8/18/2019 Fogler chapter 4 notes http://slidepdf.com/reader/full/fogler-chapter-4-notes 1/19 2/9/2016 Chapter 4 Summary Notes http://www.umich.edu/~elements/fogler&gurmen/html/course/lectur es/four/index.htm#test1b 4. ALGORITHMFOR I SOTHERMAL R EACTOR D ESIGN * Topics Part 1: Mole Balances in Terms of Conversion 1. Algorithm for Isothermal Reactor Design 2. Applications/Examples of CRE Algorithm 3. Reversible Reactions 4. ODE (Polymath) Solutions to CRE Problems 5. General Guidelines for California Problems 6. PBR with Pressure Drop 7. Engineering Analysis Part 2: Measures Other Than Conversion 1. Measures Other Than Conversion 2. Membrane Reactors 3. Semibatch Reactors Part 1: Mole Balances in Terms of Conversion 1. Algorithm for Isothermal Reactor Design top
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Visual Encyclopedia of Reaction Engineering Equipment
44 Gas Phase Reaction Example
CSTR and PFR Example
41 Calculate V for a Zero-Order Reaction
3 Reversible Reactions top
To determine the conversion or reactor volume for reversible reactions one must first calculate the maximum conversionthat can be achieved at the isothermal reaction temperature which is the equilibrium conversion (See Example 3-8 in thetext for additional coverage of equilibrium conversion in isothermal reactor design)
45 Calculate Equilibrium Conversion (Xe) for a Constant Volume System
Example Determine Xe for a PFR with no pressure drop P = P0
Given that the system is gas phase and isothermal determine the reactor volume when X = 08 Xe
Reaction Additional Information
CA0 = 02 moldm3
KC = 100 dm3 mol
k = 2 dm3 mol-min
FA0 = 5 molmin
First calculate Xe
Xe = 089
X = 08Xe = 0711
One could then use Polymath to determine the volume of the PFR The corresponding Polymath program is
shown below
4 ODE (Polymath) Solutions to CRE Problems top
Algorithm Steps Polymath Equations
Mole Balance d(X)d(V) = -rAF A0
Rate Law rA = -k((CA2)-(CBKC))
Stoichiometry CA = (CA0(1-X))(1+epsX)
CB = (CA0X)(2(1+epsX))
Parameter Evaluation eps = -05 CA0 = 02 k = 2
FA0 = 5 KC = 100
Initial and Final Values X0 = 0 V0 = 0 Vf = 500
Polymath Screen Shots
Equations
Plot of X vs V
Results in Tabular Form
A volume of 94 dm
3
(rounding up from slightly more than 93 dm
3
) appears to be our answer
46 Batch Reactor With a Reversible Reaction
5 General Guidelines for California Problems top
Every state has an examination engineers must pass to become a registered professional engineer In the past there havetypically been six problems in a three hour segment of the California Professional Engineers Exam Consequently one shouldbe able to work each problem in 30 minutes or less Many of these problems involve an intermediate calculation todetermine the final answer
1 group unknown parametersvalues on the same side of the equation example
[unknowns] = [knowns]
2 look for a Case 1 and a Case 2 (usually two data points) to make intermediate calculations3 take ratios of Case 1 and Case 2 to cancel as many unknowns as possible
4 carry all symbols to the end of the manipulation before evaluating UNLESS THEY ARE ZERO
California Professional Engineers Registration Problem
47 Batch Reactor Optimization
6 PBR with Pressure Drop top
Note Pressure drop does NOT affect liquid phase reactions
Sample Question
Analyze the following second order gas phase reaction that occurs isothermally in a PBR
Mole Balance
Must use the differential form of the mole balance to separate variables
Rate Law
Second order in A and irreversible
Stoichiometry
Isothermal T = T0
Combine
Need to find (PP0) as a function of W (or V if you have a PFR)
The two expressions are coupled ordinary differential equations We can solve them simultaneously usingan ODE solver such as Polymath For the special case of isothermal operation and epsilon = 0 we canobtain an analytical solution
Polymath will combine the mole balance rate law and stoichiometry
Analytical Solution [e] PFR with
CAUTION Never use this form if
Combine
Solve
Could now solve for X given W or for W given X
For gas phase reactions as the pressure drop increases the concentration decreases resulting in a decreased rate of reaction hence a lower conversion when compared to a reactor without a pressure drop
weight there is a greater external surgace area for smaller particles than larger particles Therefore there are more entryways into the catalyst particle
In CD-ROM chapter 12 we will learn that effectiveness factor decreases as the particle size increases
7 Engineering Analysis - Critical Thinking and Creative Thinking top
We want to learn how the various parameters (particle diameter porosity etc) affect the pressure drop and henceconversion We need to know how to respond to What if questions such as
If we double the particle size decrease the porosity by a factor of 3 and double the pipe size what will happen
to D P and X
(See Critical Thinking in Preface page xx eg Questions the probe consenquences)
To answer these questions we need to see how a varies with these parameters
Turbulent Flow
Compare Case 1 and Case 2
For example Case 1 might be our current situation and Case 2 might be the parameters we want to change to
