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CRE – 03.03.15 - Exam E (Solution) 096116 Chemical Reaction Engineering 3 March 2015 Exam E Family name _________________________________________________ First name _________________________________________________ ID number _________________________________________________ Signature _________________________________________________ 1. First order reaction in a CSTR (20%) Let us consider the following reaction occurring in liquid phase in a CSTR with volume of 10,000 l: 𝐴𝐴→ 𝐵𝐵 𝑟𝑟= 𝑘𝑘𝐶𝐶𝐴𝐴 where the rate constant is equal to 2.5·10-3 min-1. a) What is the conversion of A if the feed rate is 0.3 l/s and the feed concentration of species A equal to 0.12 mol/l? b) If the feed rate suddenly drops to 70% of its original value and is maintained there, what is the conversion of A after 60 minutes? c) What is the new steady-state conversion (i.e. the conversion after a very long time)? Solution a) For first-order reactions in a CSTR, the solution is very simple: 𝑋𝑋= 𝐷𝐷𝐷𝐷 1 + 𝐷𝐷𝐷𝐷= 𝑘𝑘𝑘𝑘 1 + 𝑘𝑘𝑘𝑘 where the residence time is given by the ratio between the reactor volume and the feed rate of species A, i.e. 𝑘𝑘= 𝑉𝑉0 𝐹𝐹𝐴𝐴 0 b) We have to apply now the equations for the unsteady CSTR, i.e. a CSTR in which the accumulation contribution is not equal to zero: 1 CRE – 03.03.15 - Exam E (Solution) 𝑑𝑑𝑁𝑁𝐴𝐴 𝑑𝑑𝑑𝑑= 𝐹𝐹𝐴𝐴 0 − 𝐹𝐹𝐴𝐴− 𝑟𝑟𝑟𝑟 Since we are in liquid phase, with constant density, we have: 𝑑𝑑𝐶𝐶𝐴𝐴 𝑑𝑑𝑑𝑑= 𝐶𝐶𝐴𝐴 0 − 𝐶𝐶𝐴𝐴 𝑘𝑘 − 𝑘𝑘𝐶𝐶𝐴𝐴 This is a first-order, non-homogeneous, linear differential equation, which can be solved analytically: � 𝑑𝑑𝐶𝐶𝐴𝐴 𝑑𝑑𝑑𝑑+ 𝐷𝐷𝐶𝐶𝐴𝐴+ 𝑏𝑏= 0 𝐶𝐶𝐴𝐴(𝑑𝑑= 0) = 𝐶𝐶𝐴𝐴 0 where 𝐶𝐶𝐴𝐴 0 is th e same inlet concentration of point (a), 𝐷𝐷= 1+𝑘𝑘𝑘𝑘 𝑘𝑘, and 𝑏𝑏= − 𝐶𝐶𝐴𝐴 0 𝑘𝑘. Be careful: the residence time reported in the last equation is not equal to the residence time calculated at point…