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Lecture 13 Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. Today’s lecture Complex Reactions A +2B C A + 3C D Liquid Phase PFR Liquid Phase CSTR Gas Phase PFR Gas Phase Membrane Reactor Sweep Gas Concentration Essentially Zero Sweep Gas Concentration Increases with Distance Semi Batch Reactor 2 Reactor Mole Balance Summary Reactor Type Gas Phase Batch dN A rA V dt Semibatch dN A rA V dt dN B rB V FB0 dt 3 Liquid Phase dC A rA dt 0 C A dC A rA dt V 0 C B0 C B dC B rB dt V Reactor Mole Balance Summary Reactor Type 4 Gas Phase Liquid Phase CA0 CA CSTR FA 0 FA V rA V 0 PFR dFA rA dV dC A 0 rA dV PBR dFA rA dW dC A 0 rA dW rA Note: The reaction rates in the above mole balances are net rates. Reactor Mole Balance Summary The new things for multiple reactions are: Rates: 1. Rate Law for every reaction 2. Relative Rates for every reaction 3. Net Rates of Reaction 5 Gas Phase Multiple Reactions 6 Note: We could use the gas phase mole balance for liquids and then just express the concentration as: Flow: CA=FA/v0 Batch: CA=NA/V0 Note: The reaction rates in the above mole balances are net rates. The new things for multiple reactions are: 1. Rate Law for every reaction 2. Relative Rates for every reaction 3. Net Rates of Reaction 7 Net Rate of Reaction for species A For N reactions, the net rate of formation of species A is: N rA riA i 1 For a given reaction i: (i) aiA+biB ciC+diD: 8 riC riD riA riB a i bi ci d i Batch Flow NB CB V NT P0 T0 V V0 NT0 P T FB CB FT P0 T0 0 FT 0 P T N B N T 0 P T0 CB N T V0 P0 T FB FT 0 P T0 CB FT 0 P0 T N B P T0 N T P0 T FB P T0 C B CT 0 FT P0 T C B CT 0 9 Last Lecture Example A: Liquid Phase PFR The complex liquid phase reactions follow elementary rate laws 2 r k C C A 2B C (1) 1A 1A A B NOTE: The specific reaction rate k1A is defined with respect to species A. 3C 2A D (2) r2C k 2CC3CC2A NOTE: The specific reaction rate k2C is defined with respect to species C. 10 Complex Reactions Example B: Liquid Phase CSTR Same reactions, rate laws, and rate constants as example A A 2B C (1) r1A k1ACAC2B NOTE: The specific reaction rate k1A is defined with respect to species A. 3C 2A D (2) r2C k 2CC3CC2A NOTE: The specific reaction rate k2C is defined with respect to species C. 11 Example B: Liquid Phase CSTR The complex liquid phase reactions take place in a 2,500 dm3 CSTR. The feed is equal molar in A and B with FA0=200 mol/min, the volumetric flow rate is 100 dm3/min and the reation volume is 50 dm3. Find the concentrations of A, B, C and D existing in the reactor along with the existing selectivity. Plot FA, FB, FC, FD and SC/D as a function ofV 12 Example B: Liquid Phase CSTR CSTR (1) A + 2B →C (2) 2A + 3C → D r1A k1A C A C 2B r2C k 2C C C 2 A 1) Mole balance: A 3 C V0 C A 0 V0 C A rA V 0 1 B V0 C B0 V0 C B rB V 0 2 C 0 V0 CC rC V 0 D 0 V0 C D rD V 0 3 4 13 2) Rates: r1A k1A C A C 2B r2 C k 2 C C 2A C3C rA r1A r2 A rC r1C r2 C 5 6 7 9 r1A r1B r1C 1 2 1 11 r1B 2r1A r2 A 2 r2 C 3 SC / D 13 rB r2 B rD r2 D 8 10 r2 A r2 C r2 D 2 3 1 12 r1C r1A r2 D 1 r2 C 3 14 FC 0CC 15 FD 0.0001 0CD 0.0001 3) Parameters: k1A , k 2C , CA0 , CB0 , V, V014 Complex Reactions Example C: Gas Phase PFR, No ΔP Same reactions, rate laws, and rate constants as example A A 2B C (1) r1A k1ACAC2B NOTE: The specific reaction rate k1A is defined with respect to species A. 3C 2A D (2) 15 r2C k 2CC3CC2A NOTE: The specific reaction