For constant mass flow through the system = constant
Laminar Flow
45 Effect of Reducing Particle Size on Conversion in a PBR
Here are more links to example problems dealing with packed bed reactors Again you could also use these problems asself tests
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
Visual Encyclopedia of Reaction Engineering Equipment
44 Gas Phase Reaction Example
CSTR and PFR Example
41 Calculate V for a Zero-Order Reaction
3 Reversible Reactions top
To determine the conversion or reactor volume for reversible reactions one must first calculate the maximum conversionthat can be achieved at the isothermal reaction temperature which is the equilibrium conversion (See Example 3-8 in thetext for additional coverage of equilibrium conversion in isothermal reactor design)
45 Calculate Equilibrium Conversion (Xe) for a Constant Volume System
Example Determine Xe for a PFR with no pressure drop P = P0
Given that the system is gas phase and isothermal determine the reactor volume when X = 08 Xe
Reaction Additional Information
CA0 = 02 moldm3
KC = 100 dm3 mol
k = 2 dm3 mol-min
FA0 = 5 molmin
First calculate Xe
Xe = 089
X = 08Xe = 0711
One could then use Polymath to determine the volume of the PFR The corresponding Polymath program is
shown below
4 ODE (Polymath) Solutions to CRE Problems top
Algorithm Steps Polymath Equations
Mole Balance d(X)d(V) = -rAF A0
Rate Law rA = -k((CA2)-(CBKC))
Stoichiometry CA = (CA0(1-X))(1+epsX)
CB = (CA0X)(2(1+epsX))
Parameter Evaluation eps = -05 CA0 = 02 k = 2
FA0 = 5 KC = 100
Initial and Final Values X0 = 0 V0 = 0 Vf = 500
Polymath Screen Shots
Equations
Plot of X vs V
Results in Tabular Form
A volume of 94 dm
3
(rounding up from slightly more than 93 dm
3
) appears to be our answer
46 Batch Reactor With a Reversible Reaction
5 General Guidelines for California Problems top
Every state has an examination engineers must pass to become a registered professional engineer In the past there havetypically been six problems in a three hour segment of the California Professional Engineers Exam Consequently one shouldbe able to work each problem in 30 minutes or less Many of these problems involve an intermediate calculation todetermine the final answer
1 group unknown parametersvalues on the same side of the equation example
[unknowns] = [knowns]
2 look for a Case 1 and a Case 2 (usually two data points) to make intermediate calculations3 take ratios of Case 1 and Case 2 to cancel as many unknowns as possible
4 carry all symbols to the end of the manipulation before evaluating UNLESS THEY ARE ZERO
California Professional Engineers Registration Problem
47 Batch Reactor Optimization
6 PBR with Pressure Drop top
Note Pressure drop does NOT affect liquid phase reactions
Sample Question
Analyze the following second order gas phase reaction that occurs isothermally in a PBR
Mole Balance
Must use the differential form of the mole balance to separate variables
Rate Law
Second order in A and irreversible
Stoichiometry
Isothermal T = T0
Combine
Need to find (PP0) as a function of W (or V if you have a PFR)
The two expressions are coupled ordinary differential equations We can solve them simultaneously usingan ODE solver such as Polymath For the special case of isothermal operation and epsilon = 0 we canobtain an analytical solution
Polymath will combine the mole balance rate law and stoichiometry
Analytical Solution [e] PFR with
CAUTION Never use this form if
Combine
Solve
Could now solve for X given W or for W given X
For gas phase reactions as the pressure drop increases the concentration decreases resulting in a decreased rate of reaction hence a lower conversion when compared to a reactor without a pressure drop
weight there is a greater external surgace area for smaller particles than larger particles Therefore there are more entryways into the catalyst particle
In CD-ROM chapter 12 we will learn that effectiveness factor decreases as the particle size increases
7 Engineering Analysis - Critical Thinking and Creative Thinking top
We want to learn how the various parameters (particle diameter porosity etc) affect the pressure drop and henceconversion We need to know how to respond to What if questions such as
If we double the particle size decrease the porosity by a factor of 3 and double the pipe size what will happen
to D P and X
(See Critical Thinking in Preface page xx eg Questions the probe consenquences)
To answer these questions we need to see how a varies with these parameters
Turbulent Flow
Compare Case 1 and Case 2
For example Case 1 might be our current situation and Case 2 might be the parameters we want to change to
For constant mass flow through the system = constant
Laminar Flow
45 Effect of Reducing Particle Size on Conversion in a PBR
Here are more links to example problems dealing with packed bed reactors Again you could also use these problems asself tests
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
Visual Encyclopedia of Reaction Engineering Equipment
44 Gas Phase Reaction Example
CSTR and PFR Example
41 Calculate V for a Zero-Order Reaction
3 Reversible Reactions top
