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## ERT 316: REACTION ENGINEERING CHAPTER 2 CONVERSION & REACTOR SIZING

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**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**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 ; VW -rA-r’A**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 ?