Chapter 8: Multiple Reactions
Topics
 Types of Multiple Reactions Selectivity and Yield
 Parallel Reactions
 Reactions in Series
 Algorithm for Complex Reactions
 Applications of Algorithm
Types of Multiple Reactions Selectivity and Yield  top 
Types of Multiple Reactions
Use molar flow rates and concentrations; DO NOT use conversion!
There are 4 classes of Multiple Reactions.
1. Parallel Reactions
2. Series Reactions
3. Complex Reactions: Series and Parallel aspects combined
4. Independent Reactions
Independent reactions typically occur in the catalytic cracking of crude oil to form gasoline.
Selectivity and Yield
There are two types of selectivity and yield: Instantaneous and Overall.
Instantaneous  Overall  
Selectivity  
Yield  
Example:  undesired product , r_{U}=k_{2}C_{A}C_{B} To maximize the selectivity of D with respect to U run at high concentration of A and use PFR 
Parallel Reactions  top 
The net rate of disappearance of A
Instantaneous selectivity
$ S_{D/\upsilon} = \frac{r_{D}}{r_{U}} = \frac{k_{1}{C_{A}^{\alpha}}}{k_{2}{C_{A}^{\beta}}} = \frac{k_1}{k_2}{C_{A}}^{\alpha  \beta}$
If α > β use high concentration of A. Use PFR.If α < β use low concentration of A. Use CSTR.
Series Reactions  top 
Example: Series Reaction in a batch reactor
This series reaction could also be written as
Reaction (1) : r_{1A}=k_{1}C_{A}
Reaction (2): r_{2B}=k_{2}C_{B}
Mole Balance on every species
Schemes for maximizing the selectivity for Van Der Vusse Kinetics
Can be found at the following web site http://www.wits.ac.za/centres/comps/AR/index.htm
Algorithm for Complex Reactions  top 
Reactor Type  Gas Phase  Liquid Phase 

Batch  
Semibatch  
CSTR  
PFR  
PBR 
Rates NOTE: The reaction rates in the above mole balances are net rates.
The new things for multiple reactions that build on Table 6.1 and 6.2 are

Stoichiometry
NOTE: We could use the gas phase mole balance for liquids and then just express the concentration as
Flow C_{A} = F_{A}/υ_{0}
Batch C_{A} = N_{A}/V_{0}
Applications of Algorithm  top 

These reactions will be used in the following 5 examples
• Liquid Phase PFR
• Liquid Phase CSTR
• Gas Phase PFR no ΔT
• Gas Phase Membrane Reactor with ΔT
• Liquid Phase Semibatch Reactor
Example A: Liquid Phase PFR
The complex liquid phase reactions follow elementary rate laws
(1)  A + 2B → C  r_{1A} = k_{1A}C_{A}C_{B}^{2} 
(2)  2A + 3C → D  r_{2C} = k_{2C}C_{A}^{2}C_{B}^{3} 
and take place in a PFR. The feed is equal molar in A and B with F_{A0} = 200 mol/min and the volumetric flow rate is 100 dm^{3}/min. The reaction volume is 50 dm^{3} and the rate constants are
Plot F_{A}, F_{B}, F_{C}, F_{D} and S_{C/D} as a function of V
Solution
Liquid PFR
Mole Balances
Net Rates
Rate Laws
Relative Rates
Selectivity
If one were to write S_{C/D} = F_{C}/F_{D} in the Polymath program, Polymath would not execute because at V = 0, F_{C} = 0 resulting in an undefined volume (infinity) at V = 0. To get around this problem we start the calculation 10^{4} dm^{3} from the reactor entrance where F_{D} will note be zero and use the following IF statement.
Stoichiometry
Parameters
Would you like to see the results for Example A: Multiple Reactions, PFR, Liquid Phase
Would you like to run for Example A: Multiple Reactions, PFR, Liquid Phase
Example B: Liquid Phase CSTR
Same reactions, rate laws, and rate constants as example A
(1) 
NOTE: The specific reaction rate k_{1A} is 

(2) 
NOTE: The specific reaction rate k_{2C} is 
The complex liquid phase reactions take place in a 2,500 dm^{3} CSTR. The feed is equal molar in A and B with F_{A0} = 200 mol/min, the volumetric flow rate is 100 dm^{3}/min and the reaction volume is 50 dm^{3}.
Find the concentrations of A, B, C, and D exiting the reactor along with the exiting selectivity.
Plot F_{A}, F_{B}, F_{C}, F_{D} and S_{C/D} as a function of V
Solution
Liquid CSTR
Mole Balances
Net Rates
Rate Laws
Relative Rates
Selectivity
Parameters
Would you like to see the results for Example B: Multiple Reactions, CSTR, Liquid Phase
Would you like to run for Example B: Multiple Reactions, CSTR, Liquid Phase
Example C: Gas Phase PFR, No Pressure Drop
Same reactions and rate laws as previous two examples
(1) 
NOTE: The specific reaction rate k_{1A} is 