To determine the conversion or reactor volume for reversible reactions one must first calculate the maximum conversionthat can be achieved at the isothermal reaction temperature which is the equilibrium conversion (See Example 3-8 in thetext for additional coverage of equilibrium conversion in isothermal reactor design)
45 Calculate Equilibrium Conversion (Xe) for a Constant Volume System
Example Determine Xe for a PFR with no pressure drop P = P0
Given that the system is gas phase and isothermal determine the reactor volume when X = 08 Xe
Reaction Additional Information
CA0 = 02 moldm3
KC = 100 dm3 mol
k = 2 dm3 mol-min
FA0 = 5 molmin
First calculate Xe
Xe = 089
X = 08Xe = 0711
One could then use Polymath to determine the volume of the PFR The corresponding Polymath program is
shown below
4 ODE (Polymath) Solutions to CRE Problems top
Algorithm Steps Polymath Equations
Mole Balance d(X)d(V) = -rAF A0
Rate Law rA = -k((CA2)-(CBKC))
Stoichiometry CA = (CA0(1-X))(1+epsX)
CB = (CA0X)(2(1+epsX))
Parameter Evaluation eps = -05 CA0 = 02 k = 2
FA0 = 5 KC = 100
Initial and Final Values X0 = 0 V0 = 0 Vf = 500
Polymath Screen Shots
Equations
Plot of X vs V
Results in Tabular Form
A volume of 94 dm
3
(rounding up from slightly more than 93 dm
3
) appears to be our answer
46 Batch Reactor With a Reversible Reaction
5 General Guidelines for California Problems top
Every state has an examination engineers must pass to become a registered professional engineer In the past there havetypically been six problems in a three hour segment of the California Professional Engineers Exam Consequently one shouldbe able to work each problem in 30 minutes or less Many of these problems involve an intermediate calculation todetermine the final answer
1 group unknown parametersvalues on the same side of the equation example
[unknowns] = [knowns]
2 look for a Case 1 and a Case 2 (usually two data points) to make intermediate calculations3 take ratios of Case 1 and Case 2 to cancel as many unknowns as possible
4 carry all symbols to the end of the manipulation before evaluating UNLESS THEY ARE ZERO
California Professional Engineers Registration Problem
47 Batch Reactor Optimization
6 PBR with Pressure Drop top
Note Pressure drop does NOT affect liquid phase reactions
Sample Question
Analyze the following second order gas phase reaction that occurs isothermally in a PBR
Mole Balance
Must use the differential form of the mole balance to separate variables
Rate Law
Second order in A and irreversible
Stoichiometry
Isothermal T = T0
Combine
Need to find (PP0) as a function of W (or V if you have a PFR)
The two expressions are coupled ordinary differential equations We can solve them simultaneously usingan ODE solver such as Polymath For the special case of isothermal operation and epsilon = 0 we canobtain an analytical solution
Polymath will combine the mole balance rate law and stoichiometry
Analytical Solution [e] PFR with
CAUTION Never use this form if
Combine
Solve
Could now solve for X given W or for W given X
For gas phase reactions as the pressure drop increases the concentration decreases resulting in a decreased rate of reaction hence a lower conversion when compared to a reactor without a pressure drop
weight there is a greater external surgace area for smaller particles than larger particles Therefore there are more entryways into the catalyst particle
In CD-ROM chapter 12 we will learn that effectiveness factor decreases as the particle size increases
7 Engineering Analysis - Critical Thinking and Creative Thinking top
We want to learn how the various parameters (particle diameter porosity etc) affect the pressure drop and henceconversion We need to know how to respond to What if questions such as
If we double the particle size decrease the porosity by a factor of 3 and double the pipe size what will happen
to D P and X
(See Critical Thinking in Preface page xx eg Questions the probe consenquences)
To answer these questions we need to see how a varies with these parameters
Turbulent Flow
Compare Case 1 and Case 2
For example Case 1 might be our current situation and Case 2 might be the parameters we want to change to
For constant mass flow through the system = constant
Laminar Flow
45 Effect of Reducing Particle Size on Conversion in a PBR
Here are more links to example problems dealing with packed bed reactors Again you could also use these problems asself tests
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
Visual Encyclopedia of Reaction Engineering Equipment
44 Gas Phase Reaction Example
CSTR and PFR Example
41 Calculate V for a Zero-Order Reaction
3 Reversible Reactions top
To determine the conversion or reactor volume for reversible reactions one must first calculate the maximum conversionthat can be achieved at the isothermal reaction temperature which is the equilibrium conversion (See Example 3-8 in thetext for additional coverage of equilibrium conversion in isothermal reactor design)
45 Calculate Equilibrium Conversion (Xe) for a Constant Volume System
Example Determine Xe for a PFR with no pressure drop P = P0
Given that the system is gas phase and isothermal determine the reactor volume when X = 08 Xe
