Solutions

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CRE – 08.09.15 - Exam E (Solution) 1 096116 Chemical Reaction Engineering 8 September 2015 Exam E Family name _________________________________________________ First name _________________________________________________ ID number _________________________________________________ Signature _________________________________________________ 1. Packed bed reactor and CSTR in series (40%) The irreversible elementary gas phase reaction: 2𝐴𝐴→ 𝐵𝐵+ 𝐶𝐶 is currently carried out in a packed bed reactor containing 100 kg of catalyst. The entering pressure is 20 atm and the exit pressure is 4 atm. Currently, 50% conversion is achieved. It is proposed to add a CSTR with 200 Kg of catalyst downstream of the PBR. There is no pressure drop in the CSTR. The flow rate and temperature remain unchanged. a. What would be the overall conversion in such an arrangement (PBR+CSTR)? b. Is there a better way to carry out the reaction, and if so what is it? Solution Part a: new arrangement Data referring to the PBR have to be used to calculate the kinetic constant of the gas phase reaction, which is needed to perform calculations associated to the CSTR. First of all, we have to determine the pressure drop coefficient 𝛼𝛼 in our PBR, according to its definition and data provided in the main text. Reaction occurs without change of moles (i.e. 𝛿𝛿= 0 and as a consequence 𝜀𝜀= 0), thus we have: 𝑃𝑃(𝑤𝑤) 𝑃𝑃0 = √1 − 𝛼𝛼𝑤𝑤 Which means that we can easily estimate the pressure drop from data available at the exit of reactor: 𝛼𝛼= 1 𝑤𝑤𝑃𝑃𝑃𝑃𝑃𝑃 � 1 − � 𝑃𝑃𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑃𝑃0 � 2 � CRE – 08.09.15 - Exam E (Solution) 2 We know that the reactor is isothermal, but pressure changes along the PBR. So, we have: 𝐶𝐶𝐴𝐴= 𝐶𝐶𝐴𝐴 0 1 − 𝑋𝑋 1 + 𝜀𝜀𝑋𝑋 𝑃𝑃 𝑃𝑃0 𝑇𝑇0 𝑇𝑇= 𝐶𝐶𝐴𝐴 0(1 − 𝑋𝑋) 𝑃𝑃 𝑃𝑃0 Since the reaction is elementary, the reaction rate is…