Energy Engineering - Fundamentals of Chemical Processes

Full exam

1 x Fundamentals of Chemical Processes Prof. Gianpiero Groppi July 5th 2022 Problem 1 (18 points) Methane production from CO 2 is a key process for energy transition (Power to Gas-PtG). The PtG process involves two reactions: CO6+ 4H6→ CH8+ 2H6O (Sabatier) CO6+ H6→ CO + H6O (RWGS) The process layout is reported in the figure. The feed stream (1) enters in reactor R1 at 280°C and 10 bar with a molar composition consisting of 15% (mol/mol) CO 2 and 85% (mol/mol) di H 2. Outlet stream (2) from reactor R1 is cooled down in the heat exchanger HE before entering in a second reactor R2. Assuming that:  All the streams behave like ideal gases  CO 2 conversion in the first reactor (R1) is equal to 70% with a selectivity to methane, �������� 0 �� .= ��� 0(.) ���.(-)?� ��.(.) = 80%  Outlet stream (4) from the second reactor (R2) is at thermodynamic equilibrium at T 4=900 K  Heat exchanger HE is ideal  Both reactors are adiabatic and isobaric. Calculate; 1. the molar composition and temperature T 2 of the outlet stream (2) from the first reactor R1 2. the outlet molar composition of stream (4) from second reactor R2 3. the inlet temperature T3 to reactor R2 4. The heat removed from the heat exchanger HE referred to 1 mole of produced methane 5. The overall CO 2 conversion of the process. Thermodynamic data : Sabatier: KWEF co (T)= exp d 1 1.987 l56000 T6 + 34633 T − 16 .4ln(T)+ 0.00557 T p+ 33 .156 h with T in [K] RWGS: ∆GV, p[KW 4 (T) [cal /mol ]= 8514 − 7.71 ⋅T with T in [K] Reference: ideal gas - 1 bar ΔH 0f (298 K) Cp [J/mol/K] Cn(T)= A + B T + C T 6+ D T 7 [J/mol] A B *10^3 C*10^6 D*10^9 CO 2 -393510 19.78 73.39 -55.98 17.14 H2 0 27.124 9.267 -13.799 7.64 CO -110530 30.848 -12.84 27.87 -12.71 CH 4 -74520 19.238 52.09 11.966 -11.309 H2O -241810 32.22 1.923 10.548 -3.594 Nome e cognome: …………………………………………………….…… Matricola: ………………………………………………..……….. 1 x Problem 2 (12 points) Consider a mixture of 1-C 7H14, 1-C 9H18 e 1-C 10H20, with composition (z i) reported in the following table along with Antoine equation coefficients Ai, Bi, Ci: Species z [-] Ai B i C i 1-C 7H 14 0.25 4.21811 1400.674 -34.193 1-C 9H 18 0.35 4.07879 1435.359 -67.615 1-C 10 H 20 0.40 4.08526 1501.872 -75.572 The feed stream F is at 4 bar and 450 K and is split in two streams F 1 and F 2. F 1 is isoenthalpically expanded and then fed to a first flash drum D1 operating at at T 1 = 420 K a p 1 = 1.2 bar. The liquid stream L 1 from D1 is isoenthalpically expanded and then fed to a second flash D 2 operating at P 2 = 1 bar and T 2 = 415 K. The second feed stream F 2 is also is isoenthalpically expanded and fed to the second flash D 2. Flash D 2 is designed to recover in the vapor stream V 2 50% of 1-C 7H14 molar flow in the overall feed stream F. Assuming an ideal gas behaviour of the vapor phases and an ideal mixture behavior with negligible Poynting factor of the liquid phases, calculate: 1. The physical state of feed stream F 2. The vaporization factor 1 of flash drum D 1 and the amount of exchanged heat Q 3. The vaporization ratio of flash D 2 defined as V 2/(F 2+L 1) and the split ratio F 2/F 1 Data: Specific heats at constant pressure are constant with temperature for all the species in the liquid and the vapor phases. Evaporation enthalpies are provided at normal boiling temperature (Tboil at 1 bar) Species C P vap [J/mol/K] C P liq [J/mol/K] ΔH VAP (T Boil , 1 bar) [J/mol] 1-C 7H14 166 213 35700 1-C 9H18 215 270 45500 1-C 10 H20 271 300 50500 Antoine equation: P VAP [bar], T [K]: log 54 ������4= ������ �− �� �>� � Notes:  The exam is closed book. It is forbidden to use personal notes, course slides and textbooks.  Report the procedures, the explanations and the results in the paper (also the intermediate results).  Print the Excel spreadsheet: each printed page must contain your name and surname.  Both the paper and the Excel prints must be submitted for the evaluation.  No correction will be given in case only the Excel prints are submitted.  No correction will be given in case the procedure is not reported.