Reaction Additional Information
CA0 = 02 moldm3
KC = 100 dm3 mol
k = 2 dm3 mol-min
FA0 = 5 molmin
First calculate Xe
Xe = 089
X = 08Xe = 0711
One could then use Polymath to determine the volume of the PFR The corresponding Polymath program is
shown below
4 ODE (Polymath) Solutions to CRE Problems top
Algorithm Steps Polymath Equations
Mole Balance d(X)d(V) = -rAF A0
Rate Law rA = -k((CA2)-(CBKC))
Stoichiometry CA = (CA0(1-X))(1+epsX)
CB = (CA0X)(2(1+epsX))
Parameter Evaluation eps = -05 CA0 = 02 k = 2
FA0 = 5 KC = 100
Initial and Final Values X0 = 0 V0 = 0 Vf = 500
Polymath Screen Shots
Equations
Plot of X vs V
Results in Tabular Form
A volume of 94 dm
3
(rounding up from slightly more than 93 dm
3
) appears to be our answer
46 Batch Reactor With a Reversible Reaction
5 General Guidelines for California Problems top
Every state has an examination engineers must pass to become a registered professional engineer In the past there havetypically been six problems in a three hour segment of the California Professional Engineers Exam Consequently one shouldbe able to work each problem in 30 minutes or less Many of these problems involve an intermediate calculation todetermine the final answer
1 group unknown parametersvalues on the same side of the equation example
[unknowns] = [knowns]
2 look for a Case 1 and a Case 2 (usually two data points) to make intermediate calculations3 take ratios of Case 1 and Case 2 to cancel as many unknowns as possible
4 carry all symbols to the end of the manipulation before evaluating UNLESS THEY ARE ZERO
California Professional Engineers Registration Problem
47 Batch Reactor Optimization
6 PBR with Pressure Drop top
Note Pressure drop does NOT affect liquid phase reactions
Sample Question
Analyze the following second order gas phase reaction that occurs isothermally in a PBR
Mole Balance
Must use the differential form of the mole balance to separate variables
Rate Law
Second order in A and irreversible
Stoichiometry
Isothermal T = T0
Combine
Need to find (PP0) as a function of W (or V if you have a PFR)
The two expressions are coupled ordinary differential equations We can solve them simultaneously usingan ODE solver such as Polymath For the special case of isothermal operation and epsilon = 0 we canobtain an analytical solution
Polymath will combine the mole balance rate law and stoichiometry
Analytical Solution [e] PFR with
CAUTION Never use this form if
Combine
Solve
Could now solve for X given W or for W given X
For gas phase reactions as the pressure drop increases the concentration decreases resulting in a decreased rate of reaction hence a lower conversion when compared to a reactor without a pressure drop
weight there is a greater external surgace area for smaller particles than larger particles Therefore there are more entryways into the catalyst particle
In CD-ROM chapter 12 we will learn that effectiveness factor decreases as the particle size increases
7 Engineering Analysis - Critical Thinking and Creative Thinking top
We want to learn how the various parameters (particle diameter porosity etc) affect the pressure drop and henceconversion We need to know how to respond to What if questions such as
If we double the particle size decrease the porosity by a factor of 3 and double the pipe size what will happen
to D P and X
(See Critical Thinking in Preface page xx eg Questions the probe consenquences)
To answer these questions we need to see how a varies with these parameters
Turbulent Flow
Compare Case 1 and Case 2
For example Case 1 might be our current situation and Case 2 might be the parameters we want to change to
For constant mass flow through the system = constant
Laminar Flow
45 Effect of Reducing Particle Size on Conversion in a PBR
Here are more links to example problems dealing with packed bed reactors Again you could also use these problems asself tests
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
Visual Encyclopedia of Reaction Engineering Equipment
44 Gas Phase Reaction Example
CSTR and PFR Example
41 Calculate V for a Zero-Order Reaction
3 Reversible Reactions top
To determine the conversion or reactor volume for reversible reactions one must first calculate the maximum conversionthat can be achieved at the isothermal reaction temperature which is the equilibrium conversion (See Example 3-8 in thetext for additional coverage of equilibrium conversion in isothermal reactor design)
45 Calculate Equilibrium Conversion (Xe) for a Constant Volume System
Example Determine Xe for a PFR with no pressure drop P = P0
Given that the system is gas phase and isothermal determine the reactor volume when X = 08 Xe
Reaction Additional Information
CA0 = 02 moldm3
KC = 100 dm3 mol
k = 2 dm3 mol-min
FA0 = 5 molmin
First calculate Xe
Xe = 089
X = 08Xe = 0711
One could then use Polymath to determine the volume of the PFR The corresponding Polymath program is
shown below
4 ODE (Polymath) Solutions to CRE Problems top
Algorithm Steps Polymath Equations
Mole Balance d(X)d(V) = -rAF A0
Rate Law rA = -k((CA2)-(CBKC))
Stoichiometry CA = (CA0(1-X))(1+epsX)
CB = (CA0X)(2(1+epsX))
