ERT 316: REACTION ENGINEERING CHAPTER 2 CONVERSION & REACTOR SIZING

ERT 316: REACTION ENGINEERINGCHAPTER 2CONVERSION & REACTOR SIZING Lecturer: Miss Anis Atikah Ahmad Email: anisatikah@unimap.edu.my Tel: +604 976 8190

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

1. Conversion A-->B, Xmax,irr= 1 A⇌ B, Xmax,rev = Xe

1. Conversion

2. Batch Reactor Design Equation Moles of A reacted · Moles of A reacted [Moles of A reacted/consumed] = [Moles of A fed] Moles of A fed · [Moles of A reacted/consumed] = [NA0] [X] Moles of A that have been consumed by chemical reaction Moles of A initially fed to reactor at t = 0 Moles of A in reactor at time t [NA][NA0 ][NA0 X] NA NA0 (1 X)

2. Batch Reactor Design Equation Moles of A reacted NA NA0 NA0 X [1] Differentiating wrt time; [2] Recall mole balance for batch reactor (Chapter 1); [2] Rearranging and substituting into ; [Design Equation in terms of conversion]

2. Batch Reactor Design Equation Design Equation (in terms of conversion, X ): [3] What is the time required to achieve a specific conversion? Integrating [3] with limits (t=0, X=0; t=t, X=X )

2. Batch Reactor Design Equation For constant-volume batch reactor; V=V0 [ Design eq. from Chapter 1] [Rearranging] [Re-write in terms of concentration]

3. Flow Reactors Design Equation Moles of A reacted · Moles of A reacted Moles of A reacted/consumed = Moles of A fed Moles of A fed time time · = [FA0] [X] Molar rate at which A is fed to the system Molar rate at which A is consumed within the system Molar flow rate at which A leaves the system [FA][FA0 ][FA0 X] FA FA0 (1 X)

3. Flow Reactors Design Equation FA FA0 FA0X Partial Pressure

3.1 CSTR Recall Design Equation for CSTR (Chapter 1); [1] Substituting into [1] Rearranging; FA FA0 FA0X

3.2 PFR Recall Mole Balance for PFR (Chapter 1); [1] We know that [2] Differentiating [2] wrtX FA FA0 FA0X [3] Substituting [3] into [1] [4]

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

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

Summary of Reactor Mole Balance

4. Reactor Sizing: Cstr & Pfr • With a given –rA as a function of conversion, X, we can size any type of reactor. HOW??? • Construct Levenspiel Plot • FA0/-rAvs. X • Volume of the reactors can be represented as the shaded areas in the Levelspiel Plots:

4. Reactor Sizing • Consider a first order reaction; • A plot of 1/-rAvs. X can be constructed;

4. Reactor Sizing Use plot of 1/-rAvs X to size flow reactors for different entering molar flow rates, FA0 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/-rAis small (rA is big)]. 2. As X --> 1, -rA--> 0, thus 1/-rA --> ∞, V--> ∞ An infinite reactor volume is needed to reach complete conversion

4. Reactor Sizing Important Notes (cont): (For Reversible Rxn, A ⇌ B+C): 1. The max conversion is the equilibrium conversion, Xe. 2. At equilibrium, rA(net)≈ 0. X -->Xe, -rA--> 0, thus 1/-rA--> ∞, V--> ∞ An infinite reactor volume is needed to reach Xe

4.1 Reactor Sizing: Sizing A Cstr EXAMPLE 1

EXAMPLE 1 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: • Find –1/rAat X=0.8 2. Calculate V.

4.1 Sizing A Cstr EXAMPLE 1 Levelspiel Plot:

4.2 Reactor Sizing: Sizing A Pfr • 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

4.2 Reactor Sizing: Sizing A Pfr • Trapezoidal Rule (2-point): • Simpson’s One-Third Rule (3-point):

4.2 Reactor Sizing: Sizing A Pfr • Simpson’s Three-Eighths Rule (4-point): • Five-Point Quadrature Formula:

4.2 Sizing A Pfr 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.

4.2 Reactor Sizing: Sizing A Pfr • Recall the design equation of PFR: • For X=0.8,

4.2 Sizing A Pfr EXAMPLE 2 Levelspiel Plot:

4.2 Sizing A Pfr • Recall 5-Point Quadrature Rule: • Find h (∆X):

4.2 Sizing A Pfr EXAMPLE 2 Levelspiel Plot:

4.2 Sizing A Pfr • Find V: • Substituting the numerical values: --> PFR with volume of 2.165 m3 is required to reach 80% conversion

4.3 Comparing Volume of Cstr & Pfr CSTR Difference btwn CSTR & PFR volumes=4.235m3 PFR

4.3 Comparing Volume of Cstr & Pfr CSTR PFR VCSTR > VPFRfor the same conversion & rxn condition. WHY???

5. Reactors in Series • The exit stream of one reactor is fed to the next one

5.1 Cstr in Series Reactor 1: Mole Balance: In – Out + Generation = 0 FA0 – FA1 + rA1V1 = 0 [1] The molar flow rate of A at point 1: FA1 = FA0–FA0 X1 [2] Combining [1] & [2]: (1) (2)

5.1 Cstr in Series Reactor 2: Mole Balance: In – Out + Generation = 0 FA1 – FA2 + rA2V2 = 0 [3] The molar flow rate of A at point 2: FA2 = FA0–FA0 X2 [4] Combining [3] & [4]: (1) (2) Expressed in eq [2] & [4] [5]

5.1 Cstr in Series FA1 = FA0– FA0 X1 [2] (1) FA2 = FA0– FA0 X2 [4] (2) [5] Substituting [2] &[4] into [5];

5.1 Cstr in Series EXAMPLE 3 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 For reactor 1, X = 0.4 Total V= (0.82+ 3.2)m3 = 4.02 m3 For reactor 2, X = 0.8

EXAMPLE 3 5.1 Cstr in Series Levenspiel Plot of CSTR in series V2 V1

5.2 Pfr in Series V1 V2 The overall conversion of two PFRs in series is the same as ONE PFR with the same total volume. V2, PFR V1, PFR

5.2 Pfr in Series EXAMPLE 4 Calculate the reactor volume V1and V2 for the plug-flow sequence shown below when the intermediate conversion is 40% & the final conversion is 80%.

Using Simpsons One-Third Rule; For reactor 1, ∆X=0.2, X0 = 0, X1 = 0.2, X2 = 0.4

For reactor 2, ∆X=0.2, X0 = 0.4, X1 = 0.6, X2 = 0.8 Total volume;

5.3 Combination of Cstr & Pfr V3,CSTR V2,PFR V1,CSTR X3 X2 X1

5.4 Reactor Sequencing Which sequence is better to obtain the highest overall conversion? OR • The BEST sequence of reactors depend on • Levenspiel Plot • Reactor Size

6. 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=0.2m3, v0= 0.01m3/s, what is τ? Answer: τ= 20 s

7. 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)

Summary • Design equation: Batch: CSTR: PFR: PBR: • Conversion: Batch reactor: Flow Reactors • Reactor in series: Conversion: CSTR in series: PFR in series:

Exercise 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 m3/min ?

ERT 316: REACTION ENGINEERING CHAPTER 2 CONVERSION & REACTOR SIZING