Exam 05 07 2022

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1 x Fundamentals of Chemical Processes Prof. Gianpiero Groppi July 5th 2022 Problem 1 (18 points) Methane production from CO2 is a key process for energy transition (Power to Gas-PtG). The PtG process involves two reactions: COଶ +4Hଶ →CHସ +2HଶO (Sabatier) COଶ +Hଶ →CO+HଶO (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) CO2 and 85% (mol/mol) di H2. 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  CO2 conversion in the first reactor (R1) is equal to 70% with a selectivity to methane, 𝜎஼ு ర ஼ை మ = ௡಴ಹ ర (మ) ௡಴ೀ మ (భ) ି௡ ಴ೀ మ (మ) = 80%  Outlet stream (4) from the second reactor (R2) is at thermodynamic equilibrium at T4=900 K  Heat exchanger HE is ideal  Both reactors are adiabatic and isobaric. Calculate; 1. the molar composition and temperature T2 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 CO2 conversion of the process. Thermodynamic data: Sabatier: Kୗ୅୆ ୣ୯ (T) =exp൤ 1 1.987൬56000 Tଶ +34633 T −16.4ln(T)+0.00557 T൰+33.156൨ with T in [K] RWGS: ∆Gୖ, ୰୛ୋୗ଴ (T) [cal/mol] =8514−7.71⋅T with T in [K] Reference: ideal gas - 1 bar ΔH0f (298 K) Cp [J/mol/K] C୮(T)= A + B T + C Tଶ + D Tଷ [J/mol] A B *10^3 C*10^6 D*10^9 CO2 -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 CH4 -74520 19.238 52.09 11.966 -11.309 H2O -241810 32.22 1.923 10.548 -3.594 Nome e cognome:…