Parameter Evaluation eps = -05 CA0 = 02 k = 2
FA0 = 5 KC = 100
Initial and Final Values X0 = 0 V0 = 0 Vf = 500
Polymath Screen Shots
Equations
Plot of X vs V
Results in Tabular Form
A volume of 94 dm
3
(rounding up from slightly more than 93 dm
3
) appears to be our answer
46 Batch Reactor With a Reversible Reaction
5 General Guidelines for California Problems top
Every state has an examination engineers must pass to become a registered professional engineer In the past there havetypically been six problems in a three hour segment of the California Professional Engineers Exam Consequently one shouldbe able to work each problem in 30 minutes or less Many of these problems involve an intermediate calculation todetermine the final answer
1 group unknown parametersvalues on the same side of the equation example
[unknowns] = [knowns]
2 look for a Case 1 and a Case 2 (usually two data points) to make intermediate calculations3 take ratios of Case 1 and Case 2 to cancel as many unknowns as possible
4 carry all symbols to the end of the manipulation before evaluating UNLESS THEY ARE ZERO
California Professional Engineers Registration Problem
47 Batch Reactor Optimization
6 PBR with Pressure Drop top
Note Pressure drop does NOT affect liquid phase reactions
Sample Question
Analyze the following second order gas phase reaction that occurs isothermally in a PBR
Mole Balance
Must use the differential form of the mole balance to separate variables
Rate Law
Second order in A and irreversible
Stoichiometry
Isothermal T = T0
Combine
Need to find (PP0) as a function of W (or V if you have a PFR)
The two expressions are coupled ordinary differential equations We can solve them simultaneously usingan ODE solver such as Polymath For the special case of isothermal operation and epsilon = 0 we canobtain an analytical solution
Polymath will combine the mole balance rate law and stoichiometry
Analytical Solution [e] PFR with
CAUTION Never use this form if
Combine
Solve
Could now solve for X given W or for W given X
For gas phase reactions as the pressure drop increases the concentration decreases resulting in a decreased rate of reaction hence a lower conversion when compared to a reactor without a pressure drop
weight there is a greater external surgace area for smaller particles than larger particles Therefore there are more entryways into the catalyst particle
In CD-ROM chapter 12 we will learn that effectiveness factor decreases as the particle size increases
7 Engineering Analysis - Critical Thinking and Creative Thinking top
We want to learn how the various parameters (particle diameter porosity etc) affect the pressure drop and henceconversion We need to know how to respond to What if questions such as
If we double the particle size decrease the porosity by a factor of 3 and double the pipe size what will happen
to D P and X
(See Critical Thinking in Preface page xx eg Questions the probe consenquences)
To answer these questions we need to see how a varies with these parameters
Turbulent Flow
Compare Case 1 and Case 2
For example Case 1 might be our current situation and Case 2 might be the parameters we want to change to
For constant mass flow through the system = constant
Laminar Flow
45 Effect of Reducing Particle Size on Conversion in a PBR
Here are more links to example problems dealing with packed bed reactors Again you could also use these problems asself tests
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
45 Calculate Equilibrium Conversion (Xe) for a Constant Volume System
Example Determine Xe for a PFR with no pressure drop P = P0
Given that the system is gas phase and isothermal determine the reactor volume when X = 08 Xe
Reaction Additional Information
CA0 = 02 moldm3
KC = 100 dm3 mol
k = 2 dm3 mol-min
FA0 = 5 molmin
First calculate Xe
Xe = 089
X = 08Xe = 0711
One could then use Polymath to determine the volume of the PFR The corresponding Polymath program is
shown below
4 ODE (Polymath) Solutions to CRE Problems top
Algorithm Steps Polymath Equations
Mole Balance d(X)d(V) = -rAF A0
Rate Law rA = -k((CA2)-(CBKC))
Stoichiometry CA = (CA0(1-X))(1+epsX)
CB = (CA0X)(2(1+epsX))
Parameter Evaluation eps = -05 CA0 = 02 k = 2
FA0 = 5 KC = 100
Initial and Final Values X0 = 0 V0 = 0 Vf = 500
Polymath Screen Shots
Equations
Plot of X vs V
Results in Tabular Form
A volume of 94 dm
3
(rounding up from slightly more than 93 dm
3
) appears to be our answer
46 Batch Reactor With a Reversible Reaction
5 General Guidelines for California Problems top
Every state has an examination engineers must pass to become a registered professional engineer In the past there havetypically been six problems in a three hour segment of the California Professional Engineers Exam Consequently one shouldbe able to work each problem in 30 minutes or less Many of these problems involve an intermediate calculation todetermine the final answer
1 group unknown parametersvalues on the same side of the equation example
[unknowns] = [knowns]
2 look for a Case 1 and a Case 2 (usually two data points) to make intermediate calculations3 take ratios of Case 1 and Case 2 to cancel as many unknowns as possible
