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ERT 316: REACTION ENGINEERING CHAPTER 2 CONVERSION & REACTOR SIZING Lecturer: Miss Anis Atikah Ahmad Tel:

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OUTLINE Conversion Batch Reactor Design Equation Flow Reactors Design Equations CSTR PFR PBR Sizing Flow Reactors Reactors in Series Space Time Space Velocity 2

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1. C ONVERSION 3 aA + bB cC + dDTaking A as a basis, Conversion, XA, is the number of moles A that have reacted per mole of A fed to the system A-->B, X max,irr = 1 A ⇌ B, X max,rev = X e

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1. C ONVERSION Batch Reactor Continuous Flow Reactor 4

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2. B ATCH R EACTOR D ESIGN E QUATION [Moles of A reacted/consumed] = [Moles of A fed] Moles of A reacted Moles of A fed [Moles of A reacted/consumed] = [ N A0 ] [ X ] Moles of A reacted Moles of A in reactor at time t Moles of A initially fed to reactor at t = 0 Moles of A that have been consumed by chemical reaction · · [N A ] [N A0 ] [N A0 X] N A N A0 (1 X)

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2. B ATCH R EACTOR D ESIGN E QUATION Recall mole balance for batch reactor (Chapter 1); Rearranging and substituting into ; Moles of A reacted N A N A0 N A0 X Differentiating wrt time; [1] [2] [Design Equation in terms of conversion]

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2. B ATCH R EACTOR D ESIGN E QUATION Design Equation (in terms of conversion, X ): What is the time required to achieve a specific conversion? Integrating [3] with limits (t=0, X=0; t=t, X=X ) [3]

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8 For constant-volume batch reactor; V=V 0 [ Design eq. from Chapter 1] [Rearranging] [Re-write in terms of concentration] 2. B ATCH R EACTOR D ESIGN E QUATION

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3. F LOW R EACTORS D ESIGN E QUATION Moles of A reacted/consumed = Moles of A fed Moles of A reacted Moles of A fed = [ F A0 ] [ X ] Moles of A reacted Molar flow rate at which A leaves the system Molar rate at which A is fed to the system · · [F A ] [F A0 ] [F A0 X] F A F A0 (1 X) time Molar rate at which A is consumed within the system

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is given in mol/dm 3 Liquid phase Gas phase 3. F LOW R EACTORS D ESIGN E QUATION F A F A0 F A0 X F A F A0 F A0 X Partial Pressure

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3.1 CSTR 11 Recall Design Equation for CSTR (Chapter 1); [1] Substituting into [1] Rearranging; F A F A0 F A0 X F A F A0 F A0 X

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3.2 PFR 12 Recall Mole Balance for PFR (Chapter 1); [1] We know that [2] Differentiating [2] wrt X F A F A0 F A0 X F A F A0 F A0 X [3] Substituting [3] into [1] [4]

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3.2 PFR 13 Integrating [4] with limit V=0 when X=0; [4]

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3.3 PBR 14 Design equation for PBR; Similar to that of PFR except these terms: Catalyst weight ; V W -r A -r’ A

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S UMMARY OF R EACTOR M OLE B ALANCE ReactorDifferential FormAlgebraic FormIntegral Form Batch CSTR- - PFR PBR

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4. R EACTOR S IZING : C STR & P FR With a given –r A as a function of conversion, X, we can size any type of reactor. HOW??? Construct Levenspiel Plot F A0 /-r A vs. X Volume of the reactors can be represented as the shaded areas in the Levelspiel Plots: 16

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Consider a first order reaction; A plot of 1/-r A vs. X can be constructed; R EACTOR S IZING

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18 4. R EACTOR S IZING Use plot of 1/-r A vs X to size flow reactors for different entering molar flow rates, F A0 Irreversible Rxn Important Notes (For Irreversible Rxn, A --> B+C): 1. If the reaction is carried out isothermally, the rate is usually greatest at the start of the reaction, when the concentration is greatest [when X≈0, 1/-r A is small (r A is big)]. 2. As X --> 1, -r A --> 0, thus 1/-r A --> ∞, V--> ∞ An infinite reactor volume is needed to reach complete conversion

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19 4. R EACTOR S IZING Important Notes (cont): Reversible Rxn (For Reversible Rxn, A ⇌ B+C): 1. The max conversion is the equilibrium conversion, X e. 2. At equilibrium, r A (net)≈ 0. X --> X e, -r A --> 0, thus 1/-r A --> ∞, V--> ∞ An infinite reactor volume is needed to reach X e

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EXAMPLE R EACTOR S IZING : S IZING A C STR

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21 Calculate the volume to achieve 80% conversion in a CSTR. Given, species A enters the reactor at a molar flow rate of 0.4 mol/s. SOLUTION: 1.Find –1/r A at X =0.8 EXAMPLE 1 2. Calculate V.

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22 Levelspiel Plot: 4.1 S IZING A C STR EXAMPLE 1 X rArA F A0 /r A

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Volume of a PFR can be calculated using integration formulas: Trapezoidal Rule (2-point) Simpson’s One-Third Rule (3-point) Simpson’s Three-Eighths Rule (4-point) Five-Point Quadrature Formula R EACTOR S IZING : S IZING A P FR

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Trapezoidal Rule (2-point): R EACTOR S IZING : S IZING A P FR Simpson’s One-Third Rule (3-point):

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Simpson’s Three-Eighths Rule (4-point): R EACTOR S IZING : S IZING A P FR Five-Point Quadrature Formula:

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S IZING A P FR EXAMPLE 2 Calculate the volume to achieve 80% conversion in a PFR. Given, species A enters the reactor at a molar flow rate of 0.4 mol/s.

