Chemical Reaction Engineering Fundamentals

Lecture 2 Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. 1 1

Lecture 2 Lecture 2 Tuesday Tuesday Review of Lecture 1 Definition of Conversion, X Develop the Design Equations in terms of X Size CSTRs and PFRs given rA= f(X) Conversion for Reactors in Series Review the Fall of the Tower of CRE 2 2

Review Lecture 1 Reactor Reactor Mole Balances Mole Balances Summary Summary The GMBE applied to the four major reactor types (and the general reaction A B) Reactor Differential Algebraic Integral NA N dN A 0 A N dN = A t Batch A= r V A r V dt A t V =FA0 FA CSTR rA FA F dF A dFA dV A PFR = A V = rA dr A F 0 V FA F dF A PBR dFA dW= r A A = A W A r F 3 3 0 W

Review Lecture 1 CSTR CSTR Example Problem Example Problem Given the following information, Find V 3 dm = 10 3 dm min 0 = = 10 min 0 1 . 0 C V =? 0 A = C C = 0 A A F C 0 0 0 A A = F C A A Liquid phase = 0 FA= 0CA 4 4

Review Lecture 1 CSTR CSTR Example Problem Example Problem (1) Mole Balance: F V 0 F C C C C = = = 0 0 0 0 0 A A A A A A r r r A A A (2) Rate Law: r = kC A A (3) Stoichiometry: F C = F = A A A 0 5 5

Review Lecture 1 CSTR CSTR Example Problem Example Problem (4) Combine: V = 0CA0 CA kCA (5) Evaluate: 1 . 0 C A = C 0 A 3 10 dm 1 . 0 C C 23 ) 1 . 0 10 1 0 0 A A min = = 3 V dm ( . 0 )( ) ( . 0 )( 1 23 min 1 . 0 1 . 0 C 0 A 900 = = 3 391 V dm 3 . 2 6 6

Define conversion, X Define conversion, X Consider the generic reaction: b + d + a A B c C D Chose limiting reactant A as basis of calculation: b c d + + A B C a D a a Define conversion, X moles reacted A = X moles A fed 7 7

Batch Batch Moles A Moles A Moles A = remaining initially reacted = N = N N X 0 0 A 0 A A dN N dX 0 A A dN dX = = A N r V A 0 A dt dt 8 8

Batch Batch = = dN dt r V N 0 0 t X = A A = = t t X X 0 A Integrating, X dX 0 = t N 0 A r V A The necessary t to achieve conversion X. 9 9

CSTR CSTR Consider the generic reaction: b + d + a A B c C D Chose limiting reactant A as basis of calculation: b c d + + A B C a D a a Define conversion, X moles reacted A = X moles A fed 10 10

CSTR CSTR dNA dt Steady State = 0 V =FA0 FA Well Mixed rA = r dV r V A A 11 11

CSTR CSTR Moles A Moles A Moles A = leaving entering = reacted F F F X 0 0 A A A + = 0 F F r dV 0 A A A ( ) V =FA0 FA0 FA0X rA F X = 0 A V r A CSTR volume necessary to achieve conversion X. 12 12

PFR PFR dF = A r A dV = 0 F F F X 0 A A A = 0 dF F X Steady State 0 A A dX r = A dV F 0 A 13 13

PFR PFR = = 0 0 V X = = V V X X Integrating, X 0 F = 0 A V dX r A PFR volume necessary to achieve conversion X. 14 14

Reactor Reactor Mole Balances Mole Balances Summary in terms of conversion, X Summary Reactor Differential Algebraic Integral X X dX dX 0 = Batch t N = N r V A A r V 0 A dt A 0 t V =FA0X CSTR rA X F dX dX dV= rA 0 = 0 A V FA0 PFR r A X X F dX dX dW= r A 0 = PBR 0 A W FA0 A r 15 15 W

Levenspiel Levenspiel Plots Reactor Sizing Given rA as a function of conversion, -rA= f(X), one can size any type of reactor. We do this by constructing a Levenspiel plot. Here we plot either (FA0/-rA) or (1/-rA) as a function of X. For (FA0/-rA) vs. X, the volume of a CSTR and the volume of a PFR can be represented as the shaded areas in the Levenspiel Plots shown as: Plots F A= ( ) 0 g X r A 16 16

Levenspiel Levenspiel Plots Plots FA0 rA X 17 17

CSTR CSTR Area = Volume of CSTR FA0 rA F = 0 A V X 1 r A X 1 X1 18 18

PFR PFR 19 19

Levenspiel Levenspiel Plots Plots 20 20

Numerical Evaluations of Integrals Numerical Evaluations of Integrals The integral to calculate the PFR volume can be evaluated using method as Simpson s One-Third Rule: (See Appendix A.4) X 3 1 4 X 1 F x = = + + 0 A V dX F 0 A 1 ) 0 ( A ( ) 2 / ( ) r r r r X A A A 0 ( ) rA X 2 1 Ar Other numerical methods are: Trapezoidal Rule (uses two data points) Simpson s Three-Eight s Rule (uses four data points) Five-Point Quadrature Formula 1 ( ) rA X 1 1 ) 0 ( Ar X X 0 1 2 21 21

Reactors in Series Reactors in Series Given: rA as a function of conversion, one can also design any sequence of reactors in series by defining X: reacted A of moles total Xi= up point to i moles of A fed to first reactor Only valid if there are no side streams. Molar Flow rate of species A at point i: = F F F X 0 0 Ai A A i 22 22

Reactors in Series Reactors in Series 23 23

Reactors in Series Reactors in Series Reactor 1: = F F F X 1 0 0 1 A A A ( ) F F F F F X F X = = = 0 1 0 0 r 0 1 0 r 1 A A A A A A V 1 r 1 1 1 A A A F V1 A r 0 A X 24 24 X 1

Reactors in Series Reactors in Series Reactor 2: X 1 F 2 = 0 A V dX 2 r A X V2 F 0 A r A X X 1 2 X 25 25

Reactors in Series Reactors in Series Reactor 3: + X = F 0 F F r V 2 3 3 3 A A A ( V3=FA0X3 X2 ) ( ) + = 0 F F F X r V 0 0 ( 2 0 0 3 3 3 A A A ) A A rA3 V3 F A r 0 A 26 X X X X 3 1 2

Reactors in Series Reactors in Series 27 27

Reactors in Series Reactors in Series Space time is the time necessary to process 1 reactor volume of fluid at entrance conditions. =V 0 28 28

KEEPING UP KEEPING UP The tower of CRE, is it stable? 29 29

Reaction Engineering Reaction Engineering Mole Balance Rate Laws Stoichiometry These topics build upon one another. 30 30

Heat Effects Isothermal Design Stoichiometry Rate Laws Mole Balance CRE Algorithm 31 31

Rate Laws Mole Balance Be careful not to cut corners on any of the CRE building blocks while learning this material! 32 32

Heat Effects Isothermal Design Stoichiometry Rate Laws Mole Balance Otherwise, your Algorithm becomes unstable. 33 33

End of End of Lecture Lecture 2 2 34 34