6. Multiple Reactions
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1 6. Multiple Reactions o Selectivity and Yield o Reactions in Series - To give maximum selectivity o Algorithm for Multiple Reactions o Applications of Algorithm o Multiple Reactions-Gas Phase
2 0. Types of Multiple Rxns I o Parallel Reactions A A - Oxidation of ethylene k1 B k2 C o Series Reactions A 2 k 1 B k C - Reaction of EO with ammonia Apr/ Spring 2
3 0. Types of Multiple Rxns II o Complex Reactions: Series and Parallel aspects k1 combined A 2B C k2 A 2C 3D - Formation butadiene from ethanol o Independent Reactions - Cracking crude oil k1 A B k2 C D Apr/ Spring 3
4 1. Selectivity and Yield I Apr/ Spring 4 o Two types of selectivity Instantaneous Overall Selectivity Yield Example U D DU r r S A D D r r Y U D DU ~ F F S A A0 D D ~ F F F Y B A 2 U k B 2 A 1 D k undesired product, U, B A desired product, D, B A 2 1 C C k r C C k r A 2 1 B A 2 B 2 A 1 U D DU C k k C C k C k C r r S
5 Apr/ Spring 5
6 1. Selectivity and Yield II o Self Test 1-3 species were found in a CSTR, C A0 = 2moles/dm 3 Run T ( o C) C A (mole/dm 3 ) C B (mole/dm 3 ) C C (mole/dm 3 ) Apr/ Spring 6
7 1. Selectivity and Yield III o Self Test 2 - At low temperatures 1) Little conversion of A 2) Little B formed 3) Mostly C formed (but not too much because of the low conversion - 15 to 30% - of A) - At high temperatures 1) Virtually complete conversion of A 2) Mostly B formed Apr/ Spring 7
8 1. Selectivity and Yield IV o Self Test 3 - Data suggest 2 reactions - Reaction (1) is dominant at high temperatures with k 1» k 2, A 1» A 2 - Reaction (2) is dominant at low temperatures k 2» k 1, E 2 > E 1 Apr/ Spring 8
9 1. Selectivity and Yield V o Self Test 4 Apr/ Spring 9
10 2. Parallel Reactions I A A k1 k2 D(Desired), U(Undesired), r D r U k C 1 α A k 2 C β A o The net rate of disappearance of A r A r D o Instantaneous selectivity S D/U r r D U r U k1c k C 2 α A β A k k 1 2 C (α-β) A - If α > β use high concentration of A. Use PFR. - If α < β use low concentration of A. Use CSTR. Apr/ Spring 10
11 Reactor Selection I o Criteria - Selectivity - Yield - Temperature control - Safety - Cost Apr/ Spring 11
12 Reactor Selection II o Application of Batch - High A with low B (d) - High B with low A (e) Apr/ Spring 12
13 Reactor Selection III o Application of PFR (Membrane) - High A with low B (f) - High B with low A (g) Apr/ Spring 13
14 Reactor Selection IV o Low A & B with temp. control Apr/ Spring 14
15 Reactor Selection V o Reversible reaction - Shift equilibrium by removing C Apr/ Spring 15
16 2. Parallel Reactions II o Maximizing the Selectivity - Parallel Reactions 1 - Determine the instantaneous selectivity, S D/U, for the liquid phase reactions: Sketch the selectivity as a function of the concentration of A. Is there an optimum and if so what is it? Apr/ Spring 16
17 2. Parallel Reactions III o Maximizing the Selectivity - Parallel Reactions 2 Use CSTR with exit concentration C * A Apr/ Spring 17
18 3. Series Reactions (p. 283) o Example: Series reaction in a batch reactor 1 - This series reaction could also be written as Reaction (1) : -r 1A =k 1 C A Reaction (2) : -r 2B =k 2 C B - Mole balance on every species Species A Apr/ Spring 18
19 3. Series Reactions II o Example: Series reaction in a batch reactor 2 - Net rate of reaction of A, r A =r 1A +0 - Rate law, r 1A =-k 1A C A - Relative rates, r 1B =-r 1A - Integrating with C A = C A0 at t = 0 and then rearranging Apr/ Spring 19
