General Procedures for deriving Energy balances for Reactive Processes: (Q1) Method 1: Heat of Reaction method 1. Compete the material balance calculations on the reactor to the greatest extent possible 2. Choose reference states for specific enthalpy calculations - Best choices are generally reactant and product species at 25C and 1atm 3. For a single reaction in a continuous process, calculate the extent of reaction (ξ) |ππ΄,ππ’π‘ −ππ΄,ππ | ππ΄ ,π π= = |ππ΄ | |ππ΄ | π€βπππ ππ΄ ππ π‘βπ π π‘πππβπππππ‘πππ πππππππππππ‘ ππ π πππππ‘πππ‘ ππ πππππ‘πππ πππππ’ππ‘ π΄ 4. Prepare the inlet-outlet enthalpy table, inserting know molar amounts (ni) or flow rates (nΝ¦ i) for all inlet and outlet stream components. 5. Calculate each unknown stream component enthalpy, Hi, as ΔH for the species going from its reference state to the process state, and insert the enthalpies in the table. 6. Calculate ΔH for the reactor. Use one of the following formulas: Δπ» = πΔπ»π + Σπππ’π‘ π»ππ’π‘ − Σπππ π»ππ (π πππππ πππππ‘πππ) Δπ» = Σππ Δπ»°π π + Σπππ’π‘ π»ππ’π‘ + Σπππ π»ππ Method 2: Heat of Formation Method 1. Compete the material balance calculations on the reactor to the greatest extent possible 2. Choose reference states for specific enthalpy calculations - Best choices are generally reactant and product species at 25C and 1atm 3. Prepare the inlet-outlet enthalpy table, inserting know molar amounts (ni) or flow rates (nΝ¦ i) for all inlet and outlet stream components. 4. Calculate each unknown specific enthalpy (use process paths) - For a reactant or product, start with the elemental species at 25C and 1 atm and form 1 mol of the process species at 24C and 1 atm - Then bring the species from 25C and 1 atm to its processs state, calculating the change in enthalpies, specific enthalpies, and latent heats from their corresponding tables 5. Calculate ΔH for the reactor 6. Substitute the calculated value of ΔH in the energy balance equation and complete the required calculations Question 1: The Army has, for many years, funded direct methanol fuels cells to power portable electronic devices like your smartphone because methanol is much more energy dense than Li-ion batteries. The unbalanced reaction is as follows and occurs isothermally at 25oC and 1 atm: πΆπ»3 ππ»(π) + π2(π) → π»2 π(π) + πΆπ2(π) In order to determine how long 20 mL of liquid methanol can power your iPhone/Android device, answer the following questions: a. (5 pts) Write a stoichiometrically balanced reaction for the process. 7. Count components on each side of the equation Left side: 1 Carbon, 4 Hydrogen, 3 Oxygen Right side: 1 Carbon, 2 Hydrogen, 3 Oxygen 8. Hydrogen appears to be unbalanced 9. Use guess & check until balanced: ππΆπ»3 ππ»(π) + ππ2(π) → ππ»2 π(π) + ππΆπ2(π) 10. Final: 2 Carbons, 8 Hydrogen, 8 Oxygen b. (5 pts) Determine the initial amount of methanol in g-moles. NOTE: g-mole is equivalent to “mole” (just another way of writing it to try and trick you) 