Exercise 5 Solution

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Prof. Gianpiero Groppi – Exercises – Fundamentals of Chemical Processes – A.A. 2023-2024 1 EXERCISE 5 Estimation of the heat supply required by the first stage of a steam reformer In the first stage of the steam reforming process, synthesis gas is prepared starting from natural gas. The process can be summarized with the following two reactions: SMR) CH4 + H2O ↔ CO + 3 H2 WGS) CO + H2O ↔ CO2 + H2 The steam methane reforming (SMR) reaction is highly endothermic and the necessary heat is supplied via exchange at the reactor walls. In a typical process, the feed gas es – with known flowrates and composition reported in the table below – enter the reactor at 550°C and leaves at 800°C. Assuming that the process reaches thermodynamic equilibrium, estimate the composition of the outlet stream and the heat supply Q required by the reactor. DATA Stream IN: T = 550°C P = 30 atm Stream OUT: T = 800°C P = 30 atm Volumetric behavior: ideal gases Inlet flowrates Species Flowrate (Nm3/h) CH4 22.486 H2O 94.015 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 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 ad 1 atm SOLUTION The problem requires the calculation of the equilibrium composition at the outlet stream and the heat supply required by the reformer. First of all we can write the material balance for the reacting system 𝑛̇𝑖 (𝑂𝑈𝑇)=𝑛̇𝑖 (𝐼𝑁)+∑𝜈𝑖𝑗𝜀𝑗 𝑁𝑅 𝑗=1 In order…