rate k2C is defined with respect to species C. Example C: Gas Phase PFR, No ΔP 1) Mole balance: A B dFC dFA rA 1 C rC R C dV dV dFB dFD rB 2 D rD 4 dV dV 3 2) Rates: Same as CSTR (5)-(14) 16 Example C: Gas Phase PFR, No ΔP 3) Stoich: C A CT 0 FA y 15 FT CC CT 0 FC y 17 FT C B CT 0 FB y 16 FT C D CT 0 FD y 18 FT FT FA FB FC FD 19 4) Selectivity: FC FC S if V 0.00001 then else 0 20 FD FD y 1 21 17 Complex Reactions Example D: Membrane Reactor with ΔP Same reactions, rate laws, and rate constants as example A A 2B C (1) r1A k1ACAC2B NOTE: The specific reaction rate k1A is defined with respect to species A. 3C 2A D (2) 18 r2C k 2CC3CC2A NOTE: The specific reaction rate k2C is defined with respect to species C. Example D: Membrane Reactor with ΔP We need to reconsider our pressure drop equation. When mass diffuses out of a membrane reactor there will be a decrease in the superficial mass flow rate, G. To account for this decrease in calculating our pressure drop parameter, we will take the ratio of the superficial mass velocity at any point in the reactor to the superficial mass velocity at the entrance to the reactor. The superficial mass flow rates can be obtained by multiplying the species molar flow rates, Fi, by their respective molecular weights, Mwi, and then summing over all species: 19 Fi MWi A C1 G 2 m 2 A C2 Fi MWi A C2 G1 m1 A C1 Fi 0 MWi A C1 Fi 0 MWi A C2 Example D: Membrane Reactor with ΔP Because the smallest molecule is the one diffusing out and has the lowest molecular weight, we will neglect the changes in the mass flow rate down the reactor and will take as first 0 m ) approximation. (m 1) Mole Balance: dFC dFA A rA 1 C rC R C 3 dV dV dFB dFD B rB 2 D rD 4 dV dV We also need to account for the molar rate of desired product C leaving in the sweep gas FCsg dFCsg 20 dV RC Example D: Membrane Reactor with ΔP 2) Rates: Same (5)-(14) 3) Stoich: Same (15)-(20) dy FT ; dW 2y FT 0 dy FT dV 2 y FT 0 21 R C k C CC CCSweep 4) Sweep Gas Balance: FCsg V dFCsg dV FCsg V V R C V 0 RC 21 Example D: Membrane Reactor with ΔP Case 1 Large sweep gas velocity CC CCsg CCsg 0 RC kCC CC Case 2 Moderate to small sweep gas velocity 22 C Csg FCsg sg F0sg FCsg sg sg 0 F 0 sg Vary υsg to see changes in profiles Complex Reactions Example E: Liquid Semibatch Same reactions, rate laws, and rate constants as example A A 2B C (1) r1A k1ACAC 2 B NOTE: The specific reaction rate k1A is defined with respect to species A. 3C 2A D (2) r2C k 2CC3CC2A NOTE: The specific reaction rate k2C is defined with respect to species C. 23 Example E: Liquid Semibatch The complex liquid phase reactions take place in a semibatch reactor where A is fed to B with FA0=3 mol/min. The volumetric flow rate is 10 dm3/min and the initial reactor volume is 1,000 dm3. The maximum volume is 2,000 dm3 and CA0=0.3 mol/dm3 and CB0=0.2 mol/dm3. Plot CA, CB, CC, CD and SS/D as a function of time. 24 Example E: Liquid Semibatch FA0 (1) A + 2B →C (2) 2A + 3C → D 1) Mole balance: dN A dt dN B dt dN C dt dN D dt B rA V FA 0 NA0 0 rB V NB0 CB0V0 2.000 rC V N C0 0 rD V N D0 0 25 Example E: Liquid Semibatch 2) Rates: Same (5)-(14) Net Rates, Rate Laws and relative rates – are the same as Liquid and Gas Phase PFR and Liquid Phase CSTR V V0 v 0 t 15 NA 16 CA V NC 18 CC V NB CB V ND CD V 17 19 3) Selectivity: NC else (0) 20 SC / D if ( t 0.0001) then ND 4) Parameters: 3 0 10dm3 min V0 100dm FA0 3 mol min 26 End of Lecture 13 27