PTT 255 REACTION ENGINEERING CONVERSION REACTOR SIZING PART

PTT 255 REACTION ENGINEERING CONVERSION & REACTOR SIZING PART 2 – REACTOR SIZING 1 Department of Chemical Engineering Technology

OUTLINE Sizing Flow Reactors in Series Space Time Space Velocity 2

REACTOR SIZING: CSTR & PFR Sizing a reactor means determine the reactor volumes With a given –r. A as a function of conversion, X, we can know the size of reactor By sizing a chemical reactor we mean we're either determine the reactor volume to achieve a given conversion or determine the conversion that can be achieved in a given reactor type and size Commonly applied to CSTR and PFR as volume could be their crucial factor HOW? ? ? Construct Levenspiel Plot FA 0 (1/-r. A ) vs. X A plot to determine the where FA 0 is a constant volume of chemical reactor and it was named after a professor Octave 3 Levenspiel

LEVENSPIEL PLOT Use plot of 1/-r. A vs X to size flow reactors for different entering molar flow rates, FA 0 Volume of the reactors can be represented as the shaded areas in the Levenspiel Plots: 4

REACTOR SIZING For Irreversible Rxn, Rxn (A --> B+C): • 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)]. • As X --> 1, -r. A --> 0, thus 1/-r. A --> ∞, V--> ∞ An infinite reactor volume is needed to reach complete conversion For Reversible Rxn, Rxn (A ⇌ B+C): • The max conversion is the equilibrium conversion, Xe. (At equilibrium, r. A(net)≈ 0. ) • X --> Xe, -r. A --> 0, thus 1/-r. A --> ∞, V--> ∞ An infinite reactor volume is needed to reach Xe 5

EXERCISE 3 : CSTR SIZING 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. 6

Levenspiel Plot: X r. A 0 0. 45 0. 1 0. 37 0. 2 0. 3 0. 4 0. 195 0. 6 0. 113 0. 7 0. 079 0. 8 0. 05 FA 0/-r. A 0. 89 1. 08 1. 33 2. 05 3. 54 5. 06 8. 00 7

REACTOR SIZING: PFR SIZING 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 8

PFR SIZING: INTEGRATION FORMULA Trapezoidal Rule (2 -point): Simpson’s One-Third Rule (3 -point): 9

PFR SIZING: INTEGRATION FORMULA Simpson’s Three-Eighths Rule (4 -point): Five-Point Quadrature Formula: 10

EXERCISE 4 : PFR SIZING Species A enters the PFR at a molar flow rate of 0. 4 mol/s. Calculate the volume to achieve 80% conversion, considering three level of conversion. 11

Levenspiel Plot: X r. A FA 0/r. A 0 0. 45 0. 89 0. 4 0. 195 2. 05 0. 8 0. 05 8. 00 12

COMPARING VOLUME OF CSTR & PFR Difference btwn CSTR & PFR volumes=4. 235 m 3 13

REACTORS IN SERIES The exit stream of one reactor is fed to the next one 14

CSTR IN SERIES EXAMPLE X [FA 0/-r. A](m 3) 0. 0 0. 89 0. 1 1. 08 0. 2 1. 33 0. 4 2. 05 0. 6 3. 54 0. 7 5. 06 0. 8 8. 0 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? 15

EXAMPLE 3 X [FA 0/-r. A](m 3) 0. 0 0. 89 0. 1 1. 08 0. 2 1. 33 0. 4 2. 05 0. 6 3. 54 0. 7 5. 06 0. 8 8. 0 For reactor 1, X = 0. 4 For reactor 2, X = 0. 8 Total V= (0. 82 + 3. 2)m 3 = 4. 02 m 3 16

EXAMPLE 3 CSTR IN SERIES Levenspiel Plot of CSTR in series V 1 V 2 17

PFR IN SERIES EXAMPLE X [FA 0/-r. A](m 3) 0. 0 0. 89 0. 1 1. 08 0. 2 1. 33 0. 4 2. 05 0. 6 3. 54 0. 7 5. 06 0. 8 8. 0 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%. 18

PFR IN SERIES V 1 V 2 The overall conversion of two PFRs in series is the same as ONE PFR with the same total volume. V 1, PFR V 2, PFR 19

X [FA 0/-r. A](m 3) 0. 0 0. 89 0. 1 1. 08 0. 2 1. 33 0. 4 2. 05 0. 6 3. 54 0. 7 5. 06 0. 8 8. 0 Using Simpsons One-Third Rule; For reactor 1, ∆X=0. 2, X 0 = 0, X 1 = 0. 2, X 2 = 0. 4 20

X [FA 0/-r. A](m 3) 0. 0 0. 89 0. 1 1. 08 0. 2 1. 33 0. 4 2. 05 0. 6 3. 54 0. 7 5. 06 0. 8 8. 0 For reactor 2, ∆X=0. 2, X 0 = 0. 4, X 1 = 0. 6, X 2 = 0. 8 Total volume; 21

COMBINATION OF CSTR & PFR V 1, CSTR X 1 V 3, CSTR V 2, PFR X 2 X 3 22

REACTOR SEQUENCING Which sequence is better to obtain the highest overall conversion? OR The BEST sequence of reactors depend on 1. Levenspiel Plot 2. Reactor Size 23

SPACE TIME Measures entering flow rate at the entrance condition Space time/Mean residence time : time taken for a fluid to either completely enter or completely exit the reactor Eg: If V=0. 2 m 3, v 0= 0. 01 m 3/s, what is τ? Answer: τ = 20 s 24

SPACE VELOCITY, 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) 25

SUMMARY Conversion: Batch reactor: Design equation: Batch: Flow Reactors CSTR: PFR: PBR: Reactor in series: Conversion: CSTR in series: PFR in series: 26

THANK YOU 27