4 carry all symbols to the end of the manipulation before evaluating UNLESS THEY ARE ZERO
California Professional Engineers Registration Problem
47 Batch Reactor Optimization
6 PBR with Pressure Drop top
Note Pressure drop does NOT affect liquid phase reactions
Sample Question
Analyze the following second order gas phase reaction that occurs isothermally in a PBR
Mole Balance
Must use the differential form of the mole balance to separate variables
Rate Law
Second order in A and irreversible
Stoichiometry
Isothermal T = T0
Combine
Need to find (PP0) as a function of W (or V if you have a PFR)
The two expressions are coupled ordinary differential equations We can solve them simultaneously usingan ODE solver such as Polymath For the special case of isothermal operation and epsilon = 0 we canobtain an analytical solution
Polymath will combine the mole balance rate law and stoichiometry
Analytical Solution [e] PFR with
CAUTION Never use this form if
Combine
Solve
Could now solve for X given W or for W given X
For gas phase reactions as the pressure drop increases the concentration decreases resulting in a decreased rate of reaction hence a lower conversion when compared to a reactor without a pressure drop
weight there is a greater external surgace area for smaller particles than larger particles Therefore there are more entryways into the catalyst particle
In CD-ROM chapter 12 we will learn that effectiveness factor decreases as the particle size increases
7 Engineering Analysis - Critical Thinking and Creative Thinking top
We want to learn how the various parameters (particle diameter porosity etc) affect the pressure drop and henceconversion We need to know how to respond to What if questions such as
If we double the particle size decrease the porosity by a factor of 3 and double the pipe size what will happen
to D P and X
(See Critical Thinking in Preface page xx eg Questions the probe consenquences)
To answer these questions we need to see how a varies with these parameters
Turbulent Flow
Compare Case 1 and Case 2
For example Case 1 might be our current situation and Case 2 might be the parameters we want to change to
For constant mass flow through the system = constant
Laminar Flow
45 Effect of Reducing Particle Size on Conversion in a PBR
Here are more links to example problems dealing with packed bed reactors Again you could also use these problems asself tests
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
1 group unknown parametersvalues on the same side of the equation example
[unknowns] = [knowns]
2 look for a Case 1 and a Case 2 (usually two data points) to make intermediate calculations3 take ratios of Case 1 and Case 2 to cancel as many unknowns as possible
4 carry all symbols to the end of the manipulation before evaluating UNLESS THEY ARE ZERO
California Professional Engineers Registration Problem
47 Batch Reactor Optimization
6 PBR with Pressure Drop top
Note Pressure drop does NOT affect liquid phase reactions
Sample Question
Analyze the following second order gas phase reaction that occurs isothermally in a PBR
Mole Balance
Must use the differential form of the mole balance to separate variables
Rate Law
Second order in A and irreversible
Stoichiometry
Isothermal T = T0
Combine
Need to find (PP0) as a function of W (or V if you have a PFR)
The two expressions are coupled ordinary differential equations We can solve them simultaneously usingan ODE solver such as Polymath For the special case of isothermal operation and epsilon = 0 we canobtain an analytical solution
Polymath will combine the mole balance rate law and stoichiometry
Analytical Solution [e] PFR with
CAUTION Never use this form if
Combine
Solve
Could now solve for X given W or for W given X
For gas phase reactions as the pressure drop increases the concentration decreases resulting in a decreased rate of reaction hence a lower conversion when compared to a reactor without a pressure drop
weight there is a greater external surgace area for smaller particles than larger particles Therefore there are more entryways into the catalyst particle
In CD-ROM chapter 12 we will learn that effectiveness factor decreases as the particle size increases
7 Engineering Analysis - Critical Thinking and Creative Thinking top
We want to learn how the various parameters (particle diameter porosity etc) affect the pressure drop and henceconversion We need to know how to respond to What if questions such as
If we double the particle size decrease the porosity by a factor of 3 and double the pipe size what will happen
to D P and X
(See Critical Thinking in Preface page xx eg Questions the probe consenquences)
To answer these questions we need to see how a varies with these parameters
Turbulent Flow
Compare Case 1 and Case 2
For example Case 1 might be our current situation and Case 2 might be the parameters we want to change to
For constant mass flow through the system = constant
Laminar Flow
45 Effect of Reducing Particle Size on Conversion in a PBR
Here are more links to example problems dealing with packed bed reactors Again you could also use these problems asself tests
