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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

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

aA + bB cC + dD Taking 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, Xmax,irr = 1 A⇌ B, Xmax,rev = Xe

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**Continuous Flow Reactor**

1. Conversion Batch Reactor Continuous Flow Reactor

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**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 NA ( X)

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**2. Batch Reactor Design Equation**

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

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**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 )

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**2. Batch Reactor Design Equation**

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

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**3. Flow Reactors Design Equation**

Moles of A reacted Moles of A reacted/consumed = Moles of A fed Moles of A reacted time time Moles of A fed = [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 FA ( X)

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**3. Flow Reactors Design Equation**

FA FA FA0 X Liquid phase is given in mol/dm3 Gas phase Partial Pressure

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**3.1 CSTR FA FA0 FA0 X Recall Design Equation for CSTR (Chapter 1); [1]**

Substituting into [1] Rearranging; FA FA FA0 X

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**3.2 PFR FA FA0 FA0 X Recall Mole Balance for PFR (Chapter 1); [1]**

We know that [2] Differentiating [2] wrt X FA FA FA0 X [3] Substituting [3] into [1] [4]

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

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**3.3 PBR Design equation for PBR; Catalyst weight ; VW -rA -r’A**

Similar to that of PFR except these terms: Catalyst weight ; VW -rA -r’A

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**Summary of Reactor Mole Balance**

Differential Form Algebraic Form Integral Form Batch CSTR - - PFR PBR

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**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/-rA vs. X Volume of the reactors can be represented as the shaded areas in the Levelspiel Plots:

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**4. Reactor Sizing Consider a first order reaction;**

A plot of 1/-rA vs. X can be constructed;

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**An infinite reactor volume is needed to reach complete conversion**

4. Reactor Sizing Use plot of 1/-rA vs 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/-rA is small (rA is big)]. 2. As X --> 1, -rA --> 0, thus 1/-rA --> ∞, V--> ∞ An infinite reactor volume is needed to reach complete conversion

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**An infinite reactor volume is needed to reach Xe**

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

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**4.1 Reactor Sizing: Sizing A Cstr**

EXAMPLE 1

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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/rA at X=0.8 2. Calculate V.

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**4.1 Sizing A Cstr Levelspiel Plot: X 0.1 0.2 0.4 0.6 0.7 0.8 rA 0.45**

EXAMPLE 1 Levelspiel Plot: X 0.1 0.2 0.4 0.6 0.7 0.8 rA 0.45 0.37 0.3 0.195 0.113 0.079 0.05 FA0/rA 0.89 1.08 1.33 2.05 3.54 5.06 8.00

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**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

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**4.2 Reactor Sizing: Sizing A Pfr**

Trapezoidal Rule (2-point): Simpson’s One-Third Rule (3-point):

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**4.2 Reactor Sizing: Sizing A Pfr**

Simpson’s Three-Eighths Rule (4-point): Five-Point Quadrature Formula:

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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.

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**4.2 Reactor Sizing: Sizing A Pfr**

Recall the design equation of PFR: For X=0.8,

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**4.2 Sizing A Pfr Levelspiel Plot: X 0.1 0.2 0.4 0.6 0.7 0.8 rA 0.45**

EXAMPLE 2 Levelspiel Plot: X 0.1 0.2 0.4 0.6 0.7 0.8 rA 0.45 0.37 0.3 0.195 0.113 0.079 0.05 FA0/rA 0.89 1.08 1.33 2.05 3.54 5.06 8.00

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

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**4.2 Sizing A Pfr Levelspiel Plot: X 0.1 0.2 0.4 0.6 0.7 0.8 rA 0.45**

EXAMPLE 2 Levelspiel Plot: X 0.1 0.2 0.4 0.6 0.7 0.8 rA 0.45 0.37 0.3 0.195 0.113 0.079 0.05 FA0/rA 0.89 1.08 1.33 2.05 3.54 5.06 8.00

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**4.2 Sizing A Pfr Find V: Substituting the numerical values:**

--> PFR with volume of m3 is required to reach 80% conversion

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**4.3 Comparing Volume of Cstr & Pfr**

Difference btwn CSTR & PFR volumes=4.235m3 PFR

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**4.3 Comparing Volume of Cstr & Pfr**

VCSTR > VPFR for the same conversion & rxn condition. WHY???

