Exercise 6 Solution

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Prof. Gianpiero Groppi – Exercises – Fundamentals of Chemical Processes – A.A. 2023-2024 1 EXERCISE 6 Estimation of temperature and composition at the exit of an adiabatic reactor for the partial oxidation of CH4 The autothermal reforming of CH4 is carried out in an adiabatic reactor: CH4 + 0.5 O2 ↔ CO + 2 H2 Evaluate the composition and temperature of the gas stream at the outlet of the adiabatic reactor, assuming that the thermodynamic equilibrium conditions are reached. CH 4, CO, H2, H2O and CO2 are present at the outlet, while O2 is absent. DATA Stream IN: T = 500°C P = 30 atm Stream OUT: T = ? P = 30 atm Volumetric behavior: ideal gases Inlet flowrates Species Flowrate (Nm3/h) CH4 1 O2 0.6 H2O 1 Prof. Gianpiero Groppi – Exercises – Fundamentals of Chemical Processes – A.A. 2023-2024 2 Thermodynamic properties 0B0 BSpecies H0F(298K) [cal/mol] a b x 103 c x 105 d x 109 H2 0 6.483 2.215 -3.298 1.826 CO -26420 7.373 -3.070 6.662 -3.037 CO2 -94050 4.728 17.54 -13.38 4.097 CH4 -17890 4.598 12.450 2.860 -2.709 H2O -57800 7.701 0.4595 2.521 -0.859 O2 0 6.7150 -8.791E-4 4.1710 -2.5440 𝐶𝑝𝑖=𝑎+𝑏∙𝑇+𝑐∙𝑇2+𝑑∙𝑇3 T in K Cp in cal/mol/K ∆𝐺𝑅,𝑆𝑅 0 (𝑇)=53717−60.25∙𝑇 cal/mol 600 K < T < 1500 K ∆𝐺𝑅,𝑊𝐺𝑆 0 (𝑇)=−8514+7.71∙𝑇 cal/mol 600 K < T < 1500 K Reference: ideal gas at 1 atm SOLUTION We have to evaluate composition and temperature at the outlet of the adiabatic reactor assuming that the thermodynamic equilibrium is reached at the outlet, where no O2 is present. Let’s start as usual with the material balances: 𝑛̇𝑖 (𝑂𝑈𝑇)=𝑛̇𝑖 (𝐼𝑁)+∑𝜈𝑖𝑗𝜀𝑗 𝑁𝑅 𝑗=1 In order to characterize the outlet stream we need to know the inlet flowrates, the number of reactions (NR) to use and the respective stoichiometric coefficients ( 𝜈) and the extent of reaction (𝜀). We are given volumetric flowrates of the two…