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
The two expressions are coupled ordinary differential equations We can solve them simultaneously usingan ODE solver such as Polymath For the special case of isothermal operation and epsilon = 0 we canobtain an analytical solution
Polymath will combine the mole balance rate law and stoichiometry
Analytical Solution [e] PFR with
CAUTION Never use this form if
Combine
Solve
Could now solve for X given W or for W given X
For gas phase reactions as the pressure drop increases the concentration decreases resulting in a decreased rate of reaction hence a lower conversion when compared to a reactor without a pressure drop
weight there is a greater external surgace area for smaller particles than larger particles Therefore there are more entryways into the catalyst particle
In CD-ROM chapter 12 we will learn that effectiveness factor decreases as the particle size increases
7 Engineering Analysis - Critical Thinking and Creative Thinking top
We want to learn how the various parameters (particle diameter porosity etc) affect the pressure drop and henceconversion We need to know how to respond to What if questions such as
If we double the particle size decrease the porosity by a factor of 3 and double the pipe size what will happen
to D P and X
(See Critical Thinking in Preface page xx eg Questions the probe consenquences)
To answer these questions we need to see how a varies with these parameters
Turbulent Flow
Compare Case 1 and Case 2
For example Case 1 might be our current situation and Case 2 might be the parameters we want to change to
For constant mass flow through the system = constant
Laminar Flow
45 Effect of Reducing Particle Size on Conversion in a PBR
Here are more links to example problems dealing with packed bed reactors Again you could also use these problems asself tests
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
The two expressions are coupled ordinary differential equations We can solve them simultaneously usingan ODE solver such as Polymath For the special case of isothermal operation and epsilon = 0 we canobtain an analytical solution
Polymath will combine the mole balance rate law and stoichiometry
Analytical Solution [e] PFR with
CAUTION Never use this form if
Combine
Solve
Could now solve for X given W or for W given X
For gas phase reactions as the pressure drop increases the concentration decreases resulting in a decreased rate of reaction hence a lower conversion when compared to a reactor without a pressure drop
weight there is a greater external surgace area for smaller particles than larger particles Therefore there are more entryways into the catalyst particle
In CD-ROM chapter 12 we will learn that effectiveness factor decreases as the particle size increases
7 Engineering Analysis - Critical Thinking and Creative Thinking top
We want to learn how the various parameters (particle diameter porosity etc) affect the pressure drop and henceconversion We need to know how to respond to What if questions such as
If we double the particle size decrease the porosity by a factor of 3 and double the pipe size what will happen
to D P and X
(See Critical Thinking in Preface page xx eg Questions the probe consenquences)
To answer these questions we need to see how a varies with these parameters
Turbulent Flow
Compare Case 1 and Case 2
For example Case 1 might be our current situation and Case 2 might be the parameters we want to change to
For constant mass flow through the system = constant
Laminar Flow
45 Effect of Reducing Particle Size on Conversion in a PBR
Here are more links to example problems dealing with packed bed reactors Again you could also use these problems asself tests
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
weight there is a greater external surgace area for smaller particles than larger particles Therefore there are more entryways into the catalyst particle
In CD-ROM chapter 12 we will learn that effectiveness factor decreases as the particle size increases
7 Engineering Analysis - Critical Thinking and Creative Thinking top
We want to learn how the various parameters (particle diameter porosity etc) affect the pressure drop and henceconversion We need to know how to respond to What if questions such as
If we double the particle size decrease the porosity by a factor of 3 and double the pipe size what will happen
to D P and X
(See Critical Thinking in Preface page xx eg Questions the probe consenquences)
To answer these questions we need to see how a varies with these parameters
Turbulent Flow
Compare Case 1 and Case 2
For example Case 1 might be our current situation and Case 2 might be the parameters we want to change to
For constant mass flow through the system = constant
Laminar Flow
45 Effect of Reducing Particle Size on Conversion in a PBR
Here are more links to example problems dealing with packed bed reactors Again you could also use these problems asself tests
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
weight there is a greater external surgace area for smaller particles than larger particles Therefore there are more entryways into the catalyst particle
