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

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.

Selectivity and Yield

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

	Instantaneous	Overall
Selectivity
Yield
Example:	desired product , r_D=k₁C_A²C_B undesired product , r_U=k₂C_AC_B To maximize the selectivity of D with respect to U run at high concentration of A and use PFR

Parallel Reactions

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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

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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

Net Rate of Reaction of A
Species A: Combined mole balance and rate law for a control volume batch reactor.
	r_A=r_1A+0
Rate Law
	r_1A=-k_1AC_A
Relative Rates
	r_1B=-r_1A

Integrating with C_A=C_A0 at t=0 and then rearranging
Mole Balance
Species B:
Net Rate of Reaction of B

Rate Law
	r_2B=-k₂C_B
Relative Rates


Combine

Using the integrating factor i.f.:
Evaluate

at t = 0, C_B = 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	C_C = C_A0 - C_B - C_A
And

in a CSTR

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

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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.

The new things for multiple reactions that build on Table 6.1 and 6.2 are

Number every reaction
Rate Law for every reaction
Relative Rates for every reaction
Net Rates of Reaction

Number every reaction
Rate Laws for every reaction
Relative Rates for each reaction

For a given reaction i
Net Rate of Formation for Species A that appears in N reactions,

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

Applications of Algorithm

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	(1)		NOTE: The specific reaction rate k_1A is defined with respect to species A.
	(2)		NOTE: The specific reaction rate k_2C 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

(1)	A + 2B → C	-r_1A = k_1AC_AC_B²
(2)	2A + 3C → D	-r_2C = k_2CC_A²C_B³

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

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: 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 defined with respect to species A.
	(2)		NOTE: The specific reaction rate k_2C 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

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 defined with respect to species A.
	(2)		NOTE: The specific reaction rate k_2C 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: 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 defined with respect to species A.
	(2)		NOTE: The specific reaction rate k_2C 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

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 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: 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 defined with respect to species A.
	(2)		NOTE: The specific reaction rate k_2C 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: Semibatch, Liquid Phase

Would you like to run for Example E: Semibatch, Liquid Phase

What's wrong with this solution?

What type of reaction is taking place (parallel, series, independent or complex)?

Maximizing the Selectivity - Parallel Reactions

Finding the Selectivity

Concentration-Time Trajectories

Writing Net Rates of Formation

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

ODE Solver Algorithm

Object Assessment of Chapter 8

Explore the cobra bites web module

^* All chapter references are for the 1st Edition of the text Essentials of Chemical Reaction Engineering .

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Chapter 8: Multiple Reactions

Topics

Types of Multiple Reactions

Selectivity and Yield

$S_{D/\upsilon} = \frac{r_{D}}{r_{U}} = \frac{k_{1}{C_{A}^{\alpha}}}{k_{2}{C_{A}^{\beta}}} = \frac{k_1}{k_2}{C_{A}}^{\alpha - \beta}$

Mole Balance on every species

Species A:

Net Rate of Reaction of A

Rate Law

Relative Rates

Mole Balance

Species B:

Net Rate of Reaction of B

Rate Law

Relative Rates

Combine

Evaluate

Optimization of the Desired Product B

The new things for multiple reactions that build on Table 6.1 and 6.2 are

Example A: Liquid Phase PFR

Solution

Example B: Liquid Phase CSTR

Solution

Example C: Gas Phase PFR, No Pressure Drop

Solution

Example D: Membrane Reactor with Pressure Drop

Solution

Example E: Liquid Semibatch

Solution

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Chapter 8: Multiple Reactions

Topics

Types of Multiple Reactions

Selectivity and Yield

SD/υ=rDrU=k1CαAk2CβA=k1k2CAα−β 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}

Mole Balance on every species

Species A:

Net Rate of Reaction of A

Rate Law

Relative Rates

Mole Balance

Species B:

Net Rate of Reaction of B

Rate Law

Relative Rates

Combine

Evaluate

Optimization of the Desired Product B

The new things for multiple reactions that build on Table 6.1 and 6.2 are

Example A: Liquid Phase PFR

Solution

Example B: Liquid Phase CSTR

Solution

Example C: Gas Phase PFR, No Pressure Drop

Solution

Example D: Membrane Reactor with Pressure Drop

Solution

Example E: Liquid Semibatch

Solution

$S_{D/\upsilon} = \frac{r_{D}}{r_{U}} = \frac{k_{1}{C_{A}^{\alpha}}}{k_{2}{C_{A}^{\beta}}} = \frac{k_1}{k_2}{C_{A}}^{\alpha - \beta}$