6. Multiple Reactions^*

Topics

1. Types of Multiple Reactions Selectivity and Yield
2. Parallel Reactions
3. Reactions in Series
4. Algorithm for Complex Reactions
5. Applications of Algorithm

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.

Reaction Video: Some multiple reaction systems oscillate, recreating the reactants when certain conditions are met.

6.1 What type of reaction is taking place?

Selectivity and Yield (Section 6.1)

There are two types of selectivity and yield: Instantaneous and Overall.

	Instantaneous	Overall
Selectivity
Yield
Example:	desired product , rD=k1CA2CB                     undesired product , rU=k2CACB                          To maximize the selectivity of D with respect to U run at high concentration of A and use PFR

6.2 Maximizing the Selectivity - Parallel Reactions

Example: Series Reaction in a batch reactor

This series reaction could also be written as         

Reaction (1) : -r_1A=k₁C_A

Reaction (2): -r_2B=k₂C_B

Mole Balance on every species

Species A: Combined mole balance and rate law for a control volume batch reactor.
Net Rate of Reaction of A
	rA=r1A+0
Rate Law
	r1A=-k1ACA
Relative Rates
	r1B=-r1A
Integrating with CA=CA0 at t=0 and then rearranging
Mole Balance
Species B:
Net Rate of Reaction of B
Rate Law
	r2B=-k2CB
Relative Rates
Combine
Using the integrating factor, i.f.:
Evaluate
at t = 0, CB = 0
When should you stop the reaction to obtain the maximum amount of B? Let's see.
Optimization of the Desired Product B
Then
Species C	CC = CA0 - CB - CA
And

6.3 Finding the Selectivity

in a CSTR

6.4 Concentration-Time Trajectories

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

Mole Balances

Reactor Type	Gas Phase	Liquid Phase
Batch
Semibatch
CSTR
PFR
PBR

Rates

NOTE: The reaction rates in the above mole balances are net rates.

Stoichiometry

NOTE: We could use the gas phase mole balance for liquids and then just express the concentration as
Flow C_A = F_A/υ₀
Batch C_A = N_A/V₀

6.5 Writing Net Rates of Formation

(1) NOTE: The specific reaction rate k1A is defined with respect to species A. (2) NOTE: The specific reaction rate k2C is defined with respect to species C.

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

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 dm³/min. The reaction volume is 50 dm³ and the rate constants are

Plot F_A, F_B, F_C, F_D and S_C/D as a function of V

6.6 Multiple Reactions - Sketch what you think the profile will look like a priori

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 dm³ 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

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Example B: Liquid Phase CSTR

Same reactions, rate laws, and rate constants as example A

	(1)		NOTE: The specific reaction rate k1A is defined with respect to species A.
	(2)		NOTE: The specific reaction rate k2C is defined with respect to species C.

The complex liquid phase reactions take place in a 2,500 dm³ CSTR. The feed is equal molar in A and B with F_A0 = 200 mol/min, the volumetric flow rate is 100 dm³/min and the reaction volume is 50 dm³.

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

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Example C: Gas Phase PFR, No Pressure Drop

Same reactions and rate laws as previous two examples

	(1)		NOTE: The specific reaction rate k1A is defined with respect to species A.
	(2)		NOTE: The specific reaction rate k2C is defined with respect to species C.

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 dm³/min. The reactor volume is 1,000 dm³, there is no pressure drop, the total entering concentration is C_T0 = 0.2 mol/dm³ 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

Would you like to run for Example C

Example D: Membrane Reactor with Pressure Drop

Same reactions and rate laws as previous two examples

	(1)		NOTE: The specific reaction rate k1A is defined with respect to species A.
	(2)		NOTE: The specific reaction rate k2C is defined with respect to species C.

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 dm³ and the total entering concentration is C_T0 = 0.2 mol/dm³. 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

1. Net rates, rate laws and relative rates same as Liquid and Gas Phase PFR and Liquid Phase CSTR.
2. 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 Drop

Stoichiometry

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 = T₀) 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

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Example E: Liquid Semibatch

Same reactions, rate laws, and rate constants as example A

	(1)		NOTE: The specific reaction rate k1A is defined with respect to species A.
	(2)		NOTE: The specific reaction rate k2C is defined with respect to species C.

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 dm³/min and the initial reactor volume is 1,000 dm³.

The maximum volume is 2,000 dm³ and C_A0 = 0.3 mol/dm³ and C_B0 = 0.2 mol/dm³. 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

Would you like to run for Example E

6.7 What's wrong with this solution?

6.1 ODE Solver Algorithm

Object Assessment of Chapter 6

Explore the cobra bites web module

^* All chapter references are for the 4th Edition of the text Elements of Chemical Reaction Engineering .

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