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# HW9-Key - 123456789 8 24.1 a i First model(full...

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24-1 ±²³´µ¶·¸¹º¸ 24.1 a) i. First model (full compositions model): Number of variables: N V = 22 w 1 x R,A x 2 B w 2 x R,B x 2 D w 3 x R,C x 4 C w 4 x R,D x 5 D w 5 x T,D x 6 D w 6 V T x 7 D w 7 H T x 8 D w 8 Number of Equations: N E = 17 Eqs. 2-8, 9, 10, 12, 13, 15, 16, 18, 20(3X), 21, 22, 27, 28, 29, 31 Number of Parameters: N P = 4 V R , k, α , ρ Degrees of freedom: N F = 22 – 17 = 5 Number of manipulated variables: N MV = 4 w 1 , w 2 , w 6 , w 8 Number of disturbance variables: N DV = 1 x 2 D Number of controlled variables: N CV = 4 x 4 A , w 4 , H T , x 8 D Solution Manual for Process Dynamics and Control, 2 nd edition, Copyright © 2004 by Dale E. Seborg, Thomas F. Edgar and Duncan A. Mellichamp

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24-2 ii. Second model (simplified compositions model): Number of variables: N V = 14 w 1 x R,A w 4 w 2 x R,B x 4 A w 6 x R,D x 8 D w 8 x T,D H T x 2 D V T Number of Equations: N E = 9 Eq. 2-33 through Eq. 2-41 Number of Parameters: N P = 4 V R , k, α , ρ Degrees of freedom: N F = 14 – 9 = 5 Number of manipulated variables: N MV = 4 w 1 , w 2 , w 6 , w 8 Number of disturbance variables: N DV = 1 x 2 D Number of controlled variables: N CV = 4 x 4 A , w 4 , H T , x 8D iii.Third model (simplified holdups model): Number of variables: N V = 14 w 1 H R,A w 4 w 2 H R,B x 4 A w 6 H R,D x 8 D w 8 H T,B H T x 2 D H T,D
24-3 Number of Equations: N E = 9 Eq. 2-48 through Eq. 2-56 Number of Parameters: N P = 3 V R , k, α Degrees of freedom: N F = 14 – 9 = 5 Number of manipulated variables: N MV = 4 w 1 , w 2 , w 6 , w 8 Number of disturbance variables: N DV = 1 x 2 D Number of controlled variables: N CV = 4 x 4A , w 4 , V T , x 8 D b) Model 1: The first model is left in an intermediate form, i.e., not fully reduced, so the key equations for the units are more clearly identifiable. Also, such a model is easier to develop using traditional balance methods because not as much algebraic effort is expended in simplification. Models 2 and 3: Both of the reduced models are easier to simulate (fewer equations), yet contain all of the dynamic relations needed to simulate the plant. Model 3: The “holdups model” has the further advantage of being easier to analyze using a symbolic equation manipulator because of its more symmetric organization. Also, it requires one less parameter for its specification. c) Each model can be simulated using the equations given in Appendix E of the text. Models 2 and 3 are simulated using the differential equation editor (dee) in Matlab. An example can be found by typing dee at the command prompt. Step changes are made in the manipulated variables w 1 , w 2 , w 6 and w 8 and in disturbance variable x 2 D to illustrate the dynamics of the entire plant.

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24-4 Figure S24.1a. Simulink-MATLAB block diagram for first model 2 x3 1 w3 [-0.5 -0.5 1 0] stoich. factors 3000 rho*VR 330 k generation & Accumulation T2 T1 Sum input flows1 Sum input flows Mux 3000 HR em Demux 1 s D 1 s C 1 s B 1 s A -out + in +generated 6 w2 5 x2 4 w1 3 x1 2 x8 1 w8 Figure S24.1b. Simulink-MATLAB block diagram for the reactor block
24-5 4 x4 3 w4 2 x5 1 w5 Product5 Product4 Product3 Product2 Product1 Product em 2 x3 1 w3 Figure S24.1c. Simulink-MATLAB block diagram for the flash block 2 x7 1 w7 3 x5

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