[Luyben] Process Mod.. - Student subdomain for University of Bath

More documents

Recommendations

Info

70 MATHEMATICAL MODELS OF CHEMICAL ENGINEERING SYSTEMS controlled (can be fixed). The two variables that must somehow be specified are reflux flow R and vapor boilup Y (or heat input to the reboiler). They can be held constant (an openloop system) or they can be changed by two controllers to try to hold some other two variables constant. In a digital simulation of this column in Part II we will assume that two feedback controllers adjust R and V to control overhead and bottoms compositions xD and xB . 3.12 MULTICOMPONENT NONIDEAL DISTILLATION COLUMN As a more realistic distillation example, let us now develop a mathematical model for a multicomponent, nonideal column with NC components, nonequimolal overflow, and inehicient trays. The assumptions that we will make are: 1. 2. 3. 4. Liquid on the tray is perfectly mixed and incompressible. Tray vapor holdups are negligible. Dynamics of the condenser and the reboiler will be neglected. Vapor and liquid are in thermal equilibrium (same temperature) but not in phase equilibrium. A Murphree vapor-phase efficiency will be used to describe the departure from equilibrium. E ,=Ynj-YLI,i n’ Yn*j-YynT-1.j (3.96) where yzj = composition of vapor in phase equilibrium with liquid on nth tray with composition xnj ynj = actual composition of vapor leaving nth tray y,‘_ i, j = actual composition of vapor entering nth tray Enj = Murphree vapor efficiency forjth component on nth tray Multiple feeds, both liquid and vapor, and sidestream drawoffs, both liquid and vapor, are permitted. A general nth tray is sketched in Fig. 3.13. Nomenclature is summarized in Table 3.1. The equations describing this tray are: Total continuity (one per tray): dM A = L,+1 + F;4 + F,Y-, + v,-, - v, - L, -s; - s.’ dt (3.97) Component continuity equations (NC - 1 per tray): 4Mn Xnj) = L “+I x n+l,j + Fkx$ + FL-d-1.j + K-IYn-1,j dt - Vn Y,j - L, Xnj - Sf; X,j - S,’ )‘,I (3.98)
EXAMPLES OF MATHEMATICAL MODELS OF CHEMICAL ENGINEERING SYSTEMS 71 FIGURE 3.13 nth tray of multicomponent column. Energy equation (one per tray): hd&f, M _ L n+1 n+1+ F;4hf + ~,Y_Je-1+ I/,-lH,-, dt where the enthalpies have units of energy per mole. Phase equilibrium (NC per tray): - ~‘,H,-L,h,-S;4h,-S,YH” (3.99) Y,*j = Lj, Pm. T-1 (3.100) An appropriate vapor-liquid equilibrium relationship, as discussed in Sec. 2.2.6, must be used to find y~j. Then Eq. (3.96) can be used to calculate the ynj for the inefficient tray. The y,‘_ r, i would be calculated from the two vapors entering the tray: FL-, and V,-,. Additional equations include physical property relationships to get densities and enthalpies, a vapor hydraulic equation to calculate vapor flow rates from known tray pressure drops, and a liquid hydraulic relationship to get liquid flow TABLE 3.1 Streams on nth tray Nlllllber Flow rate Composition Temperature F: c 1 L“+I v, K-1 s: L” S.’
