1The UNIVERSITY OF BRITISH COLUMBIA Department of CHEMICAL and BIOLOGICAL ENGINEERING CHBE 241: MATERIAL and ENERGY BALANCES MIDTERM โ EXAMINATION October 23, 2013: 3 โ 5 PM Instructions: - Hand calculators (including programmable calculators) are allowed The only allowed material is the one page of formula sheet provided to you with this exam. You can detach the formula sheet for easier handling. Solve individually all 2 problems. If any of these rules are not respected, it will be dealt with according to University Policy on student ethics during examination. *** use a maximum of two significant figures after the decimal point **** 2 Formula Sheet ๐น๐๐๐๐ก๐๐๐๐๐ ๐ถ๐๐๐ฃ๐๐๐ ๐๐๐ ๐ (๐ด) ๐๐๐๐ข๐๐ก ๐๐ ๐๐๐๐๐ก๐๐๐ก ๐จ ๐ถ๐๐๐๐๐๐ธ๐ท ๐๐ ๐กโ๐ ๐๐๐๐๐ก๐๐ = ๐๐๐๐ข๐๐ก ๐๐ ๐๐๐๐๐ก๐๐๐ก ๐จ ๐น๐ธ๐ท(๐ ๐ข๐๐๐๐๐๐) ๐ก๐ ๐กโ๐ ๐๐๐๐๐ก๐๐ ๐๐๐๐๐๐ก๐๐ฃ๐๐ก๐ฆ (๏) = ๐๐๐๐๐(๐) = ๐๐๐๐๐ ๐๐ ๐ท๐ธ๐๐ผ๐ ๐ธ๐ท ๐๐๐๐๐ข๐๐ก ๐๐๐๐๐๐๐ก๐๐ ๐๐๐ก๐๐ ๐๐๐๐๐ ๐๐ ๐๐๐๐๐ก๐๐๐ก ๐จ ๐ถ๐๐๐๐๐๐ธ๐ท ๐๐ ๐๐๐๐๐ก๐๐ ๐๐๐๐๐ ๐๐ ๐ท๐ธ๐๐ผ๐ ๐ธ๐ท ๐๐๐๐๐ข๐๐ก ๐๐๐๐๐๐๐ก๐๐ ๐๐๐๐๐ ๐๐ ๐๐๐๐๐ก๐๐๐ก ๐จ ๐น๐ธ๐ท ๐ก๐ ๐กโ๐ ๐๐๐๐๐ก๐๐ ๐น๐๐๐๐ก๐๐๐๐๐๐ ๐๐๐๐ฃ๐๐๐ฆ ๐๐ ๐จ = ๐๐๐๐ข๐๐ก๐๐ ๐๐๐๐๐๐๐๐๐ก ๐จ ๐๐ ๐ ๐๐๐๐๐๐ก๐๐ ๐๐๐๐๐ข๐๐ก ๐ ๐ก๐๐๐๐ ๐ ๐๐๐๐ข๐๐ก ๐๐ ๐๐๐๐๐๐๐๐๐ก ๐จ ๐๐๐ ๐ก๐ ๐กโ๐ ๐ ๐๐๐๐๐๐ก๐๐ (Accumulation in the system) = (IN) โ (OUT) + (Generated in the system) โ (Consumed in the system) 1 atm = 1.013x105 Pa = 760 mmHg R = 8.314 J / (mol K) 3 Problem 1 (60% of the mark): Canexus corporation at its plant in North Vancouver is producing NaOH, Cl2,(g) and H2,(g) by electrolysis of NaCl in water (i.e. a brine solution). As a recently hired process engineer, after the first week on the job, your manager asks you to submit a report that contains the following material balance analysis of their process. In the process, salt (solid) is mixed with water to produce a 30 %wt. salt solution. This salt solution is fed to the electrolysis unit, where NaOH solution, Cl2,(g) and H2,(g) are produced, each in separate streams. The aqueous solution containing NaOH and un-reacted NaCl is introduced to an evaporator where some of the water is removed as steam. The concentrated product solution coming out from the evaporator has the following composition (in weight %): 50 % NaOH, 7 % NaCl and 43 % H2O. The plant has a production rate of 5000 kg/h product solution. The atomic masses are (in [kg/kmol]): Na = 23, Cl = 35.5, H = 1, O = 16. Perform the following assuming steady-state: A) [10%] Draw the block flow diagram, label streams and write down the balanced reaction occurring in the electrolysis unit between salt and water. B) [10%] Calculate the extent of reaction in [kmol/h]. C) [20%] Calculate the fractional conversion of NaCl and the Cl2,(g) volumetric production rate in [m3/h] at 40 oC and 1.5 atm absolute pressure. Note: 1 atm = 1.013x105 Pa. R = 8.314 J/(mol K) D) [20%] How much water is removed in the evaporator? 