Textbook: Elements of Chemical Reaction Engineering, 4 th Edition 1 CHE 404 Chemical Reaction Engineering Chapter 8 Steady-State Nonisothermal Reactor Design
Contents 2 PART 1. Steady-State Energy Balance and Adiabatic PFR Applications Energy Balance User Friendly Energy Balance Equations Adiabatic Operation Adiabatic Equilibrium Conversion and Reactor Sizing PART 2. Flow Reactors with Heat Exchange Steady-State Tubular Reactor with Heat Exchange Balance on the Heat Transfer Fluid Algorithm for PFR/PBR Design with Heat Effects CSTR with Heat Effects Multiple Steady State (MSS) Non-isothermal Multiple Chemical Reactions
8.4 Steady-State Tubular Rxtr with Heat Exchange 3 Assumption: No radial gradients in the reactor U : Heat transfer coefficient ΔA : Heat exchange area DL D 2 L/4 a : heat exchange area/unit volume of the reactor (= 4/D)
4 For exothermic reactions, Q g > Q r : T Q g < Q r : T For endothermic reactions, Q g, Q r : negative (T a > T) (-Q g ) > (-Q r ) : T (-Q g ) < (-Q r ) : T
5 For PFR For PBR dw = b dv ( b = bulk density) From energy balance, From mole balance, Coupled ODEs have to be solved simultaneously From the coolant balance, if the coolant temperature varies down the reactor Coupled 3 ODEs have to be solved simultaneously
Applying the Algorithm 6 Gas Phase Liquid Phase Energy Balance Mole Balance Pressure Drop Heat Exchanger
8.5 Equilibrium Conversion 7 8.5.1 Adiabatic Temperature and Equilibrium Conversion For a 1 st -order reaction, at equil = 0 For exothermic reactions, equilibrium conversion decreases with increasing temperature.
8 Note that as the inlet temperature increases, the adiabatic equilibrium conversion decreases. If the entering temperature is increased from T 0 to T 01, the energy balance line will be shifted to the right and will be parallel to the original line, as shown by the dashed line.
Ex 8-6. Calculating the Adiabatic Eq. Temp. 9 A Determine the adiabatic equilibrium temperature and conversion when pure A is fed to the reactor at a temperature of 300 K. B C At eq., -r A = 0. Ae C K Be e C C X CAe CA0 (1 Xe ) K K Be A0 e e e
Cp = 0 10 Adiabatic Eq. conversion = 0.42 Adiabatic Eq. Temperature = 465 K
11 8.5.1 Adiabatic Reactor Staging with Interstage Cooling or Heating Exothermic Reactions 1 st rxtor 2 nd rxtor 3 rd rxtor 1 st cooler 2 nd cooler 3 rd rxtor 2 nd 2 nd rxtor cooler 1 st cooler 1 st rxtor 2 interstage cooler X e = 90% No cooling stage X e = 40%
12 Endothermic Reactions 1 st heater 2 nd heater 3 rd rxtor 1 st rxtor 2 nd rxtor The allowable temperature range for which this reaction can be carried out is quite narrow: Above 530 C undesirable side reaction occur, and below 430 C the reaction virtually does not take place.
Ex 8-7. Interstage Cooling for Exothermic Rxns 13 Problem. What conversion can be achieved in Ex 8-6 if two interstage coolers that had the capacity the exit stream to 350 K were available? Also determine the heat duty of each exchanger for a molar feed of A of 40 mol/s. Assume that 95% of equilibrium conversion is achieved in each reactor. The feed temp. to the first reactor is 300 K. 1 st cooler If the entering temp. is 300 K, Adiabatic Eq. conversion = 0.42
14 Calculate the Heat Load F F F (1 X) F X F C PA = C PB A B A0 A0 A0 220 kcal/s must be removed to cool the reacting mixture from 460 K to 350 K for a feed rate of 40 mol/s.
15 Second Reactor For the 1 st reactor, T = 300 + 400X For the 2 nd reactor, (T 350) = 400(X 0.4) T = 350 + 400(0.6 0.4) = 430 K Adiabatic Eq. Conversion = 0.63 95% x 0.63 = 0.6 Heat-exchange duty for 2 nd cooler (430 K, 0.76) 430 (350 K, 0.6) (350 K, 0.4) (430 K, 0.6) (460 K, 0.4) 160 Third Reactor (T 350) = 400(X 0.6) Intersection X = 0.8 95% x 0.8 = 0.76
Adiabatic Equilibrium Conversion 16 8.5.2 Optimum Feed Temperature Entering Feed Temperature X e, (-r A ) Entering Feed Temperature X e, (-r A ) C H i p i Rx 0.069 X 0.069( T T ) EB 0
Optimum inlet temperature 17 If the inlet temperature was 600 K, the adiabatic equilibrium conversion is 0.15. because of the high entering temp., the rate is so rapid and equilibrium is achieved very near the reactor entrance. If the inlet temperature were lowered to 500 K, the corresponding equilibrium conversion is increased to 0.38. however, the reaction rate is slower at this temperature so that this conversion is not achieved until closer to the end of the reactor. If the entering temperature were lowered further to 350 K, the corresponding equilibrium conversion is 0.75, but the rate is so slow that a conversion of 0.05 is achieved.