ChE 430 Exam 3 Thursday, April 25, 2002NAME:Instructions: Parts I and II of the exam are closed book and notes. You may useanything you have on your laptops for both Part I and Part II.Remove your wireless network card during the exam.Part I does not require any numerical calculation using the laptop. Part I is worth 50points and part II is worth 50 points. Write all answers on separate paper. Do not writeany answers on the exam itself. Hand in your exam as well as your solution at the end.Make sure your name is on your solution and your exam.Part I.Problem 1. PFR Energy Balance. 25 pts.The first-order reactionA −→ Bis carried out in a tubular reactor. Costs dictate that we must reach 90% conversionfor this process to be feasible. We would like to operate the reactor adiabatically, butproduct B degrades if the reactor temperature exceeds 500 K.(a) Is it poss ible to operate the reactor adiabatically with this constraint (i.e. whatis the outlet temperature)? The inlet flow is pure A, inlet temperature is 300 K,inlet pressure is 10 atm, NA0= 2 kmol/hr, MA= 50 kg/kmol,ˆCp= 3.09 kJ/kg·K,∆HR= −41, 900 kJ/kmol, Ea= 37, 700 kJ/kmol, and k0= 3.27 × 1061/hr. Val-ues of the gas constant include R = 8.314 J/mol·K and R = 82.06 atm· cm3/mol·K.(b) If adiabatic operation is not possible, assume we have a heating/cooling systemavailable to help us reach the desired conversion. We now will use two reactorsin series, operating the first adiabatically to 500 K, and the second isothermallyin order to obtain the desired conversion. What is the outlet conversion from theadiabatic reactor, and what are the re actor volumes required for each reactor?(Note: If finding the reactor volume requires a numerical solution, set up but donot solve the equations that are needed to obtain the reactor volume.) How muchheat must be added or removed from the isothermal reactor?1ChE 430 Exam 3 Thursday, April 25, 2002Problem 2. CSTR Energy Balance. 25 pts.The liquid-phase reactionsA −→ BA −→ Care each first order in the concentration of A. The feed to a nonisothermal CSTRcontains pure A at 45◦C and 5 mol/lit. Table 1 lists additional information for thereactions and the reactor. We want to operate this reactor such that the se lectivity toB is greater than the selectivity to C, i.e., the rate at which B forms is greater than therate at which C forms.Item value unitsVR1000 litQf100 lit/minρf932 g/litk13.16 × 1014exp(−12, 500/T ) min−1; T in Kk22.52 × 109exp(−8, 500/T ) min−1; T in K∆HR1−12, 000 cal/mol∆HR2−15, 000 cal/molˆCP0.22 cal/(g K)Table 1: Kinetic and reactor paramete rs.(a) Defining the selectivity as S = RB/RC, determine the rate at which heat istransferred to the surroundings to achieve a selectivity of 5.(b) Determine the rate at which heat is transferred to the surroundings to achieve aselectivity of 4.(c) Explain why the answer to part (a) or part (b) is greater.2ChE 430 Exam 3 Thursday, April 25, 2002Part II.Instructions: You will require your laptops for Part II of the e xam.Write any answe rs on separate paper. Do not write any answers on the exam itself.Hand in your exam as well as your solution at the end. Make sure your name is on yoursolution and your exam.When you have finished, insert your wireless network card and email to your TA theprogram you have written to solve the problem and plot the solution.Problem 3. Steady-state multiplicity in a CSTR. 50 pts.Consider the liquid phase, elementary reactionAk−→ BThe rate constant is temperature dependent:k(T ) = kmexp−E1T−1TmSince the chemical B is currently in great demand, Badger Chemic als has decided tostart producing B. They have hired you as a consultant to address operational issues fortheir constant-volume, nonisothermal, nonadiabatic CSTRs. Heat is removed from thereactor by use of a cooling coil. You may assume that the cooling medium maintains aconstant temperature of Ta. Also, define: θ = VR/Qf.Table 2 contains the data for the reaction system.Parameter Value UnitsTf298 KTm298 KTa300 KˆCP4.0 kJ/kg KcAf2.0 kmol/m3km0.001 min−1E 8.0 × 103Kρ 103kg/m3∆HR−3.0 × 105kJ/kmolTable 2: Parameter values.(a) Write down the material and energy balance equations for this system. State allassumptions.3ChE 430 Exam 3 Thursday, April 25, 2002(b) The available cooling coils can provide heat exchange in the range:UoA/VR= 0 − 100kJmin K m3Generate two plots:1. the steady-state conversion of A as a function of θ, and2. the steady-state temperature as a function of θcomparing the steady-state solutions for UoA/VRvalues of 0, 20, 40, 60, 80,and 100kJmin K m3. For which of these UoA/VRvalues are multiple steady statespossible?(c) For safety reasons, the reactor temperature must not exceed 350 K. Accordingly,Badger Chemicals decides to operate at the following reactor conditions:Parameter Value UnitsUoA/VR40kJmin K m3θ 44 mincA1.76 kmol/m3T 311 KTable 3: CSTR conditions.You are asked to monitor the test run of the reactor. Unfortunately, you fall asleepon the job! When you wake up, you discover that the flow rate has changed, sofor the past five hours θ = 46 minutes. You quickly adjust the flow rate so thatθ = 44 minutes again. Now you are face d with the decision: should you shut downthe reactor?Plot the dynamic response of the reactor temperature for twenty-four hours, start-ing when the feed flow rate first changed (i.e., θ = 46 minutes). Assume that thereactor was initially at the steady state corresponding to the values given in Ta-ble