4 Product soln. A: [10%]) NaCl 4 1 H2O Cl2,(g) H2,(g) Solution Problem 1: 30 %wt NaCl Mixer NaOH, NaCl, 6 H2O Electrolysis 3 2 7 5 5000 kg/h Evaporator 8 NaOH 50% NaCl 7% H2O H2O 43% 2NaCl + 2H2O ๏ฎ 2NaOH + H2 + Cl2 B: [10%]) = ๐ฬ NaOH mass balance for the overall process: ๐ฬ ๐ where, ๐ฬ = ๐ฬ = Thus, = = ๐ฬ = = ๐ = ๐ ๐๐๐ . C: [20%]) NaCl fractional conversion: ๐ = ๐ฬ Thus, ๐ฬ ๐ ๐ฬ ( ฬ = ) Cl2 mole balance: ๐ฬ = Use ideal gas law: ฬ = = ๐ฬ = ๐ฬ ๐ = = ๐๐๐โ ( = -we need the NaCl molar feed rate. ๐ฬ = ๐ฬ = = ) = ๐ฬ NaCl overall process mole balance: ๐ฬ ( = ) ๐๐๐โ ๐ ๐; ฬ = = ๐โ ๐๐๐โ 5 D: [20%]) H2O overall process mass balance: = ๐ฬ ๐ฬ ๐ฬ ๐ We want ๐ฬ but we also do not know ๐ฬ The latter can be easily calculated from a water mass balance on the mixer: Hence: ๐ฬ = ๐ ๐ฬ = = ฬ ฬ = ๐โ Thus, the water removed in the evaporator: ๐ฬ = answer is acceptable. = ๐โ or 337.36 kmol/h. Either ----------------------------------------------------------------------------------------Verify the calculations by performing a total mass balance on the process: ๐ฬ ๐ฬ = ๐ฬ Note that: ๐ฬ ๐ฬ = = ๐ฬ = ๐ฬ ๐ฬ ๐โ and ๐ฬ = = = ๐โ = Thus: = (๐ฃ๐๐๐ฆ ๐๐๐๐ ๐๐๐ ๐ ๐๐๐๐๐๐ ๐๐๐๐ ๐ข๐๐) ------------------------------------------------------------------------------------------ ๐โ 6 Problem 2 (40% of the mark): Ethylene oxide (C2H4O) is a high volume chemical intermediate that is used to produce glycol and polyethylene glycol. Ethylene oxide is produced in a catalytic reactor by the partial oxidation of ethylene (C2H4) using air: C2H4 + 1/2O2 ๏ฎ C2H4O [1] In addition to reaction [1], a secondary reaction takes also place in the same reactor: C2H4 + 3O2 ๏ฎ 2CO2 + 2H2O [2] The product gas leaving the reactor has the following composition [in % kmol]: 40% C2H4O, 3% CO2, 3% H2O (as steam), 10% C2H4 and the rest (to 100%) is air. The plant has a production capacity of 105 kmol/year C2H4O. The air molar composition is: 21% O2 and 79% N2. Perform the following assuming steady-state: A) [10%] Perform a DOF (degree of freedom) analysis on the reactor and comment briefly on your result. B) [10%] Calculate the ethylene (C2H4) feed to the reactor expressed in [lb/h] necessary to assure the plant production of ethylene oxide. The molar mass [kg/kmol]: C2H4O = 44, C2H4 = 28. C) [10%] Prove by calculation whether C2H4 or O2 is the limiting reactant in the reactor D) [10%] Determine the selectivity and yield of C2H4O with respect to the limiting reactant. 