20 3. Series Reactions III o Example: Series reaction in a batch reactor 3 - Net species B: Net rate of reaction of B Rate law, r 2B =-k 2 C B Relative rates Combine 1 st order ODE Apr/ Spring 20
21 3. Series Reactions IV o Example: Series reaction in a batch reactor 4 - Using the integrating factor, i.f.: (p 1012, A 3) Evaluate at t = 0, C B = 0 Apr/ Spring 21
22 3. Series Reactions V o Example: Series reaction in a batch reactor 5 - Optimization of the desired product B - Species C, C C = C A0 - C B - C A Apr/ Spring 22
23 3. Series Reactions VI o Self Test 1 - Concentration-time trajectories - Which of the following reaction pathways best describes the data: Apr/ Spring 23
24 3. Series Reactions VII o Self Test 2 - Concentration-time trajectories - Sketch the concentration-time trajectory for the reaction Apr/ Spring 24
25 4. Algorithm for Complex Reactions I Apr/ Spring 25
26 4. Algorithm for Complex Reactions II Apr/ Spring 26
27 4. Algorithm for Complex Reactions III o Mole Balances (p 327) Reactor Type Gas Phase Liquid Phase Batch Semibatch CSTR PFR PBR Apr/ Spring 27
28 4. Algorithm for Complex Reactions IV o Rates 1 - Number every reaction - Rate laws for every reaction - Relative rates for each reaction for a given reaction i Apr/ Spring 28
29 4. Algorithm for Complex Reactions V o Rates 2 - Relative rates for each reaction 2 Apr/ Spring 29
30 4. Algorithm for Complex Reactions VI o Rates 3 - Net rate of formation for species A that appears in N reactions Apr/ Spring 30
31 4. Algorithm for Complex Reactions VII o Stoichiometry - Net rate of formation for species A that appears in N reactions - NOTE: We could use the gas phase mole balance for liquids and then just express the concentration as Flow C A = F A /v 0 Batch C A = N A /V 0 Apr/ Spring 31
32 4. Algorithm for Complex Reactions VIII o Self Test - Writing net rates of formation The reactions are elementary. Write the net rates of formation for A, B, C and D Sol) A Apr/ Spring 32
33 4. Algorithm for Complex Reactions IX o Self Test 2 B Apr/ Spring 33
34 4. Algorithm for Complex Reactions X o Self Test 3 C Apr/ Spring 34
35 4. Algorithm for Complex Reactions XI o Self Test 4 D - These net rates of reaction are now coupled with the appropriate mole balance of A, B, C, and D and solved using a numerical software package. For example for a PFR: Apr/ Spring 35
36 5. Applications of Algorithm I (1) (2) NOTE: The specific reaction rate k 1A is defined wrt species A. NOTE: The specific reaction rate k 2C is defined wrt species C. Apr/ Spring 36
37 5. Applications of Algorithm II o Example A: Liquid phase PFR 1 - The complex liquid phase reactions follow elementary rate laws (1) A + 2B C -r 1A = k 1A C A C B 2 (2) 2A + 3C D -r 2C = k 2C C A2 C B 3 - Equal molar in A and B with F A0 = 200 mol/min and the volumetric flow rate is 100 dm 3 /min. The reaction volume is 50 dm 3 and the rate constants are - Plot F A, F B, F C, F D and S C/D as a function of V Apr/ Spring 37
38 5. Applications of Algorithm III o Example A: Liquid phase PFR 2 - Solution Mole balances Apr/ Spring 38
39 5. Applications of Algorithm IV o Example A: Liquid phase PFR 3 - Solution Net rates Rate laws Apr/ Spring 39
40 5. Applications of Algorithm V o Example A: Liquid phase PFR 4 - Solution Relative rates Apr/ Spring 40
