is defined as the feed flow rate divided by the bioreactor volume. D is the input, while the cell concentration X and substrate concentration S are the state variables. Typically, the rate of reaction is referred to as the specific growth rate u and is modeled by a Monod equation: HS Ks+S μ=- Assume μ = 0.20 hr¹, Ks = 1.0 g/L, and Yx/s = 0.5 g/g. Use a steady-state operating point of D = 0.1 hr¹, X = 2.25 g/L, S = 1.0 g/L, and S; = 10 g/L. Using linearization, derive a transfer function relating the deviation variables for cell concentration, X'(s), to the dilution rate, D'(s).

A chemostat is a continuous stirred tank bioreactor that can carry out fermentation of a plant cell culture. Its dynamic behavior can be described by the following equations: dX -= μX-DX dt ds dt ux YX/S -D(S-S,). X and S are the cell and substrate concentrations, respectively., and S, is the substrate feed concentration. The dilution rate D is defined as the feed flow rate divided by the bioreactor volume. D is the input, while the cell concentration X and substrate concentration S are the state variables. Typically, the rate of reaction is referred to as the specific growth rate u and is modeled by a Monod equation: HS Ks+S μ=- Assume μ = 0.20 hr¹, Ks = 1.0 g/L, and Yx/s = 0.5 g/g. Use a steady-state operating point of D = 0.1 hr¹, X = 2.25 g/L, S = 1.0 g/L, and S; = 10 g/L. Using linearization, derive a transfer function relating the deviation variables for cell concentration, X'(s), to the dilution rate, D'(s).

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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A chemostat is a continuous stirred tank bioreactor that can carry out fermentation of a plant cell culture. Its dynamic behavior can be described by the following equations: dx dt ds μ.Χ -D(S-S₂). dt Yx/s = µX - DX X and S are the cell and substrate concentrations, respectively., and S, is the substrate feed concentration. The dilution rate D is defined as the feed flow rate divided by the bioreactor volume. D is the input, while the cell concentration X and substrate concentration S are the state variables. Typically, the rate of reaction is referred to as the specific growth rate μ and is modeled by a Monod equation: HS Ks+S μ=. Assume μ = 0.20 hr¹, Ks =1.0 g/L, and Yx/s =0.5 g/g. Use a steady-state operating point of D = 0.1 hr¹, X = 2.25 g/L, S* = 1.0 g/L, and S; = 10 g/L. Using linearization, derive a transfer function relating the deviation variables for cell concentration, X'(s), to the dilution rate, D'(s).
Transcribed Image Text:A chemostat is a continuous stirred tank bioreactor that can carry out fermentation of a plant cell culture. Its dynamic behavior can be described by the following equations: dx dt ds μ.Χ -D(S-S₂). dt Yx/s = µX - DX X and S are the cell and substrate concentrations, respectively., and S, is the substrate feed concentration. The dilution rate D is defined as the feed flow rate divided by the bioreactor volume. D is the input, while the cell concentration X and substrate concentration S are the state variables. Typically, the rate of reaction is referred to as the specific growth rate μ and is modeled by a Monod equation: HS Ks+S μ=. Assume μ = 0.20 hr¹, Ks =1.0 g/L, and Yx/s =0.5 g/g. Use a steady-state operating point of D = 0.1 hr¹, X = 2.25 g/L, S* = 1.0 g/L, and S; = 10 g/L. Using linearization, derive a transfer function relating the deviation variables for cell concentration, X'(s), to the dilution rate, D'(s).
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