2 Cascades 逐级接触设备One class of mass-transfer devices consists of assembliesof individual units, or stages,interconnected so that the materials being processed pass through each stage in turn. The two streams move counter currently through the assembly; in each stage they are brought into contact, mixed, and then separated. Such multistage systems are called cascades.
3 Ideal Stage理想级/Equilibrium Stage平衡级/theoretical Stage理论级 y2 is in equilibrium with x2.
4 Ideal Plate/Equilibrium Plate/Theoretical Plate/Perfect plate y2 is in equilibrium with x2.
5 1. Equipment for stage contacts 1) Typical distillation equipmentFig Equipment for continuous distillation.
6 Equipment for continuous distillation. Rectifying sectionStripping /Enriching sectionFeed plateEquipment for continuous distillation.
11 1) Terminology for stage-contact plants In this book,the stages are numbered in the direction of flow of the L phase, and the last stage is that discharging the L phase.2)Material balancesUnder steady flow, there is neither accumulation nor depletion, the input and the output are equal andTotal material balance:
12 Material balance for component A: Entire cascade:Total material balance:component A material balance :
13 For two-component system: 3) Enthalpy balancesThe general energy balance can be simplified by neglecting mechanical potential energy and kinetic energy . If in addition, the process is worklessand adiabatic, a simple enthalpy balance applies.For two-component system:Where HL and HV are the enthalpies per mole of L phase and V phase, respectively.overall cascade:
14 4) Graphical methods for two-component system to find stage numbers The methods are based on material balances and equilibrium relationships; some more complex methods require enthalpy balances as well.
15 5)Operating line diagram From eq.(7.2-2):Operating-line equation操作线方程:(7.2-7)When the flow rates are not constant in the column, the operating line on a simple arithmetic plot is not straight.
16 If Ln and Vn+1 are constant through the column, the equation is that of a straight line with slope斜率 L/V and intercept截距:Operating-line equation becomes:Operating line:When
17 Operating lineEquilibrium curveOperating-line diagram for gas absorber（吸收）
18 The position of the operating line relative to the equilibrium line: (1) For rectification（精馏） in a distillation column, the operating line must lie below the equilibrium line (Fig.7.2-4a, p.48), why?is in equilibrium with
19 y= mole fraction of more volatile component A Plate 1Plate n-1Plate nPlate n+1Plate NFor rectification:y= mole fraction of more volatile component A
20 is in equilibrium with Driving force: Equilibrium curve Operating line Fig.7.2-4(a) for rectificationDriving force:is in equilibrium with
21 (2) Absorption: When one component is to be transferred from the V phase to L phase, as in the absorption of soluble material from an inert gas, the operating line must lie above the equilibrium line (Fig.7.2-4b), why?is in equilibrium withy=concentration of soluble component in an inert gas
22 y=conc. of soluble material in an inert gas Plate 1Plate n-1Plate nPlate n+1Plate N稀端Lean terminalFor absorption:y=conc. of soluble material in an inert gas浓端Thick terminal
23 Driving force: yn+1 - yn is in equilibrium with Operating line Equilibrium curveFig.7.2-4(b) for gas absorptionis in equilibrium withDriving force:yn+1 - yn
24 (3) Desorption/stripping: the reverse of gas absorption: recover valuable solute from the absorbing solution and regenerate the solvents. The operating line must lie below the equilibrium line (Fig.7.24c), why?is in equilibrium withx=concentration of solute in absorbing solution
25 For desorption or stripping: Plate 1Plate n-1Plate nPlate n+1Plate NFor desorption or stripping:y=conc. of soluble material in an inert gasx=conc. of solute in absorbing solution
26 is in equilibrium with Driving force: Equilibrium curve Operating line Fig (c) for strippingis in equilibrium withDriving force:
27 6) Ideal contact stagesIdeal Stage /Equilibrium Stage /theoretical StageIdeal Plate/Equilibrium Plate /Theoretical Plate/ Perfect platey2 is in equilibrium with x2.
28 Plate (Murfree) efficiency: To use ideal stages in design, it is necessary to apply a correction factor, called the stage efficiency级效率 or plate efficiency板效率, which relates the ideal stage to an actual one. (See Chapter 9 and 12)Overall efficiency:Plate (Murfree) efficiency:（默弗里效率）
29 7) Determining the number of ideal stages The usual method of designing cascades:Determining the number of ideal stagesFinding the stage efficienciesCalculating the number of actual stages
30 A simple method of determining the number of ideal stages when there are only two components in each phase is a graphical construction using the operating-line diagram.E.g.: Gas absorption:
31 y=conc. of soluble material in an inert gas. For absorption:y=conc. of soluble material in an inert gas.FromHow many ideal stages are needed?Plate N
32 Utilize alternately the operating and equilibrium lines Fig.20.5 Operating-line diagram for gas absorber.Operating-lineEquilibrium curveUtilize alternately the operating and equilibrium linesPoints (x1,y1), (x2,y2), (x3,y3) must lie on equilibrium curve.Every step, or triangle represents one ideal stage.
33 The same construction can be used for determining the number of ideal stages needed in any cascade, whether it is used for gas absorption, distillation, leaching, or liquid extraction.The graphical step-by-step construction can be started at either end of the column.Fractional stage? (See example 7.4)
34 When the operating and equilibrium lines are both straight: 8) Absorption factor method吸收因数法 for calculating the number of ideal stagesWhen the operating and equilibrium lines are both straight:Let the equation of the equilibrium line beWhere, by definition, m and B are constant. If stage n is ideal,
35 Substitution for xn into Eq. (20. 7)[p Substitution for xn into Eq.(20.7)[p.628] gives, for ideal stages and constant L/V,DefineWhere A=absorption factor, ratio of the slope of the operating line L/V to that of the equilibrium line m.
36 ThereforeBecause, the total number of stages,and
37 ThenThe sum of geometric series is=sum of first n terms of series=first term=constant ratio of each term to preceding term（公比）There
38 (Kremser equation克列姆塞尔方程) Equation(20.16) can then be written(Kremser equation克列姆塞尔方程)Other Forms of Kremser equation[For absorption]:
39 When A=1, (the operating line and the equilibrium line are parallel):
40 Question: If the operating line and equilibrium line are straight and parallel, A=1, Where, N=NTP=Number of theoretical platesWhy?
41 When the operating line is straight but steeper than the equilibrium line, as in Fig.8.2-2b, NTP=N=Number of theoretical platesWhy? [Refer to chapter 8.]For case of N=NTP=1,
42 9)L-phase form of Eq.(20.24):Where x*=equilibrium concentration corresponding to yS=stripping factorEq.(20.28) mainly for stripping.
43 The stripping factor is the ratio of the slope of the equilibrium line to that of the operating line.It is not assumed that the linear extension of the equilibrium line passes through the origin. It is only necessary that the line be linear in the range where the steps representing the stages touch the line.
44 For absorption, using Eq.(20.22) or (22.24) or eq.(20.21); Summary:In the design of a plant, N is calculated from the proposed terminal concentrations and a selected value of A or S.For absorption, using Eq.(20.22) or (22.24) or eq.(20.21);For stripping, using eq.(20.28) or (20.30). [Because equations in x are more common.][EXAMPLE 20.2.]
45 *10)Equilibrium-Stage Calculations for Multicomponent system(自学)