(a) Interpretation: The given model is to be linearized and deviation variables are to be introduced. Concept introduction: For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances. The process models generally include algebraic relationships which commence from thermodynamics , transport phenomena , chemical kinetics, and physical properties of the processes. The difference in the actual variable ( y ) and the original variable ( y ¯ ) is known as deviation variable ( y ′ ) . It is generally used while modelling a process. Mathematically it is defined as: y ′ = y − y ¯ In steady-state process, the accumulation in the process is taken as zero.

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Answer 1

Question

Chapter 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

In steady-state process, the accumulation in the process is taken as zero.

Interpretation Introduction

(b)

Interpretation:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

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Problem 2. For an irreversible liquid phase reaction A -> B, the reaction rate is of the first order with respect to the reactant concentration C_A. this reaction is performed in a cascade of two identical CSTRs at 100 degrees Celsius. (same reactor size and isothermal). The inlet concentration of A of the first CSTR is 2mol/L. The outlet concentration of A of the 2nd CSTR is 0.5 mol/L. the inlet flow rate of the 1st reactor is 100 L/h. and the feed temperature is 20 degrees Celsius. The average heat capacity of the reactant/product/solvent mixture is a constant: 2J/g*K, the density of the mixture is a constant: 1 kg/L. The heat of reaction is 50 kJ/mol (exothermic). The reaction rate constant at 100 degrees Celsius is 0.5/h. (a) Determine the outlet concentration of A of the first CSTR (b) What is the heat transfer requirement for the first CSTR? (c) if this reaction is performed in a plug-flow reactor, what is the size of plug-flow reactor required for achieving the same conversion…

The energy release (Q_g) and energy loss (Q_r) curves of an irreversible oxidation reaction are shown below. Q_r curves can be shifted by adjusting the feed temperature. Q,& QE E Qg (a) Are these points of intersection between energy release and energy loss curves stable operating conditions? Point of Intersection A Stable or Unstable B A D T (b) Which point represents the ignition condition? B с D E F G

Problem 1. For an irreversible liquid phase reaction 2A -> B, the reaction rate is of the 2nd order with respect to the reactant concentration CA. The concentration-dependent reaction rate is plotted below. This reaction is performed in a cascade of two identical CSTRS (same reactor size and temperature). The inlet concentration of A of the 1st CSTR is 2 mol/L. The outlet concentration of A of the 2nd CSTR is 1 mol/L. The inlet flow rate of the 1st reactor is 100 L/h. Please use the graphical method to determine the outlet concentration of A of the first CSTR and the size of each CSTR. Please briefly show the procedure for reactor size calculation. (-4-7) 15225050 45 40 35 30 0 0.5 11.761.5 C₂ Q C (mol.L¹) Co 20 2.5

Answer 2

Question

Chapter 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

In steady-state process, the accumulation in the process is taken as zero.

Interpretation Introduction

(b)

Interpretation:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

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Answer 3

Question

Chapter 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

In steady-state process, the accumulation in the process is taken as zero.

Interpretation Introduction

(b)

Interpretation:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

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Answer 4

Question

Chapter 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

In steady-state process, the accumulation in the process is taken as zero.

Interpretation Introduction

(b)

Interpretation:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

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Answer 5

Chapter 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

In steady-state process, the accumulation in the process is taken as zero.

Interpretation Introduction

(b)

Interpretation:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Answer 6

Chapter 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

In steady-state process, the accumulation in the process is taken as zero.

Answer 7

Chapter 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

In steady-state process, the accumulation in the process is taken as zero.

Answer 8

Interpretation Introduction

(b)

Interpretation:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Answer 9

Interpretation Introduction

(b)

Interpretation:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Answer 10

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Answer 13

Ch. 4 - Prob. 4.1E Ch. 4 - Prob. 4.2E Ch. 4 - Prob. 4.3E Ch. 4 - Prob. 4.4E Ch. 4 - Prob. 4.5E Ch. 4 - A stirred-tank blending system can be described by...Ch. 4 - Prob. 4.7E Ch. 4 - Prob. 4.8E Ch. 4 - Prob. 4.9E Ch. 4 - Prob. 4.10E

Solution Summary: The author explains the linearization of a given model and the introduction of deviation variables for chemical processes.

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Chapter 4 Solutions