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unsw ceic3000 tutorial w4 process modeling and analysis

# unsw ceic3000 tutorial w4 process modeling and analysis -...

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School of Chemical Engineering CEIC3000 Process Modelling and Analysis Tutorial 4 1. Consider the following set of series and parallel reactions A k 1 B k 2 C (1) A + A k 3 D (2) Material balances on components A and B yield the following two equations dc A dt = F V ( c Af - c A ) - k 1 c A - k 3 c 2 A (3) dc B dt = - F V c B + k 1 c A - k 2 c B (4) where k 1 = 5 6 min 1 k 2 = 5 3 min 1 , k 3 = 1 6 liters mol min , c Af = 10 mol liter . (a) Assume the steady-state value of c A is c As = 3 mol liter . Linearize the model given in Equations (3) and (4) around this equilibrium point and write the linearized model in the state-space form:
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Unformatted text preview: ˙ x ′ = Ax ′ + Bu ′ (5) y = Cx ′ , (6) (i.e., to ﬁnd the numerical values of the A , B and C matrices), assuming that the input variable is dilution rate ( F/V ), and the output variable is c B . (b) Based on the linearized model, ﬁnd the initial conditions that are in the faster and slower directions. (c) Determine the stability of the linearized model. 1...
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