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A continuous stirred tank reactor is used to break down a chemical in an irreversible first-order reaction. The reactor has a volume of 10 m³ and nominal inlet and outlet concentrations of the chemical of 5 kg m-³ and 0.1 kg m-³ respectively. The flowrate through the reactor is perfectly controlled at 0.5 m³ h-¹. a) Derive a dynamic model for the reactor. b) By considering steady state, calculate the reaction rate constant. c) Using deviation variables, derive the response when the inlet concentration increase in a step by 1 kg m-³.

A continuous stirred tank reactor is used to break down a chemical in an irreversible first-order reaction. The reactor has a volume of 10 m³ and nominal inlet and outlet concentrations of the chemical of 5 kg m-³ and 0.1 kg m-³ respectively. The flowrate through the reactor is perfectly controlled at 0.5 m³ h-¹. a) Derive a dynamic model for the reactor. b) By considering steady state, calculate the reaction rate constant. c) Using deviation variables, derive the response when the inlet concentration increase in a step by 1 kg m-³.

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
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1. A continuous stirred tank reactor is used to break down a chemical in an irreversible first-order reaction. The reactor has a volume of 10 m³ and nominal inlet and outlet concentrations of the chemical of 5 kg m-³ and 0.1 kg m-³ respectively. The flowrate through the reactor is perfectly controlled at 0.5 m³ h-¹. a) Derive a dynamic model for the reactor. b) By considering steady state, calculate the reaction rate constant. c) Using deviation variables, derive the response when the inlet concentration increase in a step by 1 kg m-³.
Transcribed Image Text:1. A continuous stirred tank reactor is used to break down a chemical in an irreversible first-order reaction. The reactor has a volume of 10 m³ and nominal inlet and outlet concentrations of the chemical of 5 kg m-³ and 0.1 kg m-³ respectively. The flowrate through the reactor is perfectly controlled at 0.5 m³ h-¹. a) Derive a dynamic model for the reactor. b) By considering steady state, calculate the reaction rate constant. c) Using deviation variables, derive the response when the inlet concentration increase in a step by 1 kg m-³.
1. Most managed this question well: a) Derive a dynamic model for the reactor. The model is the same as the one we found during the lecture. b) By considering steady state, calculate the reaction rate constant. Set the accumulation term to zero for steady-state. Sub in the steady-state values of concentration that were provided and rearrange for k. Pay attention that the units of k are consistent with the order of reaction. Ꮎ = V F = 20 h k = c* (t) 1 Cin - Css Ꮎ Css c) Using deviation variables, derive the response when the inlet concentration increase in a step by 1 kg m-³. = Again the solution is the one we obtained during the lecture, although in this case with specific numerical values for the time constant and steady-state gain. 1 50 4.9 0.1 × 20 = 2.45 h-¹ [1 - exp(-2.5t)]
Transcribed Image Text:1. Most managed this question well: a) Derive a dynamic model for the reactor. The model is the same as the one we found during the lecture. b) By considering steady state, calculate the reaction rate constant. Set the accumulation term to zero for steady-state. Sub in the steady-state values of concentration that were provided and rearrange for k. Pay attention that the units of k are consistent with the order of reaction. Ꮎ = V F = 20 h k = c* (t) 1 Cin - Css Ꮎ Css c) Using deviation variables, derive the response when the inlet concentration increase in a step by 1 kg m-³. = Again the solution is the one we obtained during the lecture, although in this case with specific numerical values for the time constant and steady-state gain. 1 50 4.9 0.1 × 20 = 2.45 h-¹ [1 - exp(-2.5t)]
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