Energy Engineering - Fundamentals of Chemical Processes

Full exam

Dipartimento di Energia Politecnico di Milano Via Lambruschini 4 - 20156 MILANO “ Fundamentals of Chemical Processes” Prof. Gianpiero Groppi June 29 th, 2020 Exercise 1 (18 points) The synthesis of methanol is performed according to the process scheme reported below: In both reactor R 1 and reactor R 2 the synthesis of methanol (MeOH) takes place according to the following stoichiometry: CO + 2 H 2 ↔ CH 3OH Inlet current (1), which is maintained at 453 K and has the composition reported in Table 1, is split in two parts, current (2) and current (3). Current (2) is supplied to reactor R 1. Reactor R 1 operates at 70 bar and is cooled by 1500 cal per mole of feed current (2). Current (4) exits from reactor R 1 at thermodynamic equilibrium conditions. Current (4) is then mixed with current (3), which acts as a quench. Current (5) obtained from the mixing is supplied to reactor R 2, which is adiabatic and also operates at 70 bar. Current (6) which exits from reactor R 2 reaches the thermodynamic equilibrium conditions at the outlet temperature T 6 which is equal to 560 K. Assuming that: • the reacting mixture is an ideal mixture of real gases, assuming ������������ ������������������������������������������������������������ as reported in the thermodynamic dataset • pressure drops are negligible through the reactors, which can be considered as isobaric • CH 4 and CO 2 can be treated as inert species calculate: 1. temperature T 4 and the molar composition of current (4) at the outlet of reactor R 1 2. the ratio of flow rate of quench current (3) to the flowrate or current (2) 3. the molar composition of current (6) at the outlet of reactor R 2 4. temperature T 5 of current (5) which enters reactor R 2. Table 1 – molar composition of current (1) CH 4 H2 CO CO 2 CH 3OH Current (1) 0.05 0.70 0.15 0.10 0 Thermodynamic data Methanol synthesis ∆������������ ������������,������������������������������������������������ 0 ( ������������) =−22828+56.02 ������������ � ������������������������������������ ������������������������������������ � T is K, 600 K < T < 1500 K ������������ ������������������������������������������������������������ = ������������ ������������������������������������������������ ������������������������22������������������������ ������������ =0.9 Reference state: ideal gas, 1 bar, 298 K ������������̃ ������������ ,������������ =������������ ������������+������������ ������������∙������������+������������ ������������∙������������ 2+������������ ������������∙������������ 3 [cal/mol/K] Species ΔH 0F(298K) [cal/mol] a b x 10 3 c x 10 6 d x 10 9 H2 0 6.483 2.215 -3.298 1.826 CO -26420 7.373 -3.070 6.662 -3.037 CO 2 -94050 4.728 17.54 -13.38 4.097 CH 4 -17890 4.598 12.45 2.86 -2.709 CH 3OH -48080 5.062 16.94 6.179 -6.811 Exercise 2 (12 points) Consider the mixture of n-C 5H10, n-C 6H12 and n-C 8H16 whose composition in terms of molar fractions (z i) is reported in the following table: Species z [ -] Ai Bi Ci n-C 5H10 0.40 3.91058 1014.294 -43.367 n-C6H12 0.35 3.99063 1152.971 -47.301 n-C 8H16 0.25 4.05752 1353.486 -60.386 For each species in the table, A i, B i and C i are the parameters of the Antoine’s equation for the estimation of the vapor pressure. The feed mixture is initially at 5 bar and 375 K. The fraction F 1 of the feed mixture is expanded isoenthalpically and supplied to the adiabatic flash drum D 1 maintained at P 1 = 2 bar. Both the liquid stream L 1 produced by the flash drum D 1 and the fraction F 2 of the feed mixture are isoenthalpically expanded and supplied to the flash drum D 2. The flash drum D 2 is adiabatic, operates at P 2 = 1 bar and achieves a vaporization ratio equal to 0.25, which is calculated as V 2/(L 1+F 2). Assuming ideal gas and ideal mixtures, calculate: 1 – the physical state of the feed stream F; 2 – the vaporization ratio and temperature achieved in the flash drum D 1; 3 – the ratio F 2/F1 between the flow rate supplied to D 2 and the flow rate supplied to flash drum D 1; 4 – the temperature T 2 of the flash drum D 2; For each species, the specific heat in the liquid phase, the specific heat in the vapor phase and the enthalpy of vaporization (∆H VAP ) can be assumed constant. The enthalpies of vaporization are given at the boiling temperature at 1 bar. Species C P vap [J/mol/K] C P liq [J/mol/K] ΔH VAP (T Boil , 1 bar) [J/mol] n-C 5H10 109.7 154.9 25500 n-C 6H12 132.7 183.3 30600 n-C 8H16 178.6 242.2 38000 Antoine’s Equation: P VAP is bar, T is K i i i VAP C T B A P Log + − = 10