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Recall the design equation of PFR: R EACTOR S IZING : S IZING A P FR For X =0.8,

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28 Levelspiel Plot: 4.2 S IZING A P FR EXAMPLE 2 X rArA F A0 /r A

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Recall 5-Point Quadrature Rule: 4.2 S IZING A P FR 29 Find h ( ∆X ):

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30 Levelspiel Plot: 4.2 S IZING A P FR EXAMPLE 2 X rArA F A0 /r A

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Find V: S IZING A P FR Substituting the numerical values: --> PFR with volume of m 3 is required to reach 80% conversion

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4.3 C OMPARING V OLUME OF C STR & P FR 32 Difference btwn CSTR & PFR volumes=4.235m 3

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4.3 C OMPARING V OLUME OF C STR & P FR 33 V CSTR > V PFR for the same conversion & rxn condition. WHY???

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5. R EACTORS IN S ERIES The exit stream of one reactor is fed to the next one 34

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5.1 C STR IN S ERIES 35 Reactor 1: Mole Balance : In – Out + Generation = 0 F A0 – F A1 + r A1 V 1 = 0 [1] The molar flow rate of A at point 1: F A1 = F A0 – F A0 X 1 [2] Combining [1] & [2]: (1) (2)

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5.1 C STR IN S ERIES 36 (1) (2) [5] Expressed in eq [2] & [4] Reactor 2: Mole Balance : In – Out + Generation = 0 F A1 – F A2 + r A2 V 2 = 0 [3] The molar flow rate of A at point 2: F A2 = F A0 – F A0 X 2 [4] Combining [3] & [4]:

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37 F A1 = F A0 – F A0 X 1 [2] F A2 = F A0 – F A0 X 2 [4] [5] Substituting [2] &[4] into [5]; 5.1 C STR IN S ERIES (1) (2)

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X [F A0 /-r A ](m 3 ) C STR IN S ERIES For the two CSTRs in series, 40% conversion is achieved in the first reactor. What is the volume of each of the two reactors necessary to achieve 80% overall conversion of entering species? EXAMPLE 3

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X [F A0 /-r A ](m 3 ) EXAMPLE 3 For reactor 1, X = 0.4 For reactor 2, X = 0.8 Total V= ( )m 3 = 4.02 m 3

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Levenspiel Plot of CSTR in series 40 V1V1 V2V2 5.1 C STR IN S ERIES EXAMPLE 3

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5.2 P FR IN S ERIES 41 The overall conversion of two PFRs in series is the same as O NE PFR with the same total volume. V 1, PFR V 2, PFR V1V1 V1V1 V2V2 V2V2

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X [F A0 /-r A ](m 3 ) P FR IN S ERIES Calculate the reactor volume V 1 and V 2 for the plug-flow sequence shown below when the intermediate conversion is 40% & the final conversion is 80%. EXAMPLE 4

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X [F A0 /-r A ](m 3 ) Using Simpsons One-Third Rule; For reactor 1, ∆ X =0.2, X 0 = 0, X 1 = 0.2, X 2 = 0.4

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X [F A0 /-r A ](m 3 ) For reactor 2, ∆ X =0.2, X 0 = 0.4, X 1 = 0.6, X 2 = 0.8 Total volume;

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45 X1X1 X2X2 X3X3 5.3 C OMBINATION OF C STR & P FR V 1,CSTR V 2,PFR V 3,CSTR

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5.4 R EACTOR S EQUENCING 46 Which sequence is better to obtain the highest overall conversion? OR The BEST sequence of reactors depend on 1.Levenspiel Plot 2.Reactor Size

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Space time/Mean residence time : time taken for a fluid to either completely enter or completely exit the reactor Eg: If V =0.2m 3, v 0 = 0.01m 3 /s, what is τ ? Answer: τ = 20 s 6. S PACE T IME 47 Measures entering flow rate at the entrance condition

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7. S PACE V ELOCITY, SV Space velocity can be defined as: 2 types of SV that is commonly used in industry: Liquid-hourly space velocity (LHSV) –measures liquid volumetric rate at 60 °F or 75°F Gas-hourly space velocity (GHSV)-measures gas volumetric at standard temperature & pressure (STP) 48

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S UMMARY Conversion: Batch reactor:Flow Reactors 49 Design equation: Batch: CSTR: PFR: PBR: Reactor in series: Conversion: CSTR in series: PFR in series:

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E XERCISE The irreversible gas-phase non-elementary reaction A + 2B --> C is to be carried out isothermally in a constant pressure batch reactor. The feed is at a temperature of 227 °C, a pressure of 1013 kPa, and its composition is 30% A and 60% B. Laboratory data taken under identical conditions are as follows : (a) What is PFR volume necessary to achieve 30 % conversion for an entering flow rate of 2 m 3 /min ? 50 -r A (mol/dm 3.s) X

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Given: We know that and for gas phase: E XERCISE 51 (a) What is PFR volume necessary to achieve 30 % conversion for an entering flow rate of 2 m 3 /min ? 1. Find C A0 2. Find F A0 3. Calculate V PFR using Integration Rule

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Using Simpson One-Third Rule: -r A (mol/dm 3.s) X F A0 /-r A (dm 3 ) E XERCISE

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(b) What is CSTR volume necessary to take the effluent from PFR above and achieve 60% total conversion (based on species A fed to the PFR)? -r A (mol/dm 3.s) X F A0 /-r A (dm 3 ) E XERCISE X=0.6 X=0.3 F A0 =2.43 mol/s

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E XERCISE 54 X=0.6 X=0.3 F A0 =2.43 mol/s

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