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unsw ceic3000 tutorial w3 process modeling and analysis

unsw ceic3000 tutorial w3 process modeling and analysis -...

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School of Chemical Engineering CEIC3000 Process Modelling and Analysis Tutorial 3 1. Consider the following linearized process model of an exothermic reactor: ˙ x 1 = 2 x 1 + x 2 (1) ˙ x 2 = 2 x 1 - x 2 (2) where x 1 and x 2 are the temperature of the reactor and the mass of the product in the reactor. (a) For an arbitrary initial condition x 0 = [ x 10 , x 20 ] T , will the trajectories of x ( t ) = [ x 1 ( t ) , x 2 ( t )] T be bounded when t → ∞ ? Why? (b) Find perturbations in initial conditions that are in the fastest and slowest directions. 2. The chemical reaction sequence A B A + B C takes place isothermally in a continuous, stirred-tank reactor. Batch kinetic studies have indicated that the first reaction is second order with respect to c A while the reaction rate for the second reaction is first order with respect to both c A and c B : r 1 = k 1 c 2 A r 2 = k 2 c A c B } r 1 , r 2 [=] mol ( ft 3 ) (h) It can be assumed that the reactor has a constant volume V and constant
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Unformatted text preview: feed rate q , and that the feed contains traces of B but no C . The molar concentrations of species A and B in the feed are c Ai , c Bi respectively. The molar concentrations of species A , B and C in the exit stream are c A , c B and c c . (a) Using the 7-step procedure, derive an dynamic model that will yield the concentrations of A , B , and C (i.e., c A , c B and c c ) for variations in the concentrations of A and B in the feed (i.e., c Ai , c Bi ) (b) Write a general vector form of this model, in terms of input variable vector u , output variable vector y and state variable vector x . (c) Linearize the nonlinear model at the nominal operating point of u = [ c Ai , c Bi ] T , x = [ c A , c B , c C ] T (assume u and x is at steady-state). 1...
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