INSTRUCTIONS FOR REGRADES:

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1 Chemical Engineering 140 November 21, 2005 Midterm #3 INSTRUCTIONS FOR REGRADES: Requests for regrades must be submitted in writing to one of the GSI s by FRIDAY, DECEMBER 2. Please photocopy your exam and explain on this copy specifically (circles and arrows are helpful in addition to words) what you want addressed. Submit both the copy and original to your GSI.

2 Chemical Engineering 140 November 21, 2005 Midterm #3 (170) Researchers at the University of Wisconsin-Madison have recently developed an alternative process for producing H 2 for the hydrogen economy 1. This approach uses renewable resources such as biomass as opposed to nonrenewable resources such as natural gas and petroleum. In this process, glucose (obtained from starch) is first converted to sorbitol, which is then reformed over a platinum catalyst to form hydrogen. Sorbitol is reformed over a Pt/Al 2 O 3 catalyst in a tubular reactor at 498K and 29 bar according to the following stoichiometry. C 6 O 6 H 14(liq) +6H 2 O (liq) 13H 2(gas) + 6CO 2(gas) where the subscripts (liq) and (gas) denote liquid and gas states. Sorbitol is the limiting reactant. The reaction is run with 10% excess water.. Conversion of sorbitol in the tubular reactor is 60%. As a side reaction, carbon dioxide and hydrogen readily react to form methane and water. CO 2(gas) + 4H 2(gas) CH 4(gas) + 2H 2 O (gas) The effluent of the reactor is sent to a flash tank where a vapor phase and liquid phase exit in equilibrium. Upon analysis of the vapor stream exiting the flash tank, only 40% of the H 2 that would be produced under complete conversion with only the primary reaction is present. Approximate that H 2, CH 4, and CO 2 are not present in the liquid phase and that the vapor pressure of sorbitol is negligible. 1 Cortright, R. D., Davda, R. R. & Dumesic, J. A. Hydrogen from catalytic reforming of biomass-derived hydrocarbons in liquid water. Nature (2002). 50 a) Determine the overall composition of the species leaving the reactor. What is the conversion of the side reaction? Define conversion of the side reaction as: F = Basis mols/time Sorbitol in feed EMBED MathType 4.0 Equation

3 G = 6*(1.1F) = 6.6F = mols/time water in feed Splitting the first process unit into two reactors; one for the primary reaction and one for the secondary, the conversion of the second reactor is EMBED Microsoft Equation 3.0 After the primary reaction: Species mass (mol) balances: Sorbitol: F 0.6F = 0.4F mols Sorbitol (+5) Water: 6.6F 0.6*6F = 6.6F 3.6F = 3.0F mols water (+5) Hydrogen: 13*0.6F = 7.8F mols hydrogen (+5) CO2: 6*0.6F = 3.6F mols carbon dioxide (+5) Conversion of the side reaction= EMBED Microsoft Equation % (+7 eqn with correct numbers, +3 final number) After the secondary reaction: Hydrogen: 7.8F 0.33*(7.8F) = 5.23F (+10/+5 if credit given for first reaction product) Sorbitol: Same as before: 0.4F CO2: 3.6F 0.33*0.25*7.8F = 2.96F (+10/+5 if credit given for first reaction product) H2O: 3F + 0.5*0.33*7.8F = 4.29F (+10/+5 if credit given for first reaction product) CH4: *0.25*7.8F = 0.644F (+5) mols: 38.6% hydrogen 3.0% sorbitol 21.9% CO2 31.7% H2O 4.8% CH4 Correctly applied equations with incorrect numerical results are worth all except for 2 points. Properly notated equations without numbers get 80% credit. Severe error early on: 40% credit for remainder In cases of an error in the basis, 5 points were taken if at least 15 were given (not to fall below 15) and the maximum score allowed was 40. The 40% credit for severe

4 error was not applied. b) Determine the compositions of the vapor and liquid streams leaving the flash tank. The vapor pressure of water at 498K is a weighted average of 2181 kpa ( K (+5) and 2637 kpa ( K (+5). EMBED Microsoft Equation 3.0 (+10) (+10 for vapor pressure overall if they use only one lookup) Antoine eqn method: 19 total (lose 1 b/c out of T range for constants in book) Antoine eqn: (+7) filled: (+10) Answer: (+2) Water is the only material which will be split between the liquid and vapor streams leaving the tank. EMBED Microsoft Equation 3.0 (x and y: +8 each) in: +5. Not filled in -> +0) (Raoult's law filled EMBED Microsoft Equation 3.0 (Quadratic setup: +5) EMBED Microsoft Equation 3.0 (Solve quadratic: +5) Roots: 4.23F and F - negative 14.75F is obviously incorrect F is the number of mols of water in the vapor phase. (+7) 0.06F is the number of mols of water in the liquid phase. (+7) K method: get Ki via simple method: (+7) acknowledge that Ki via simple method not applicable (polar compound under pressure): (+7) mass balance: (+8 w/o #s, +8 more with) Apply to get x and y: (+15) Explaination instead of application: (up to 15 pts)

5 c) Endothermic reactions in tubular reactors are often heated by condensing steam on the exterior side of the tubes at about 10 C above the reaction temperature. If we wish to heat the reactor using this method, what pressure steam (in bar) should be used? Reaction temperature=498k; Temperature wanted=508k (+2) The minimum pressure of steam that could be used for this task is the weighted average of 2637 kpa (@500) and 3163 kpa (@510). (+4, +4) Wtd average calculation: EMBED Microsoft Equation 3.0 (+5) The result is 3058 kpa (or bar) (+5) No obvious use of weighted average/chose to use only one value: Loose interpolation resulting in 3060: (+10 total) Simply takes value at 510K, producing 3160: (+10 total) About 30 bar from steam table lookup of K: (+10 total) Mention of 29 bar if implied lookup of pressures at 500 and 510 and use of a non-weighted average: (+9) Uses EMBED Microsoft Equation 3.0 : (no credit for 29 bar mention: shows use of reactor pressure instead of steam table) Does problem for 10C correctly: (+13) Single point lookup for 10C: (+4) More than 5 significant figures: (-2) For antoine equation method:

6 (max 18: out of temperature range listed with constants) Antoine equation: (+7) Plug in: (+5) Result: (+6) d) Taking the vapor phase as a real gas, explain how you would determine the molar volume of vapor leaving the flash tank using compressibility. Mention: Find critical temperatures and pressures (by EMBED Microsoft Equation 3.0 ), etc (+7) Mention: Use compressability chart to find z for each component (+7) (-2: use table, -4: don't say where to look) Mention: EMBED Microsoft Equation 3.0 or some equilvalent (+6) Mention: Use PV=ZnRT (+5) e) According to the Gibbs phase rule, how many intensive degrees of freedom are there in the equilibrium flash? DOF = 2+C-P. (+5) DOF = = 5. (+8 species and phases filled in correctly, +2 answer)