11. Use molecular weight to convert based on the balanced equation in part A π πππ ππππ ππππππππ = πππ ππππππππ ( ) = π. ππππππ ππππππππ ππ. πππ c. (20 pts) Assume that 90% of the methanol is consumed and that all of the change in enthalpy between the initial and final states of the system goes into usable work (e.g. efficiency is 100%). If the average power consumption of your device is 34 kJ/day, (π· = πΎ⁄π) determine how long (in days) your device can be powered. To help your calculations, please use the inlet-outlet enthalpy table below and explicitly state your reference state(s) directly on this sheet!! Substance nin (mol) Hin (kJ/mol) nout (mol) Hout (kJ/mol) CH3OH(l) 0.624 -238.6 O2(g) 0.936 0 H20(l) 1.124 -285.84 CO2(g) 0.562 -393.5 1. r.s._________________________________________________________________________ 12. Solve for change in enthalpy, use to calculate work, then plug work back into power equation (no heat of reaction calculation necessary for this problem) 13. total methanol consumed = 0.624*0.90 = 0.562 moles 14. begin by filling in “nin” column using the conversion ππππ πΆπ π. ππππππ πͺπ―π πΆπ― ( ) = π. ππππππ πΆπ ππππ πͺπ―π πΆπ― ππππ π―π πΆ π. ππππππ πͺπ―π πΆπ― ( ) = π. ππππππ π―π πΆ ππππ πͺπ―π πΆπ― ππππ πͺπΆπ π. ππππππ πͺπ―π πΆπ― ( ) = π. ππππππ πͺπΆπ ππππ πͺπ―π πΆπ― 15. Look of standard heat of formation values for all the compounds (NOTE: standard heat of formation of an elemental species is always zero) then multiply them by mole ratios to determine Hin and Hout π―°π,πͺπ―π πΆπ― = −πππ. π π²π±⁄πππ π―ππ,πͺπ―π πΆπ― = (π. πππ)(−πππ. π) = −πππ. πππ²π± π―°π,π―π πΆ = −πππ. ππ π²π±⁄πππ π―ππ,π―π πΆ = (π. πππ)(−πππ. ππ) = −πππ. πππ²π± π―°π,πͺπΆπ = −πππ. π π²π±⁄πππ π―ππ,πͺπΆπ = (π. πππ)(−πππ. π) = −πππ. πππ²π± 16. Calculate the change in enthalpy given the above values βπ― = πΊππππ ππππ − πΊπππππππππ π«π― = (−πππ. ππ − πππ. ππ) − (−πππ. ππ) = −πππ. ππKJ 17. Stated that all change in enthalpy is converted into work 18. Plug work into power equation to solve for time πΎ π«π― π· ππ π²π±⁄π ππ ππ πππππ π·= = βΉ π= = = π. πππ π πππ ( ) π π π«π― πππ. ππ π²π± π π ππ =π. ππ πππππ (π πππ ππππ) General Guidelines for Single-Unit Material Balance Calculations: 1. Choose as a basis of calculation an amount or flow rate of one of the process streams 2. Draw a flowchart and fill in all known variable values, including the basis of calculation. Then label unknown stream variables on the chart. 3. Express what the problem statement asks you to determine in terms of the labeled variables 4. If you are given mixed mass and mole units for a stream, convert all quantities for one basis or the other 5. Do the degree-of-freedom analysis 6. If the number of unknowns equals the number of equations relating them, write the equations in an efficient order (minimizing simultaneous equations) and circle the variables for which you will solve 7. Solve the equations 8. Calculate the quantities requested in the problem statement