ERT 316: REACTION ENGINEERING CHAPTER 2 CONVERSION & 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 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

Continuous Flow Reactor 1. Conversion Batch Reactor Continuous Flow Reactor

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); Rearranging and substituting into ; [2] [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/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 FA0 (1 X)

3. Flow Reactors Design Equation FA FA0 FA0 X Liquid phase is given in mol/dm3 Gas phase Partial Pressure

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

3.2 PFR FA FA0 FA0 X Recall Mole Balance for PFR (Chapter 1); [1] We know that [2] Differentiating [2] wrt X FA FA0 FA0 X [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; Catalyst weight ; VW -rA -r’A Similar to that of PFR except these terms: Catalyst weight ; VW -rA -r’A

Summary of Reactor Mole Balance Differential Form Algebraic Form Integral Form Batch   CSTR -   - PFR PBR

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:

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

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

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

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/rA at X=0.8 2. Calculate V.

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

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 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

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

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

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 Difference btwn CSTR & PFR volumes=4.235m3 PFR

4.3 Comparing Volume of Cstr & Pfr VCSTR > VPFR for 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] FA2 = FA0 – FA0 X2 [4] [5] (1) FA2 = FA0 – FA0 X2 [4] (2) [5] Substituting [2] &[4] into [5];

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?

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= (0.82 + 3.2)m3 = 4.02 m3

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. V1, PFR V2, PFR

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%.

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

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;

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

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

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

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 Conversion: Batch reactor: Flow Reactors Design equation: Batch: CSTR: PFR: PBR: 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 ? -rA (mol/dm3.s) 0.00001 0.000005 0.000002 0.000001 X 0.0 0.15 0.3 0.6

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

Exercise Using Simpson One-Third Rule: -rA (mol/dm3.s) 0.00001 0.000005 0.000002 0.000001 X 0.0 0.15 0.3 0.6 FA0/-rA (dm3) 243000 486000 1215000 2430000 Using Simpson One-Third Rule:

Exercise -rA (mol/dm3.s) 0.00001 0.000005 0.000002 0.000001 X 0.0 0.15 0.3 0.6 FA0/-rA (dm3) 243000 486000 1215000 2430000 (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

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