Chemical Reaction Engineering

Chapter 4, Part 3:

Pressure Drop in a Packed Bed Reactor

Algorithm for Isothermal Reactor Design

1. Mole Balance and Design Equation

2. Rate Law

3. Stoichiometry

4. Combine

5. Evaluate

AlgorithmAnalyze the following second order gas phase reaction that occursisothermally in a PBR: 

AlgorithmAnalyze the following second order gas phase reaction that occursisothermally in a PBR: 

Mole Balance: Must use the differential form of the mole balance to separate variables:

AlgorithmAnalyze the following second order gas phase reaction that occursisothermally 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:

AlgorithmAnalyze the following second order gas phase reaction that occursisothermally 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: with T=T0

AlgorithmAnalyze the following second order gas phase reaction that occursisothermally 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: with T=T0

Combine:

Need to find (P/P0) as a function of W (or V if you have a PFR).

dX

dW

kCA02

FA0

1 X 2

1 X 2 y2, y P

P0

Pressure Drop in Packed Bed Reactors

Pressure Drop in Packed Bed Reactors

Ergun Equation:

Pressure Drop in Packed Bed Reactors

Ergun Equation:

00

0

0

0

FT0FT

PP0

T0T

Pressure Drop in Packed Bed Reactors

Ergun Equation:

00

0

0

0

FT0FT

PP0

T0T

0FT0FT

PP0

T0T

Pressure Drop in Packed Bed Reactors

Ergun Equation:

Let

00

0

0

0

FT0FT

PP0

T0T

0FT0FT

PP0

T0T

Pressure Drop in Packed Bed Reactors

Ergun Equation:

Let

Catalyst Weight:

Let

00

0

0

0

FT0FT

PP0

T0T

and

y PP0

0FT0FT

PP0

T0T

Multiple Reactions and Pressure Drop

Multiple Reactions and Pressure Drop

dydW

2y

TT0

1X

In terms of conversion:

FT

FT0 1X

Multiple Reactions and Pressure Drop

dydW

2y

TT0

1X

FT

FT0 1X In terms of conversion:

Multiple Reactions and Pressure Drop

dydW

2y

TT0

1X

FT

FT0 1X In terms of conversion:

Analytical Solution

Analytical Solution

Analytical Solution

Separate

Integrate

dX

1 X 2 kCA 0

2

FA 01 W dW

Analytical Solution

For gas phase reactions, as the pressure drop increases, theconcentation decreases, resulting in a decreased rate of reaction,hence a lower conversion when compared to a reactor without a pressure drop.

Separate

Integrate

dX

1 X 2 kCA 0

2

FA 01 W dW

What if… Dpand Ac change?

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Laminar Turbulent

What if… Dpand Ac change?

} }

Laminar Turbulent

What if… Dpand Ac change?

} }

Laminar Turbulent

What if… Dpand Ac change?

} }

Laminar Turbulent

Polymath Solution

Polymath Solution

Polymath Solution

Polymath Solution