In CD-ROM chapter 12 we will learn that effectiveness factor decreases as the particle size increases
7 Engineering Analysis - Critical Thinking and Creative Thinking top
We want to learn how the various parameters (particle diameter porosity etc) affect the pressure drop and henceconversion We need to know how to respond to What if questions such as
If we double the particle size decrease the porosity by a factor of 3 and double the pipe size what will happen
to D P and X
(See Critical Thinking in Preface page xx eg Questions the probe consenquences)
To answer these questions we need to see how a varies with these parameters
Turbulent Flow
Compare Case 1 and Case 2
For example Case 1 might be our current situation and Case 2 might be the parameters we want to change to
For constant mass flow through the system = constant
Laminar Flow
45 Effect of Reducing Particle Size on Conversion in a PBR
Here are more links to example problems dealing with packed bed reactors Again you could also use these problems asself tests
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
weight there is a greater external surgace area for smaller particles than larger particles Therefore there are more entryways into the catalyst particle
In CD-ROM chapter 12 we will learn that effectiveness factor decreases as the particle size increases
7 Engineering Analysis - Critical Thinking and Creative Thinking top
We want to learn how the various parameters (particle diameter porosity etc) affect the pressure drop and henceconversion We need to know how to respond to What if questions such as
If we double the particle size decrease the porosity by a factor of 3 and double the pipe size what will happen
to D P and X
(See Critical Thinking in Preface page xx eg Questions the probe consenquences)
To answer these questions we need to see how a varies with these parameters
Turbulent Flow
Compare Case 1 and Case 2
For example Case 1 might be our current situation and Case 2 might be the parameters we want to change to
For constant mass flow through the system = constant
Laminar Flow
45 Effect of Reducing Particle Size on Conversion in a PBR
Here are more links to example problems dealing with packed bed reactors Again you could also use these problems asself tests
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
weight there is a greater external surgace area for smaller particles than larger particles Therefore there are more entryways into the catalyst particle
In CD-ROM chapter 12 we will learn that effectiveness factor decreases as the particle size increases
7 Engineering Analysis - Critical Thinking and Creative Thinking top
We want to learn how the various parameters (particle diameter porosity etc) affect the pressure drop and henceconversion We need to know how to respond to What if questions such as
If we double the particle size decrease the porosity by a factor of 3 and double the pipe size what will happen
to D P and X
(See Critical Thinking in Preface page xx eg Questions the probe consenquences)
To answer these questions we need to see how a varies with these parameters
Turbulent Flow
Compare Case 1 and Case 2
For example Case 1 might be our current situation and Case 2 might be the parameters we want to change to
For constant mass flow through the system = constant
Laminar Flow
45 Effect of Reducing Particle Size on Conversion in a PBR
Here are more links to example problems dealing with packed bed reactors Again you could also use these problems asself tests
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
1 For the elementary liquid phase reaction carried out in a CSTR where V vo CAo k and Kc are given and the feed
is pure A the combined mole balance rate laws and stoichiometry are
There are two equations two unknowns CA and CB
Gases Use Molar Flow Rates IE FI
2 If the above reaction carried out in the gas phase in a PFR where V voCAok and Kc are given and the feed ispure A the combined mole balance rate laws and stoichiometry yield for isothermal operation (T=To) and no pressuredrop (P=0) are
Use Polymath to plot FA and FB down the length of the reactor
49 Stoichiometry for Measures Other than Conversion
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species
For isothermal microreactors we use the same equations as a PFR as long as the flow is not laminar If the flow is laminarwe must use the techniques discussed in chapter 13 See example 48 of the text
University of Washington Transport Effects in Microreactors site
Institut fr Mikrotechnik Mainz GmbH
2 Membrane Reactors top
Membrane reactors can be used to achieve conversions greater than the original equilibrium value These higher conversionsare the result of Le Chateliers Principle you can remove one of the reaction products and drive the reaction to the right Toaccomplish this a membrane that is permeable to that reaction product but is impermeable to all other species is placedaround the reacting mixture
Example The following reaction is to be carried out isothermally in a membrane reactor with no pressure drop Themembrane is permeable to Product C but it is impermeable to all other species