CHE 402 Kinetics and Reactor Design CHAPTER TWO

CHE 402: Kinetics and Reactor Design CHAPTER TWO Conversion and Reactor Sizing Mustafa Nasser, Ph. D, MSc, BSc Chemical Engineering Dr Mustafa Nasser 2012 1

Reaction Conversion �Consider �on the general reaction; a “per mole of A basis”… Dr Mustafa Nasser 2012 2

Reaction Conversion �The conversion of A (XA) is defined as: Dr Mustafa Nasser 2012 3

Conversion (Batch System) �Consider the batch reactor mole balance: Dr Mustafa Nasser 2012 4

Batch Reactor Design Equation �Recall the batch reactor design equation differential form integral form Dr Mustafa Nasser 2012 5

Conversion (Flow System) �Consider the flow reactor mole balance: Dr Mustafa Nasser 2012 6

CSTR Design Equations �Recall the CSTR Design Equation: Dr Mustafa Nasser 2012 7

PFR Design Equations �Recall the PFR Design Equation: differential form integral form Dr Mustafa Nasser 2012 8

Application of Design Equations �Consider a single reaction system with functional dependence as; Dr Mustafa Nasser 2012 9

Application of Design Equations: Levenspiel Plots Dr Mustafa Nasser 2012 10

Application of Design Equations �For the CSTR; Dr Mustafa Nasser 2012 11

Application of Design Equations �For the PFR; Dr Mustafa Nasser 2012 12

Comparison �PFR always requires less volume than a CSTR to achieve a given conversion. Dr Mustafa Nasser 2012 13

CSTRs in Series FA, 0 FA, 1 X 1 V 2 FA, 2 X 2 Where the conversion for successive reactors is defined as: Dr Mustafa Nasser 2012 14

PFRs in Series FA, 0 V 1 FA, 1 X 1 FA, 2 X 2 V 2 Dr Mustafa Nasser 2012 15

CSTRs in Series Finally consider a number of CSTRs in series: Reactor 1: Reactor 2: We see that we approach the PFR reactor volume for a large number of CSTRs in series: Dr Mustafa Nasser 2012 X

Reactors in Series FA, 0 V 2 V 1 FA, 1 X 1 V 3 FA, 2 X 2 FA, 3 X 3 Where the conversion for successive reactors is defined as: Dr Mustafa Nasser 2012 17

Reactors in Series FA, 0 V 2 V 1 FA, 1 X 1 V 3 FA, 2 X 2 Dr Mustafa Nasser 2012 FA, 3 X 3 18

Reactors in Series FA, 0 V 2 V 1 FA, 1 X 1 V 3 FA, 2 X 2 Dr Mustafa Nasser 2012 FA, 3 X 3 19

Reactors in Series FA, 0 V 2 V 1 FA, 1 X 1 V 3 FA, 2 X 2 Dr Mustafa Nasser 2012 FA, 3 X 3 20

Reactors in Series FA, 0 V 2 V 1 V 3 FA, 1 X 1 FA, 2 X 2 FA, 3 X 3 V 2 V 1 X 2 X 3 Dr Mustafa Nasser 2012 21

Numerical Evaluation of Integrals (Appendix A. 4) he integral to calculate the PFR volume can be evaluated using a method such as Simpson's One-Third Rule (page 1014) Simpson's One-Third Rule is one of the more common numerical methods. It uses three data points. Other numerical methods (see Appendix A, pp 1009 -1015) for evaluating integrals are: • Trapezoidal Rule (uses two data points) • Simpson's Three-Eighth's Rule (uses four data points) • Five-Point Quadrature Formula Dr Mustafa Nasser 2012 22

Relative Reaction Rates �Relative reaction rates of the species involved in a reaction can be obtained from the stoichiometric coefficients: Dr Mustafa Nasser 2012 23

Space Time ( ) �Time necessary to process 1 reactor volume of fluid at entrance conditions ◦ Also called residence time or holding time ◦ 1/ is referred to as the Space Velocity ◦ For a PFR, Dr Mustafa Nasser 2012 24

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(a): V= 6. 4 m 3 = 6400 = dm 3 = 6400 l Dr Mustafa Nasser 2012 27

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(a) Dr Mustafa Nasser 2012 30

(b) Dr Mustafa Nasser 2012 31

(c) Dr Mustafa Nasser 2012 32

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Solution 2 -7 Dr Mustafa Nasser 2012 37

Read the discussion 2. 5. 4 Dr Mustafa Nasser 2012 38

Try This: Dr Mustafa Nasser 2012 39