L3b-1 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Ideal CSTR Design Eq with X A : Review: Design Eq & Conversion BATCH SYSTEM: FLOW SYSTEM: Ideal Batch Reactor Design Eq with X A : Ideal SS PFR Design Eq with X A : Ideal SS PBR Design Eq with X A : j ≡ stoichiometric coefficient; positive for products, negative for reactants

L3b-2 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Review: Sizing CSTRs We can determine the volume of the CSTR required to achieve a specific conversion if we know how the reaction rate r j depends on the conversion X j Ideal SS CSTR design eq. Volume is product of F A0 /-r A and X A Plot F A0 /-r A vs X A (Levenspiel plot) V CSTR is the rectangle with a base of X A,exit and a height of F A0 /-r A at X A,exit

L3b-3 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Area = V PFR or W catalyst, PBR Review: Sizing PFRs & PBRs We can determine the volume (catalyst weight) of a PFR (PBR) required to achieve a specific X j if we know how the reaction rate r j depends on X j Ideal PFR design eq. Plot F A0 /-r A vs X A (Experimentally determined numerical values) V PFR (W PBR ) is the area under the curve F A0 /-r A vs X A,exit Ideal PBR design eq.

L3b-4 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Numerical Evaluation of Integrals (A.4) Simpson’s one-third rule (3-point):Trapezoidal rule (2-point): Simpson’s three-eights rule (4-point): Simpson’s five-point quadrature :

L3b-5 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Review: Reactors in Series 2 CSTRs2 PFRs CSTR→PFR V CSTR1 V PFR2 V CSTR1 V CSTR2 V PFR1 V CSTR2 V CSTR1 + V PFR2 ≠ V PFR1 + C CSTR2 PFR→CSTR If is monotonically increasing then:

L3b-6 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Chapter 2 Examples

L3b-7 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. XAXA r A Calculate F A0 /-r A for each conversion value in the table F A0 /-r A Calculate the reactor volumes for each configuration shown below for the reaction data in the table when the molar flow rate is 52 mol/min. F A0, X 0 X 1 =0.3 X 2 =0.8 Config 1 X 1 =0.3 F A0, X 0 X 2 =0.8 Config 2 ←Use numerical methods to solve X A,out and X A,in respectively, are the conversion at the outlet and inlet of reactor n Convert to seconds→ -r A is in terms of mol/dm 3 ∙s

L3b-8 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign Calculate F A0 /-r A for each conversion value in the table XAXA r A F A0 /-r A 164 Calculate the reactor volumes for each configuration shown below for the reaction data in the table when the molar flow rate is 52 mol/min. F A0, X 0 X 1 =0.3 X 2 =0.8 Config 1 X 1 =0.3 F A0, X 0 X 2 =0.8 Config 2 ←Use numerical methods to solve -r A is in terms of mol/dm 3 ∙s 164 X A,out and X A,in respectively, are the conversion at the outlet and inlet of reactor n Convert to seconds→

L3b-9 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign Calculate F A0 /-r A for each conversion value in the table XAXA r A F A0 /-r A Calculate the reactor volumes for each configuration shown below for the reaction data in the table when the molar flow rate is 52 mol/min. F A0, X 0 X 1 =0.3 X 2 =0.8 Config 1 X 1 =0.3 F A0, X 0 X 2 =0.8 Config 2 ←Use numerical methods to solve -r A is in terms of mol/dm 3 ∙s 164 X A,out and X A,in respectively, are the conversion at the outlet and inlet of reactor n Convert to seconds→ For each –r A that corresponds to a X A value, use F A0 to calculate F A0 /-r A & fill in the table

L3b-10 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. X 1 =0.3 F A0, X 0 1. Calculate F A0 /-r A for each conversion value in the table XAXA r A F A0 /-r A Calculate the reactor volumes for each configuration shown below for the reaction data in the table when the molar flow rate is 52 mol/min. F A0, X 0 X 1 =0.3 X 2 =0.8 Config 1 X 2 =0.8 Config 2 ←Use numerical methods to solve Convert to seconds→ -r A is in terms of mol/dm 3 ∙s X A,out and X A,in respectively, are the conversion at the outlet and inlet of reactor n

L3b-11 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. XAXA r A F A0 /-r A F A0, X 0 X 1 =0.3 X 2 =0.8 Config 1 Reactor 1, PFR from X A0 =0 to X A =0.3: 4-pt rule: Total volume for configuration 1: dm dm 3 = dm 3 = 399 dm 3 ←Use numerical methods to solve PFR1CSTR2

L3b-12 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. XAXA r A F A0 /-r A Reactor 1, CSTR from X A0 =0 to X A =0.3: Need to evaluate at 6 pts, but since there is no 6-pt rule, break it up Total volume for configuration 2: 58 dm dm 3 = 231 dm 3 X 1 =0.3 F A0, X 0 X 2 =0.8 Config 2 3 point rule 4 point rule PFR2CSTR1 Must evaluate as many pts as possible when the curve isn’t flat

L3b-13 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. For a given C A0, the space time  needed to achieve 80% conversion in a CSTR is 5 h. Determine (if possible) the CSTR volume required to process 2 ft 3 /min and achieve 80% conversion for the same reaction using the same C A0. What is the space velocity (SV) for this system?  =5 h  0 =2 ft 3 /min Space velocity: Notice that we did not need to solve the CSTR design equation to solve this problem. Also, this answer does not depend on the type of flow reactor used. X A =0.8

L3b-14 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. A product is produced by a nonisothermal, nonelementary, multiple-reaction mechanism. Assume the volumetric flow rate is constant & the same in both reactors. Data for this reaction is shown in the graph below. Use this graph to determine which of the 2 configurations that follow give the smaller total reactor volume. F A0, X 0 X 1 =0.3 X 2 =0.7 Config 2 X 1 =0.3 F A0, X 0 X 2 =0.7 Config 1 Shown on graph Since  0 is the same in both reactors, we can use this graph to compare the 2 configurations PFR- volume is  0 multiplied by the area under the curve between X A,in & X A,out CSTR- volume is  0 multiplied by the product of C A0 /-r A,outlet times (X A,out - X A,in )

L3b-15 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. A product is produced by a nonisothermal, nonelementary, multiple-reaction mechanism. Assume the volumetric flow rate is constant & the same in both reactors. Data for this reaction is shown in the graph below. Use this graph to determine which of the 2 configurations that follow give the smaller total reactor volume. F A0, X 0 X 1 =0.3 X 2 =0.7 Config 2 X 1 =0.3 F A0, X 0 X 2 =0.7 Config 1 PFR- V is  0 multiplied by the area under the curve between X A,in & X A,out CSTR- V is  0 multiplied by the product of C A0 /-r A,outlet times (X A,out - X A,in ) Config 1 Config 2 Less shaded area Config 2 (PFR XA,out=0.3 first, and CSTR XA,out=0.7 second) has the smaller V Total X A = 0.3 X A = 0.7 X A = 0.3 X A = 0.7