1. CBE343 Jan 23, 2012

2. APPLICATION OF THE DESIGN EQUATION FOR CONTINUOUS-FLOW REACTORS X -r A [mol/m 3 ∙s] 0 0.1 0.2 0.4 0.6 0.7 0.8 0.450 0.370 0.300 0.195 0.113 0.079 0.050 A → B (gas-phase isomerization reaction in tubular reactor) Reaction conditions: T=500K and P=8.2 atm, initially pure A, F A0 = 0.4 mols/s a)Calculate volume necessary to achieve 80% conversion in a tubular reactor. b)Construct Levenspiel plot and calculate volume to achieve 80% conversion. PFR sizing

3. NUMERICAL INTEGRATION 1.Trapezoidal rule (2 point ) 2.Simpson’s 1/3 rd rule ( 3 points) 3.Simpson’s 3/8 th rule (4 points) 4.Quadrature formula (5 points) 5.N+1 points, where N/3 as integer 6.N+1 points, where ‘N’ is even y = f(x) xx0x0 x1x1 y = f(x 0 ) y = f(x 1 ) h  h = x 1 -x 0 x0x0 f(x) dx = h/2 [f(x 0 )+f(x 1 )] x1x1 Use Polymath -

4. X 1/(-r A ) X F Ao /(-r A ) f(x) dx  0 0.8 PFR sizing

5. X V

6. CSTRs in Series F Ao V 1, -r A1 V 2, -r A2 F A1, X 1 F A2, X 2 X -r A [mol/m 3 ∙s] 0 0.1 0.2 0.4 0.6 0.7 0.8 0.450 0.370 0.300 0.195 0.113 0.079 0.050 A → B Reaction conditions: T=500K and P=8.2 atm, initially pure A, F A0 = 0.4 mols/s Classroom problem- For two CSTRs, 40% conversion is achieved in 1 st reactor. What is the volume of each of the two reactors necessary to achieve 80% overall conversion of A? Analyze situation with one CSTR and with two CSTRs in series.

7. CSTRs in Series F Ao V 1, -r A1 V 2, -r A2 F A1, X 1 F A2, X 2 V 1 = F Ao.X 1 /(-r A1 ) V 2 =F Ao (X 2 -X 1 )/(-r A2 ) F A1 = F A0 – F A0.X 1 F A2 = F A0 – F A0.X 2

8. CSTRs in Series F Ao V 1, -r A1 V 2, -r A2 F A1, X 1 F A2, X 2 V 1 = F Ao.X 1 /(-r A1 ) V 2 =F Ao (X 2 -X 1 )/(-r A2 ) F Ao V 1, -r A1 V, -r A F A1, X 1 F A, X V= F Ao.X/(-r A ) V1= 820 dm 3 V2=3200 dm 3 V= ????

9. Two PFRs in Series F Ao F A1, X 1 =0.4 F A2, X 2 =0.8 F Ao. (dX/dV)= -r A V=  (F Ao /-r A ). dX V= V1 + V2 0 x V1=  (F Ao /-r A ). dX 0 0.4 V1=  (F Ao /-r A ). dX 0.4 0.8

10. Two CSTRS and One PFR in Series X 1 =0.2 X 1 =0.6 X 1 =0.65 r A1 r A2 X00.20.40.600.65 -r A (kmol/m 3.h) 3953593825 Isomerization of butane was carried out adiabatically in liquid phase. The data for irreversible reaction is given in the following table- Calculate the volume of each of the reactors for an entering molar flow rate of n-butane of 50 kmol/hr.

11. Combination of CSTRs and PFRs in Series

12. OTHER DEFINITIONS SPACE TIME,, also called holding time or mean residence time. SPACE VELOCITY, LIQUID-HOURLY SPACE VELOCITY: GAS-HOURLY SPACE VELOCITY:

13. Sample Industrial Space Times Reaction Reactor Temperature Pressure atm Space Time (1) C 2 H 6 → C 2 H 4 + H 2 PFR860°C21 s (2) CH 3 CH 2 OH + HCH 3 COOH → CH 3 CH 2 COOCH 3 + H 2 OCSTR100°C12 h (3)Catalytic crackingPBR490°C201 s < τ < 400 s (4)C 6 H 5 CH 2 CH 3 → C 6 H 5 CH = CH 2 + H 2 PBR600°C10.2 s (5)CO + H 2 O → CO 2 + H 2 PBR300°C264.5 s (6)C 6 H 6 + HNO 3 → C 6 H 5 NO 2 + H 2 OCSTR50°C120 min