41 5. Applications of Algorithm VI o Example A: Liquid phase PFR 5 - Solution Selectivity If one were to write S C/D = F C /F D in the Matlab program, Matlab would not execute because at V = 0 F C = 0 resulting in an undefined volume (infinity) at V = 0. To get around this problem we start the calculation 10-4 dm 3 from the reactor entrance where F D will note be zero and use the following IF statement. Apr/ Spring 41
42 5. Applications of Algorithm VII o Example A: Liquid phase PFR 6 - Solution Stoichiometry Parameters Apr/ Spring 42
43 5. Applications of Algorithm VIII o Example A: Liquid phase PFR 7 - Solution Apr/ Spring 43
44 5. Applications of Algorithm IX o Example B: Liquid phase CSTR 1 - Same rxns, rate laws, and rate constants as example A A + 2B C (1) -r 1A = k 1A C A C B2 NOTE: The specific reaction rate k 1A is defined wrt species A 3C + 2A D (2) r 2C = k 2C C C3 C A2 NOTE: The specific reaction rate k 2C is defined wrt species C - Liquid phase reactions take place in a 2,500 dm 3 CSTR. equal molar in A and B with F A0 = 200 mol/min, v 0 = 100 dm 3 /min, V 0 = 50 dm 3. - Find the concentrations of A, B, C, and D exiting the reactor along with the exiting selectivity. - Plot F A, F B, F C, F D and S C/D as a function of V Apr/ Spring 44
45 5. Applications of Algorithm X o Example B: Liquid phase CSTR 2 Solution - Liquid CSTR Mole balances Net rates Apr/ Spring 45
46 5. Applications of Algorithm XI o Example B: Liquid phase CSTR 2 Solution 2 Rate laws Net rates Apr/ Spring 46
47 5. Applications of Algorithm XII o Example B: Liquid phase CSTR 2 Solution 3 Selectivity Parameters Apr/ Spring 47
48 5. Applications of Algorithm XIII o Example C: Gas phase PFR, no pressure drop - Same rxns, rate laws, and rate constants as example A A + 2B C (1) -r 1A = k 1A C A C B2 3C + 2A D (2) r 2C = k 2C C C3 C A2 NOTE: The specific reaction rate k 1A is defined wrt species A NOTE: The specific reaction rate k 2C is defined wrt species C - The complex gas phase reactions take place in a PFR. feed is equal molar in A and B with F A0 = 10 mol/min volumetric flow rate is 100 dm 3 /min. reactor volume 1,000 dm 3, no pressure drop total entering concentration is C T0 = 0.2 mol/dm 3 Apr/ Spring 48
49 5. Applications of Algorithm XIV o Example C: Gas phase PFR, no pressure drop 2 - The complex gas phase reactions take place in a PFR. rate constants Plot F A, F B, F C, F D and S ~ C/D as a function of V Apr/ Spring 49
50 5. Applications of Algorithm XV o Example C: Gas phase PFR, no pressure drop 3 Sol) - Gas phase PFR, no pressure drop Mole balances Apr/ Spring 50
51 5. Applications of Algorithm XVI o Example C: Gas phase PFR, no pressure drop 4 Sol) - Gas phase PFR, no pressure drop 2 Net rates Rate law Apr/ Spring 51
52 5. Applications of Algorithm XVII o Example C: Gas phase PFR, no pressure drop 5 Sol) - Gas phase PFR, no pressure drop 3 Relative rates Apr/ Spring 52
53 5. Applications of Algorithm XVIII o Example C: Gas phase PFR, no pressure drop 6 Sol) - Gas phase PFR, no pressure drop 4 Selectivity Stoichiometry Apr/ Spring 53
54 5. Applications of Algorithm XIX o Example C: Gas phase PFR, no pressure drop 7 Sol) - Gas phase PFR, no pressure drop 5 Parameters Apr/ Spring 54
55 5. Applications of Algorithm XX o Example C: Gas phase PFR, no pressure drop 8 Sol) - Gas phase PFR, no pressure drop 5 Apr/ Spring 55
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