if they have not already been calculated 9. If a stream quantity or flow rate ng was given in the problem statement and another value nc was either chosen as a basis or calculated for this steam, scale the balanced process by the ratio ng/nc to obtain the final result Question 2: Propane (C3H8) can be dehydrogenated to form propylene (C3H6) and H2. The process flow diagram is shown below. A fresh feed of propane is mixed with a recycle stream containing 70 mol% propylene and the balance propane and fed into a reactor. The reactor products are fed to an adsorber and distillation column, and three streams emerge: a stream containing pure hydrogen, a stream of pure propylene, and the stream recycled back into the front of the column. If the recycle ratio is 8 total moles recycled per mole propane fed, and using a basis of calculation of 50 kmol/h of propylene product, calculate the single pass conversion across the reactor by answering the following questions: Balanced Reaction: πͺπ π―π → πͺπ π―π + π―π Assume basis of 50kmol/hr Multiple-unit process – may have to isolate and write balances on several subsystems to obtain enough equations to determine all unknown stream variables - Need to calculate degrees of freedom (DOF) for the overall process AND on each subsystem a. (10 pts) Draw and completely label a process flow diagram. Feed Stream: πΜ π,πͺπ π―π = ππΜ πΉ,πͺπ π―π , π. π πͺπ π―π Stream 1 (from mixer to reactor): πΜ π,πͺπ π―π , πΜ π,πͺπ π―π , πΜ π,πͺππ―π , πΜ π,πͺπ π―π Stream 2 (from reactor to absorber): πΜ π,πͺπ π―π , πΜ π,πͺπ π―π , πΜ π,π―π , πΜ π,πͺπ π―π , πΜ π,πͺπ π―π , πΜ π,π―π Stream 3 (top stream out of absorber): πΜ π,π―π = ππ ππππ⁄ππ (ππππππππ: π πππππ πππππ ππππ πͺπ π―π ), π. π π―π Product Stream: πΜ π·,πͺπ π―π = ππ ππππ⁄ππ , π. π πͺπ π―π Recycle Stream: πΜ πΉ,πͺπ π―π , πΜ πΉ,πͺπ π―π , 0.70 C3H6, 0.30 C3H8 (5 pts) Calculate the molar flow rate of the propane feed. - - - Use stoichiometry and balance around absorber first; ratio between total output of hydrogen and propylene from absorber column is 1:1 π§Μ π,ππ ππ + π§Μ π,ππ π―π = πΜ π,π―π Use Ratio given for recycle stream and recycle ratio ππΜ πΉ,πͺπ π―π = ππΜ πΉ,πͺπ π―π πΜ π,πͺπ π―π = ππΜ πΉ,πͺπ π―π ⇒ ππΜ πΉ,πͺπ π―π = (π⁄π)πΜ π,πͺπ π―π Combine two red equations above π§Μ π,ππ ππ + (π⁄ππ)π§Μ π ,ππ π―π = πΜ π,π―π ππ + (π⁄ππ)π§Μ π ,ππ π―π = πΜ π,π―π - Use overall material balance and input πΜ π,π―π calculated above πΜ π,πͺπ π―π = πΜ π·,πͺπ π―π + πΜ π,π―π = ππ + πΜ π,π―π πΜ π,πͺπ π―π = ππ + {ππ + (π⁄ππ)πΜ π,πͺπ π―π } πΜ π,πͺπ π―π = πππ. ππ ππππ⁄ππ b. (15 pts) Find the single pass conversion of propane across the reactor by solving for the other material balances. ππππππ ππππ ππππππππππ = - πΉπππππππ πππππ ππ πππ πππππππ − ππππππππ πππ πππ ππ πππ πππππππ ππππππππ πππππ ππ πππ πππππππ Only need to calculate flow rates of reactant (C3H8) for single pass conversion calculation A degree of freedom analysis is not necessarily needed here because it’s