(2) 
NOTE: The specific reaction rate k_{2C} is 
The complex gas phase reactions take place in a PFR. The feed is equal molar in A and B with F_{A0} = 10 mol/min and the volumetric flow rate is 100 dm^{3}/min. The reactor volume is 1,000 dm^{3}, there is no pressure drop, the total entering concentration is C_{T0} = 0.2 mol/dm^{3} and the rate constants are
Plot F_{A}, F_{B}, F_{C}, F_{D} and _{C/D} as a function of V
Solution
Gas Phase PFR, No Pressure Drop
Mole Balances
Net Rates
Rate Laws
Relative Rates
Selectivity
Stoichiometry
Parameters
Would you like to see the results for Example C: Multiple Reactions, Gas Phase
Would you like to run for Example C: Multiple Reactions, Gas Phase
Example D: Membrane Reactor with Pressure Drop
Same reactions and rate laws as previous two examples
(1) 
NOTE: The specific reaction rate k_{1A} is 

(2) 
NOTE: The specific reaction rate k_{2C} is 
The complex gas phase reactions take place in a catalytic packed bed with C diffusing out the sides. The feed is equal molar in A and B with F_{A0} = 10 mol/min and the volumetric flow rate is 100 ^{3}/min. The reactor volume is 50 dm^{3} and the total entering concentration is C_{T0} = 0.2 mol/dm^{3}. There is pressure drop and entering pressure is 100 atm and the rate constants are
The pressure drop parameter αρ_{b} = 0.0405 dm^{3}
The mass transfer coefficient for C is k_{cc} = 2 min^{–1}
Plot F_{A}, F_{B}, F_{C}, F_{D} and S_{C/D} as a function of V for
(a) Case 1 C_{Csg} = 0
(b) Case 2 C_{Csg} ≠ 0,
Set F_{osg} = 0.1 mol/min and vary
(5 < < 10,000)
Are there a set of conditions whereby (C_{Csg} < C_{C}) and R_{C} changes sign and Species C diffuses back into the membrane reactor near the exit? Run the Polymath program when αρ_{b} = 0 and compare R_{C} with the base case when there IS pressure drop (αρ_{b} = 0.0405 dm^{3})
Solution
Gas Phase Multiple Reactions in a Catalytic Packed Bed Membrane Reactor with Pressure Drop
Mole Balances
We also need to account for the molar rate desired product C leaving in the sweep gas F_{Csg}
Rate Laws
 Net rates, rate laws and relative rates same as Liquid and Gas Phase PFR and Liquid Phase CSTR.
 Transport Law Case 1 Large sweep gas velocity Case 2 Moderate to small sweep gas velocity
Vary to see changes in profiles
Case 2A Pressure Drop
Case 2B No Pressure DropStoichiometry
We need to reconsider our pressure drop equation when one or more species diffuse out of the reactor. Recall the pressure drop equation is
with
Warning!!
When mass diffuses out of a membrane reactor as there will be a decrease in the superficial mass flow rate and hence G. To account for this decrease in calculating our pressure drop parameter , we will take the ratio of the superficial mass velocity at any point in the reactor to the superficial mass velocity at the entrance to the reactor. The superficial mass flow rates can be obtained by multiplying the species molar flow rates, Fi, by their respective molecular weights, MWi, and then summing over all species
Because the smallest molecule is the one diffusing out and has the lowest molecular weight, we will neglect the changes in the mass flow rate down the reactor and will take as a first approximation.
Isothermal (T = T_{0}) and multiply both sides of the pressure drop equation by the bulk density, ρ_{b}
Selectivity
Need to include C collected from sweep gas
Parameters
Would you like to see the results for Example D: Multiple Reactions, Membrane, Gas Phase, with Pressure Drop
Would you like to run for Example D: Multiple Reactions, Membrane, Gas Phase, with Pressure Drop
Example E: Liquid Semibatch
Same reactions, rate laws, and rate constants as example A
(1) 
NOTE: The specific reaction rate k_{1A} is 

(2) 
NOTE: The specific reaction rate k_{2C} is 
The complex liquid phase reactions take place in a semibatch reactor where A is fed to B with F_{A0} = 3 mol/min. The volumetric flow rate is 10 dm^{3}/min and the initial reactor volume is 1,000 dm^{3}.
The maximum volume is 2,000 dm^{3} and C_{A0} = 0.3 mol/dm^{3} and C_{B0} = 0.2 mol/dm^{3}. Plot C_{A}, C_{B}, C_{C}, C_{D} and S_{C/D} as a function of time.
Solution
Liquid Phase Multiple Reactions in a Semibatch Reactor
Mole Balances
Net Rates, Rate Laws and relative rates – are the same as Liquid and Gas Phase PFR and Liquid Phase CSTR.
Stoichiometry
Selectivity
Parameters
Would you like to see the results for Example E: Semibatch, Liquid Phase
Would you like to run for Example E: Semibatch, Liquid Phase
Explore the cobra bites web module
^{*} All chapter references are for the 1st Edition of the text Essentials of Chemical Reaction Engineering .