# 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 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.

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

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

 Parallel Reactions top

The net rate of disappearance of A

Instantaneous selectivity

If α > β use high concentration of A. Use PFR.
If α < β use low concentration of A. Use CSTR.

Maximizing the Selectivity - Parallel Reactions

 Series Reactions (p. 283) top

Example: Series Reaction in a batch reactor

This series reaction could also be written as

Reaction (1) : -r1A=k1CA

Reaction (2): -r2B=k2CB

##### Species A:
Combined mole balance and rate law for a control volume batch reactor.

rA=r1A+0
r1A=-k1ACA
##### Relative Rates
r1B=-r1A
Integrating with CA=CA0 at t=0 and then rearranging

r2B=-k2CB
##### 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

Finding the Selectivity

in a CSTR

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

 Algorithm for Complex Reactions top

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 Figure 4-11 and Table 4-6 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 CA = FA0
Batch CA = NA/V0

Writing Net Rates of Formation

 Applications of Algorithm top
 (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

 (1) A + 2B → C -r1A = k1ACACB2 (2) 2A + 3C → D -r2C = k2CCA2CB3

and take place in a PFR. The feed is equal molar in A and B with FA0 = 200 mol/min and the volumetric flow rate is 100 dm3/min. The reaction volume is 50 dm3 and the rate constants are

Plot FA, FB, FC, FD and SC/D as a function of V

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 SC/D = FC/FD in the Polymath program, Polymath would not execute because at V = 0, FC = 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 FD 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 FA0 = 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 FA, FB, FC, FD and SC/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 FA0 = 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 CT0 = 0.2 mol/dm3 and the rate constants are

Plot FA, FB, FC, FD 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

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#### 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 FA0 = 10 mol/min and the volumetric flow rate is 100 3/min. The reactor volume is 50 dm3 and the total entering concentration is CT0 = 0.2 mol/dm3. There is pressure drop and entering pressure is 100 atm and the rate constants are

The pressure drop parameter αρb = 0.0405 dm-3

The mass transfer coefficient for C is kcc = 2 min–1

Plot FA, FB, FC, FD and SC/D as a function of V for

(a) Case 1    CCsg = 0
(b) Case 2    CCsg ≠ 0,

Set Fosg = 0.1 mol/min and vary

(5 < < 10,000)

Are there a set of conditions whereby (CCsg < CC) and RC changes sign and Species C diffuses back into the membrane reactor near the exit? Run the Polymath program when αρb = 0 and compare RC with the base case when there IS pressure drop (αρb = 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 FCsg

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, ρb

Selectivity

Need to include C collected from sweep gas

Parameters

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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 FA0 = 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 CA0 = 0.3 mol/dm3 and CB0 = 0.2 mol/dm3. Plot CA, CB, CC, CD and SC/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

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What's wrong with this solution?
ODE Solver Algorithm
Object Assessment of Chapter 6

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