Page 1 and 2:
I WILLIAM WIlllAM 1. LUYBEN PROCESS
Page 3 and 4:
The Series Bailey and OUii: Biochem
Page 5 and 6:
PROCESS MODELING, SIMULATION, AND C
Page 7 and 8:
ABOUT THE AUTHOR William L. Luyben
Page 9 and 10:
CONTENTS Preface Xxi 1 1.1 1.2 1.3
Page 11 and 12:
CONTENTS .. . xlu 5.7 Batch Reactor
Page 13 and 14:
CONTENTS xv 10.3 10.4 Performance S
Page 15 and 16:
comwrs xvii 151.3 Transpose of a Ma
Page 17 and 18:
CONTENTS Xix 20.4 Sampled-Data Cont
Page 19 and 20:
. Xxii PREFACE Another significant
Page 21 and 22:
PROCESS MODELING, SIMULATION, AND C
Page 23 and 24:
2 PROCESS MODELING, SIMULATION. AND
Page 25 and 26:
4 PROCESS MODELING, SIMULATION, AND
Page 27 and 28:
6 PROCESS MODELING. SIMULATION, AND
Page 29 and 30:
8 PROCESS MODELING, SIMULATION, AND
Page 31 and 32:
10 PROCESS MODELING, SIMULATION, AN
Page 33 and 34:
12 PROCESS MODELING, SIMULATION, AN
Page 35 and 36:
CHAPTER 2 FUNDAMENTALS 2.1 INTRODUC
Page 37 and 38:
FUNDAMENTALS 17 big, complex system
Page 39 and 40: FUNDAMENTALS 19 z=o I z + dz z=L FI
Page 41 and 42: FUNDAMENTALS 21 The minus sign come
Page 43 and 44: FUNDAMENTALS 23 Molar flow of A lea
Page 45 and 46: FUNDAMENTALS 25 For liquids the PP
Page 47 and 48: FUNDAMENTALS 27 Flow of energy (ent
Page 49 and 50: FUNDAMENTALS 29 The units of this f
Page 51 and 52: FUNDAMENTALS 31 FIGURE 2.9 Laminar
Page 53 and 54: FUNDAMENTALS 33 Then Eq. (2.48) bec
Page 55 and 56: FUNDAMENTALS 35 Wenzel in Chemical
Page 57 and 58: FUNDAMENTALS .37 This exponential t
Page 59 and 60: FUNDAMENTALS 39 a direction 0 = 45
Page 61 and 62: EXAMPLES OF MATHEMATICAL MODELS OF
Page 75 and 76: EXAMPLES OF MA~EMATICAL MODELS OF C
Page 81 and 82: EXAMPLES OF MATHEMATICAL MODELS OE
Page 89: EXAMPLES OF MATHEMATICAL MODELS OF
Page 107 and 108: 88 COMPUTER SIMULATION Our discussi
Page 109 and 110: 90 COMPUTER SIMULATION lation packa
Page 111 and 112: 92 COMPUTER SIMULATION For this rea
Page 113 and 114: 94 COMPUTER SIMULATION TABLE 4.1 Ex
Page 115 and 116: 96 COMPUTER SIMULATION Clearly, the
Page 117 and 118: 98 COMPUTER SIMULATION TABLE 4.2 Ex
Page 119: I()() COMPUTER SIMULATION Settingfl
Page 589 and 590:
ANALYSIS OF MULTNARIABLE SYSTEMS 57
Page 591 and 592:
ANALYSIS OF MULTIVARIABLE SYSTEMS 5
Page 593 and 594:
ANALYSIS OF MULTIYARIABLE SYSTEMS 5
Page 595 and 596:
Page 597 and 598:
Page 599 and 600:
FIGURE 16.5 Multivariable INA (- 1,
Page 601 and 602:
Page 603 and 604:
Page 605 and 606:
ANALYSIS OF MULTIYARIABLE SYSTEMS 5
Page 607 and 608:
Page 609 and 610:
Page 611 and 612:
Page 613 and 614:
DESIGN OF CONTROLLERS FOR MULTIVARI
Page 615 and 616:
Page 617 and 618:
Page 619 and 620:
Page 621 and 622:
Page 623 and 624:
Page 625 and 626:
DESIGN Ok CONTROLLERS FOR MULTIVARI
Page 627 and 628:
Page 629 and 630:
show all

[Luyben] Process Mod.. - Student subdomain for University of Bath

Create successful ePaper yourself

Delete template?

Save as template?