7 Solution Problem 2: Product gas Reactor C2H4 Air (21 % O2 + 79% N2) C2H4 + 1/2O2 ๏ฎ C2H4O C2H4 + 3O2 ๏ฎ 2CO2 + 2H2O C2H4O 40%; 105 kmol/year CO2 3% H2O 3% C2H4 10% Air (21% O2 + 79% N2) 44% A: 10%) DOF = Nvariables - Nequations Nvariables: Stream components = 3 (inlet) + 6 (outlet) = 9 System variables = 2 (reactions) Nvariables = 11 Nequations: Basis flow = 1 (C2H4O production rate) Stream compositions = 4 (independent out compositions) + 1 (indep. composition air in) + 1 (indep. composition air out) = 6 System specifications = 0 MBE = 6 (C2H4, oxygen, nitrogen, CO2, H2O, C2H4O) Nequations = 13 DOF = 11 โ 13 < 0 (overspecified: problem can be solved). [A good question would be how can the outlet air composition remain the same when O 2 is consumed whereas N2 is not consumed in the reactor? Because some of the N2 can be separated and purged from the system, such that to maintain a constant air composition (i.e. O2 and N2 ratio). However, this long story is not essential here because N2 is an inert species so it does not matter. You need to utilize the specified air composition. Thatโs all. Originally, this was a reaction, separation and purge problem but I simplified it for you guys to a reactor problem only, not to give you at this point a purge problem and to shorten the calculations in the Midterm.] 8 B: 10%) = ๐ฬ C2H4 mole balance: ๐ฬ ; Need the two extents of reactions: use 2 key products for each reaction = C2H4O mole balance: CO2 mole balance: = ๐ฬ ; hence ๐ฬ = ๐๐๐๐ฆ๐๐๐ ; (alternatively, it would be the same with H2O mole balance) where from the OUT stream composition observe that: ฬ = ฬ ๐ฬ Further: ๐ฬ = = Thus: = ๐ฬ = = ๐๐๐โ; hence ๐ฬ = ๐๐๐ = ๐ฆ๐๐๐ = = ๐๐๐๐ฆ๐๐๐ = ๐๐๐โ ๐๐๐๐ฆ๐๐๐, ๐ฬ ๐ฬ = = ๐ = โ ๐ โ C: 10%) Limiting reactant: need the ratio ฬ ฬ , compared to stoichiometric ratio in the reactor: ฬ = ฬ = ๐ฬ O2 mole balance: ๐ฬ = Thus: ฬ ฬ ๐ฬ ๐ฬ , where = = = ๐ฬ = ๐๐๐๐ฆ๐๐๐ ; ๐ฬ = = = ๐๐๐๐ฆ๐๐๐ Thus, O2 is the limiting reactant in the reactor. D: 10%) Selectivity and Yield with respect to O2 which is the limiting reactant. Desired product: C2H4O 9 ๏= ๐= = = = ๐๐๐ ๐ถ ๐ ๐๐๐๐ถ ๐ ๐๐๐๐ ๐๐๐๐ ๐ข๐๐๐ ๐๐๐๐ ๐๐๐๐ Note: the theoretical best selectivity with respect to O2 is, based on stoichiometry of reaction [1], = 1 / 0.5 = 2. In other words, without the secondary un-desired reaction in the system. Clearly, the practical selectivity is lower than the theoretical. --------------------------------------------------------------------------------------------------------------------Verify calculations: Total Mass In = Total Mass Out; Note: N2 can be neglected from the reactor because it is not reacting. ๐ฬ ๐ฬ = ๐ฬ ๐ ๐ฬ =( 6,304,200 = 6,304,200 ๏ 100% mass balance closure! ๐ฬ ๐ฬ )