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

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**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 X [2] Combining [1] & [2]: (1) (2)

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**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 X [4] Combining [3] & [4]: (1) (2) Expressed in eq [2] & [4] [5]

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**5.1 Cstr in Series FA1 = FA0 – FA0 X1 [2] FA2 = FA0 – FA0 X2 [4] [5]**

(1) FA2 = FA0 – FA0 X [4] (2) [5] Substituting [2] &[4] into [5];

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5.1 Cstr in Series EXAMPLE 3 X 0.0 0.1 0.2 0.4 0.6 0.7 0.8 [FA0/-rA](m3) 0.89 1.08 1.33 2.05 3.54 5.06 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?

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**For reactor 1, X = 0.4 For reactor 2, X = 0.8 X 0.0 0.1 0.2 0.4 0.6**

EXAMPLE 3 X 0.0 0.1 0.2 0.4 0.6 0.7 0.8 [FA0/-rA](m3) 0.89 1.08 1.33 2.05 3.54 5.06 8.0 For reactor 1, X = 0.4 For reactor 2, X = 0.8 Total V= ( )m3 = 4.02 m3

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

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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. V1, PFR V2, PFR

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5.2 Pfr in Series EXAMPLE 4 X 0.0 0.1 0.2 0.4 0.6 0.7 0.8 [FA0/-rA](m3) 0.89 1.08 1.33 2.05 3.54 5.06 8.0 Calculate the reactor volume V1 and V2 for the plug-flow sequence shown below when the intermediate conversion is 40% & the final conversion is 80%.

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**Using Simpsons One-Third Rule;**

X 0.0 0.1 0.2 0.4 0.6 0.7 0.8 [FA0/-rA](m3) 0.89 1.08 1.33 2.05 3.54 5.06 8.0 Using Simpsons One-Third Rule; For reactor 1, ∆X=0.2, X0 = 0, X1 = 0.2, X2 = 0.4

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

0.0 0.1 0.2 0.4 0.6 0.7 0.8 [FA0/-rA](m3) 0.89 1.08 1.33 2.05 3.54 5.06 8.0 For reactor 2, ∆X=0.2, X0 = 0.4, X1 = 0.6, X2 = 0.8 Total volume;

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**5.3 Combination of Cstr & Pfr**

V3,CSTR V1,CSTR V2,PFR X1 X2 X3

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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

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**Measures entering flow rate at the entrance condition**

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

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**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)

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**Summary Conversion: Batch reactor: Flow Reactors Design equation:**

Batch: CSTR: PFR: PBR: Reactor in series: Conversion: CSTR in series: PFR in series:

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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 ? -rA (mol/dm3.s) X 0.0 0.15 0.3 0.6

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Exercise (a) What is PFR volume necessary to achieve 30 % conversion for an entering flow rate of 2 m3/min ? Given: We know that and for gas phase: 1. Find CA0 2. Find FA0 3. Calculate VPFR using Integration Rule

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**Exercise Using Simpson One-Third Rule: -rA (mol/dm3.s) 0.00001**

X 0.0 0.15 0.3 0.6 FA0/-rA (dm3) 243000 486000 Using Simpson One-Third Rule:

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Exercise -rA (mol/dm3.s) X 0.0 0.15 0.3 0.6 FA0/-rA (dm3) 243000 486000 (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)? FA0=2.43 mol/s X=0.3 X=0.6

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Exercise FA0=2.43 mol/s X=0.3 X=0.6

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