obvious where to start based on the order of questions, but some teachers require it for good measure anyways (not sure what your teacher prefers)…will ultimately come down to time restraint on the exam though Material Balances around Mixer C3H8 Balance: πΜ π,πͺπ π―π + πΜ πΉ,πͺπ π―π = πΜ π,πͺπ π―π πΜ π,πͺπ π―π + (π⁄π)πΜ π,πͺππ―π = πΜ π,πͺππ―π πππ. ππ + (πππ. ππ⁄π) = πΜ π,πͺπ π―π πΜ π,πͺπ π―π = πππ. ππ ππππ⁄ππ - Calculate flow rates in recycle stream πΜ πΉ,πͺπ π―π = πππ. ππ⁄π = ππ. ππ ππππ⁄ππ ππΜπΉ,πͺπ π―π = ππΜ πΉ,πͺππ―π = π(13.21)=39.62 πΜ πΉ,πͺπ π―π = π. ππ ππππ⁄ππ Balance on C3H6: πΜ πΉ,πͺπ π―π = πΜ π,πͺπ π―π = π. ππ ππππ⁄ππ Material Balances around Reactor Overall Balance: πΜ π,πͺπ π―π + πΜ π,πͺπ π―π = πΜ π,πͺπ π―π + πΜ π,πͺπ π―π + πΜ π,π―π πΜ π,πͺπ π―π = πΜ π,π―π πππππ ππ πππππππππππππ ππ πππππππππ π. ππ + πππ. ππ = πΜ π,πͺπ π―π + ππΜ π,πͺπ π―π πΜ π,π―π = πΜ π,π―π πππππ ππ πππππππ ππ ππππππππ πΜ π,π―π = ππ + (π⁄ππ)πΜ π,πͺπ π―π = ππ + (π⁄ππ)(πππ. ππ) = ππ. ππ ⇒ πΜ π,πͺπ π―π = ππ. ππ ππππ⁄ππ ππππππ ππππ ππππππππππ = πΜ π,πͺπ π―π − πΜ π,πͺπ π―π πππ. ππ − ππ. ππ = = π. πππ πΜ π,πͺππ―π πππ. ππ Question 4: Hydrogen can be produced by the shift reaction: πΆπ + π»2 π → πΆπ2 + π»2 A process diagram is shown below. 52 mol% CO and balance water forms the fresh feed to the process and is mixed with a recycle stream containing unreacted CO and water. This combined stream is fed to a reactor where the shift reaction occurs. Downstream of the reactor, much of the unreacted CO and water is separated from the hydrogen. The product stream gives an analysis of 48 mol% CO2, 48 mol% H2, and 4 mol% CO. The water and the remaining CO is recycled and mixed with the fresh feed to the process; the recycle ratio for CO is 6 (mol CO recycled/mol CO fed). For a basis of 100 mol/s of the product stream, answer the following questions: a. (10 pts) Draw and completely label a process flow diagram. Fresh Feed Stream: ππ , ππ,πͺπΆ = π. ππ, ππ,π―π πΆ = π. ππ Stream 1 (Mixer to Reactor):ππ , ππ,π―π πΆ , ππ,πͺπΆ Stream 2 (Reactor to Separator): ππ , ππ,πͺπΆπ , ππ,π―π πΆ , ππ,πͺπΆ , ππ,π―π Recycle Stream: ππΉ , ππΉ,πͺπΆ , ππΉ,π―π πΆ Product Stream: ππ· = πππ πππ⁄π , ππ·,πͺπΆπ = π. ππ, ππ·,π―π = π. ππ, ππ·,πͺπΆ = π. ππ b. (5 pts) Determine the molar flow rate of the fresh feed to the process. Overall Balance: ππ = ππ· = πππ πππ⁄π πΜ π,πͺπΆ = π. ππ(πππ) = ππ πππ⁄π πΜ π,π―π πΆ = π. ππ(πππ) = ππ πππ⁄π c. (10 pts) Determine the single pass conversion of CO by solving some of the remaining material balances. Material Balances around Mixer CO Balance: πΜ π,πͺπΆ + πΜ πΉ,πͺπΆ = πΜ π,πͺπΆ πΜ π,πͺπΆ + (π⁄π)πΜ π,πͺπΆ = πΜ π,πͺπΆ ππ + (ππ⁄π) = πΜ π,πͺπΆ πΜ π,πͺπΆ = ππ. ππ ππππ⁄ππ Material Balances on Separator πΜ πΉ,πͺπΆ = (π⁄π)πΜ π,πͺπΆ = π. ππ ππππ⁄ππ πΜ π·,πͺπΆ = π. ππ(πππ) = π ππππ⁄ππ CO Balance: πΜ π,πͺπΆ = πΜ πΉ,πͺπΆ + πΜ π·,πͺπΆ = π. ππ + π = ππ. ππ ππππ⁄ππ ππππππ ππππ ππππππππππ = πΜ π,πͺπΆ − πΜ π,πͺπΆ ππ. ππ − π. ππ = = π. πππ πΜ π,πͺπΆ ππ. ππ