HW9-Key - 24-1 24-2 ii. Second model (simplified...

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Unformatted text preview: 24-1 24-2 ii. Second model (simplified compositions model): Number of variables: NV= 14 w1xR,Aw4w2xR,Bx4Aw6xR,Dx8Dw8xT,DHTx2D VTNumber of Equations: NE= 9 Eq. 2-33 through Eq. 2-41 Number of Parameters: NP= 4 VR, k, α, ρDegrees of freedom:NF= 14 – 9 = 5 Number of manipulated variables: NMV= 4 w1, w2, w6, w8Number of disturbance variables: NDV= 1 x2DNumber of controlled variables: NCV= 4 x4A, w4, HT, x8D iii.Third model (simplified holdups model): Number of variables: NV= 14 w1HR,Aw4w2HR,Bx4Aw6HR,Dx8Dw8HT,BHTx2D HT,D24-3 Number of Equations: NE= 9 Eq. 2-48 through Eq. 2-56 Number of Parameters: NP= 3 VR, k, αDegrees of freedom:NF= 14 – 9 = 5 Number of manipulated variables: NMV= 4 w1, w2, w6, w8Number of disturbance variables: NDV= 1 x2DNumber of controlled variables: NCV= 4 x4A, w4, VT, x8D 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 deeat the command prompt. Step changes are made in the manipulated variables w1, w2, w6and w8and in disturbance variable x2Dto illustrate the dynamics of the entire plant. 24-4 Figure S24.1a. Simulink-MATLAB block diagram for first model 2x31w3[-0.5 -0.5 1 0]stoich. factors3000rho*VR330kgeneration &AccumulationT2T1Suminput flows1Suminput flowsMux3000HRmDemux1sD1sC1sB1sA-out+ in+generated6w25x24w13x12x81w8Figure S24.1b. Simulink-MATLAB block diagram for the reactor block 24-5 4x43w42x51w5Product5Product4Product3Product2Product1Productem2x31w3Figure S24.1c. Simulink-MATLAB block diagram for the flash block 2x71w73x52w51Purge FlowFigure S24.1d. Simulink-MATLAB block diagram for purge block 24-6 xTDxTD-savexRDxRD-savexRBxRB-savexRAxRA-savex4Ax4A-save0.01x2D-setx2Dw8w8-savew6w6-savew4w4-savew2w2-savew2-change1100w2w1w1-savew1-change1010w1HTVT-save890Recycle Flow110Purge FlowEquations 2-(32-38)E.2-32-38Figure S24.1e. Simulink-MATLAB block diagram for second model 24-7 xTDxTD-savex4Ax4A-save0.01x2Dw8w8-savew6w6-savew4w4-savew2w2-save1100w2w1w1-save1010w1890Recycle Flow110Purge FlowHTDHTD-saveHTBHTB-saveHTHT-saveHRDHRD-saveHRBHRB-saveHRAHRA-saveEquations 2-(48-52)E.2-48-52Figure S24.1f. Simulink-MATLAB block diagram for third model24-8 10203040101010111012101310141015w11020304010991099.511001100.51101...
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HW9-Key - 24-1 24-2 ii. Second model (simplified...

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