unsw ceic3000 tutorial solution w3 process modeling and analysis

Unsw ceic3000 tutorial solution w3 process modeling and analysis

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Unformatted text preview: School of Chemical Engineering CEIC3000 Chemical Engineering Fundamentals-3 Brief Solution to Tutorial 3 1. Solution : (a) The matrix is A = [ 2 1 2- 1 ] The eigenvalues are: 1 =- 1 . 5616 , 2 = 2 . 5616 and the eigenvectors are: v 1 = [ . 2703- . 9628 ] , v 2 = [ . 8719 . 4896 ] Because 2 > , the corresponding dynamic mode e 2 t when t . (Because the reactor is exothermic. Higher reactor temperature leads to higher reaction rate, which in turn, generates more heat and leading to a higher tem- perature.) (b) The slow direction is v 1 (corresponding to 1 =- 1 . 5616). This is also a stable subspace. The fast direction is v 2 (corresponding to 2 = 2 . 5616). This is also an unstable subspace. x ( t ) = [ . 2703- . 9628 . 8719 . 4896 ][ e 1 . 5616 t e 2 . 5616 t ][ . 5038- . 8972 . 9907 . 2782 ] x (0) If the initial condition is in the direction of v 1 , that is x (0) = [ . 2703- . 9628 ] we find the following state solution x ( t ) = [ . 2703 e 1...
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Unsw ceic3000 tutorial solution w3 process modeling and analysis

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