Q.1. [20%] The following elementary gas phase reactions are to be carried out in a PFR with a heat exchanger:2π΄π΄ππ1βπ΅π΅ (1) , β π»π»πππ π π π 1π΄π΄(πππ π ) =β25ππππππππ πππ΄π΄2π΅π΅+π΄π΄ππ2βπΆπΆ (2) ,βπ»π»πππ π π π 2π΅π΅(πππ π ) =+35ππππππππ πππ΅π΅The feed containing 80% mol of A and 20% mol of inerts enters at a rate of 5 mol/min, pressure of 16.4 atm and 227oC. The reaction rate for (1) ππ1π΄π΄=ππ1οΏ½πΆπΆπ΄π΄2βπΆπΆπ΅π΅πΎπΎπΆπΆοΏ½The reaction rate for (2) ππ2πΆπΆ=ππ2πΆπΆπ΅π΅2πΆπΆπ΄π΄Additional information Ua=150 J/(dm3.min.K)The specific rate constant in (1) k1=50 dm3/(mol. min) at 315K with E1=8000 J/molThe specific reaction rate in (2) k2 = 400 dm6/(mol2.min) at 310K with E2=4000 J/molConcentration equilibrium constant with respect to A in reaction (1) KC= 10 dm3/mol at 315KHeat capacities of A, B, C and coolantCp,A= 20 J/(mol.K)Cp,B= 80 J/(mol.K)Cp,C= 100 J/(mol.K)Cp,coolant= 10 J/(mol.K)Mass flow rate of coolant ππΜ=30g/minThe entering of heat transfer fluid temperature is 250oC. Show your steps to derive all necessary equations and conditions to solve questions (1) and (2) below.(1) Heat exchanger with constant heat transfer fluid temperature, a. Plot profiles of molar flow rates of A, B and C (in the same graph) and temperature versus the volume of reactorb. At what reactor volume is the molar flow rate of B (FB) is maximum? What is the value of FBmax at this volume?
c. What is the maximum temperature? and at what reactor volume is the temperature maximum?
d. Vary some of parameters e.g. the ratio of A to inerts, and/or inlet temperature, explain the changes in the temperature in molar flow rates of A,B, C versus the reactor volume.(e) compare the results in (a) and (b) when the reactor is operated adiabatically(2) co-current heat exchanger with variable temperature heat transfer fluida. Plot profiles of molar flow rates of A, B and C (in the same graph) and temperature versus the volume of reactorb. At what reactor volume is the molar flow rate of B (FB) is maximum? What is the value of FBmax at this volume? c. What is the maximum temperature? and at what reactor volume is the temperature maximum? d. Vary some of parameters e.g. the ratio of A to inerts, and/or inlet temperature, explain the changes in the temperature in molar flow rates of A,B, C versus the reactor volume. (e) compare the results in (a) and (b) when the reactor is operated adiabatically
Q.2. [10%] The reversible elementary gas-phase reaction is carried out in a packed bed reactor (PBR) with a heat exchanger. The feed containing A and inerts I with the ratio of inerts to A of 2:1 enter the reactor at the molar rate of 5 mol/min and temperature of 300K. The entering heat transfer fluid temperature Ta is 300K. Additional information Initial concentration of A CAo= 2 mol/dm3Heat capacities of A Cp,A= 150 cal/(mol.K)Heat capacities of B Cp,B= 150 cal/(mol.K)Heat capacities of inerts I Cp,I= 20 cal/(mol.K) Heat capacity of coolant fluid, Cp = 20 cal/(mol.K)Activation energy, E=10 kcal/molHeat of reaction at standard temperature (TR=298K) βπ»π»π
π
π
π
ππ(πππ
π
)= – 20 kcal/molReaction rate constant (specific reaction rate) at 300K, k=0.1 min-1Equilibrium reaction rate constant at 305K, KC= 1000A B
Flow rate of the coolant, ππΜ = 50 mol/min Bulk density of catalyst, ππππ=1200 kg/m3Pressure drop parameter, Ξ±=0.02 kg-1 Ua=150 cal/(dm3.s. K) V=40dm3a. Show your steps to derive equations for rate law for A, design equation for PBR,energy balance, equilibrium conversion.b. Plot X, Xe, T, P and reaction rate down the length of reactor (or weight of catalyst) when the reaction is carried out adiabatically.c. Plot X, Xe, T, P and reaction rate down the length of reactor (or weight of catalyst) when the reaction is carried out with constant heat exchanger temperature. d. For the case constant heat exchanger temperature, vary some of parameters, i.e. ratio of inerts to A and/or inlet temperature of the feed, explain the results.