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There is a heated continuous stirred tank reactor shown below where the density is constant through out the system. On the other hand the volume of reaction mixture may vary. The thermal capacitance of the coil used to heat the tank is assumed to be negligible. There is a 2nd order elementary chemical reaction 2A → C taking place in the reactor. Cai Tai qa 2A ->C v ro Tc Ac In the figure shown above Cai, Tai,qa is the inlet concentration of component A , inlet stream temperature and inlet volumetric flow rate, V is the volume of the reaction mixture, ro is the density through out the system. Tc, Ac and U are the coil temperature, surface area of the coil and heat transfer coefficient of the coil. Cc, T and Ca are the concentration of product C, temperature of the reactor and exit concentration of component A, qc is the outlet volumetric flowrate. The rate constant is assumed to be independent of temperature denoted as ko. The heat of reaction is denoted as AHrxn. Cp is the heat capacity of component A, C and reaction mixture. Assume that the density is constant but volume of the tank is variable (cross sectional area of the reactor tank is A) and thermal capacitance of coil is negligible. a) Write down all possible balances for this system, perform a degree of freedom analysis and classify the variables for the control system you propose

There is a heated continuous stirred tank reactor shown below where the density is constant through out the system. On the other hand the volume of reaction mixture may vary. The thermal capacitance of the coil used to heat the tank is assumed to be negligible. There is a 2nd order elementary chemical reaction 2A → C taking place in the reactor. Cai Tai qa 2A ->C v ro Tc Ac In the figure shown above Cai, Tai,qa is the inlet concentration of component A , inlet stream temperature and inlet volumetric flow rate, V is the volume of the reaction mixture, ro is the density through out the system. Tc, Ac and U are the coil temperature, surface area of the coil and heat transfer coefficient of the coil. Cc, T and Ca are the concentration of product C, temperature of the reactor and exit concentration of component A, qc is the outlet volumetric flowrate. The rate constant is assumed to be independent of temperature denoted as ko. The heat of reaction is denoted as AHrxn. Cp is the heat capacity of component A, C and reaction mixture. Assume that the density is constant but volume of the tank is variable (cross sectional area of the reactor tank is A) and thermal capacitance of coil is negligible. a) Write down all possible balances for this system, perform a degree of freedom analysis and classify the variables for the control system you propose

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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There is a heated continuous stirred tank reactor shown below where the density is constant through out the system. On the other hand the volume of reaction mixture may vary. The thermal capacitance of the coil used to heat the tank is assumed to be negligible. There is a 2nd order elementary chemical reaction 2A → C taking place in the reactor. Cai Tai qa 2A ->C v „ro Tc Ac In the figure shown above Cai, Tai,qa is the inlet concentration of component A , inlet stream temperature and inlet volumetric flow rate, V is the volume of the reaction mixture, ro is the density through out the system. Tc, Ac and U are the coil temperature, surface area of the coil and heat transfer coefficient of the coil. Cc, T and Ca are the concentration of product C, temperature of the reactor and exit concentration of component A, qc is the outlet volumetric flowrate. The rate constant is assumed to be independent of temperature denoted as ko. The heat of reaction is denoted as AHrxn. Cp is the heat capacity of component A, C and reaction mixture. Assume that the density is constant but volume of the tank is variable (cross sectional area of the reactor tank is A) and thermal capacitance of coil is negligible. a) Write down all possible balances for this system, perform a degree of freedom analysis and classify the variables for the control system you propose b) Construct a state space model for this system symbolically. c) Determine T'(s)/qa'(s), Cc'(s)/Cai'(s) d) If there is a negative unit step change in qa derive T'(t)
Transcribed Image Text:There is a heated continuous stirred tank reactor shown below where the density is constant through out the system. On the other hand the volume of reaction mixture may vary. The thermal capacitance of the coil used to heat the tank is assumed to be negligible. There is a 2nd order elementary chemical reaction 2A → C taking place in the reactor. Cai Tai qa 2A ->C v „ro Tc Ac In the figure shown above Cai, Tai,qa is the inlet concentration of component A , inlet stream temperature and inlet volumetric flow rate, V is the volume of the reaction mixture, ro is the density through out the system. Tc, Ac and U are the coil temperature, surface area of the coil and heat transfer coefficient of the coil. Cc, T and Ca are the concentration of product C, temperature of the reactor and exit concentration of component A, qc is the outlet volumetric flowrate. The rate constant is assumed to be independent of temperature denoted as ko. The heat of reaction is denoted as AHrxn. Cp is the heat capacity of component A, C and reaction mixture. Assume that the density is constant but volume of the tank is variable (cross sectional area of the reactor tank is A) and thermal capacitance of coil is negligible. a) Write down all possible balances for this system, perform a degree of freedom analysis and classify the variables for the control system you propose b) Construct a state space model for this system symbolically. c) Determine T'(s)/qa'(s), Cc'(s)/Cai'(s) d) If there is a negative unit step change in qa derive T'(t)
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