Unit Operations-III

Distillation is defined as:A process in which a liquid or vapor mixture of two or more substances is separated into its component fractions of desired purity, by the application and removal of heat.1EQUILIBRIUM-STAGE OPERATIONSOne class of mass-transfer devices consists of assemblies of individual units, or stages, interconnected so that the materials being processed pass through each stage in turnThe two streams move countercurrently through the assembly; in each stage they are brought into contact, mixed, and then separatedSuch multistage systems are called cascadesFor mass transfer to take place the streams entering each stage must not be in equilibrium with each other, for it is the departure from equilibrium conditions that provides the driving force for transferThe leaving streams are usually not in equilibrium either but are much closer to being so than the entering streams are

2Equilibrium-stage OperationsThe closeness of the approach to equilibrium depends on the effectiveness of mixing and mass transfer between the phasesTo simplify the design of a cascade, the streams leaving each stage are often assumed to be in equilibrium, which, by definition, makes each stage idealA correction factor or efficiency is applied later to account for any actual departures from equilibriumTo illustrate the principle of an equilibrium-stage cascade, two typical countercurrent multistage devices, one for distillation and one for leaching, will be discussed here

3TYPICAL DISTILLATION EQUIPMENTA plant for continuous distillation is shown in FigureReboiler A is fed continuously with the liquid mixture to be distilledThe liquid is converted partially into vapor by heat transferred from the heating surface BThe vapor formed in the reboiler is richer in low boiler than the unvaporized liquid, but unless the two components differ greatly in volatility, the vapor contains substantial quantities of both components, and if it were condensed, the condensate would be far from pureTo increase the concentration of low boiler in the vapor, the vapor stream from the still is brought into intimate countercurrent contact with a descending stream of boiling liquid in the column, or tower, C

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5This liquid must be rich enough in low boiler so that there is mass transfer of the low boiler from the liquid to the vapor at each stage of the columnSuch a liquid can be obtained simply by condensing the overhead vapors and returning some of the liquid to the top of the columnThis return liquid is called refluxThe use of reflux increases the purity of the overhead product, but not without some cost, since the vapor generated in the reboiler must provide both reflux and overhead product, and this energy cost is a large part of the total cost of separation by distillation6The reflux entering the top of the column is often at the boiling point; but if it is cold, it is almost immediately heated to its boiling point by the vaporThroughout the rest of the column, the liquid and vapor are at their boiling and condensing temperatures, respectively, and the temperatures increase on going down the column because of the increase in high boiler concentration, and in some cases, becauseof increase in pressureEnrichment of the vapor occurs at each stage because the vapor coming to a stage has a lower concentration of the low boiler than the vapor that would be in equilibrium with the liquid fed to that stageeg., the vapor coming to the top stage is less rich than the overhead product, and the reflux, which has the same composition as the product, has an equilibrium vapor composition which is even richer than the product7Therefore, vapor passing through the top stage will be enriched in low boiler at the expense of the reflux liquidThis makes the reflux poorer in low boiler, but if the flow rates have been adjusted correctly, the liquid passing down to the second stage will still be able to enrich the lower quality vapor coming up to the second stageThen at all stages in the column, some low boiler diffuses from the liquid into the vapor phase, and here is a corresponding diffusion of high boiler from the vapor to the liquidThe heat of vaporization of the low boiler is supplied by the heat of condensation of the high boiler, and the total flow rate of vapor up the column is nearly constantThe enrichment of the vapor stream as it passes through the column in contact with reflux is called rectificationIt is immaterial where the reflux originates, provided its concentration in low boiler is sufficiently great to give the desired product

8The usual source of reflux is the condensate leaving condenser DPart of the condensate is withdrawn as the product, and the remainder is returned to the top of the columnReflux is sometimes provided by partial condensation of the overhead vapor; the reflux then differs in composition from the vapor leaving as overhead productProvided an azeotrope is not formed, the vapor reaching the condenser can be brought as close to complete purity as desired by using a tall tower and a large refluxFrom the reboiler, liquid is withdrawn which contains most of the high boiling component, because little of this component escapes with the overhead product unless that product is an azeotrope

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10The downcomer, D from the tray above reaches nearly to tray ALiquid flows from plate to plate down the column, passing through downcomers D and C and across the platesThe weir maintains a minimum depth of liquid on the tray, nearly Independent of the rate of flow of liquidVapor flows upward from tray to tray through the perforationsExcept at very low vapor rates, well below the normal operating range, the vapor velocity through the perforations is sufficient to prevent leakage or "weeping" of the liquid through the holes

11The vapor is subdivided by the holes into many small bubbles and passes in intimate contact through the pool of liquid on the trayBecause of the action of the vapor bubbles, the liquid is actually a boiling frothy massThe vapor space above the froth contains a fine mist of droplets formed by collapsing bubblesMost of the drops settle back into the liquid, but some are entrained by the vapor and carried to the plate aboveSieve-plate columns are representative of an entire class of equipment called plate columns.

12MATERIAL BALANCES

Consider the portion of the cascade that includes stages 1 through n, as shown by the section enclosed by the dashed line in FigureThe total input of material to this section is Ln + Va moles per hour and the total output is La + Vn+1 moles per hourSince, under steady flow, there is neither accumulation nor depletion, the input and the output are equal andLa + Vn+1 = Ln + Va (1)

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14Equation (1) is a total material balanceAnother balance can be written by equating input to output for component A Since the number of moles of this component in a stream is the product of the flow rate and the mole fraction of A in the stream, the input of component A to the section under study, for a two-component system, is La xa + Vn+1 + Vn+1 yn+1 moles per hour, the output is Ln xn + Va ya moles per hour, and

La xa + Vn+1 yn+1 = Ln xn + Va ya (2)

15A material balance can also be written for written for component B, but such an equationis not independent of Eqs. (1) and (2), since if Eq. (2) is subtracted fromEq. (1), the result is the material-balance equation for component BEquations(1) and (2) yield all the information that can be obtained from materialbalances alone written over the chosen section.Overall balances covering the entire cascade are found in the same manner:

Total material balance: La + Vb = Lb + Va(3)Component A balance: Laxa + Vbyb = La xb + Va ya(4)

16ENTHALPY BALANCESIn many equilibrium-stage processes the general energy balance can be simplified by neglecting mechanical potential energy and kinetic energyIf, in addition, the process is workless and adiabatic, a simple enthalpy balance applies. Then, for a two-component system, for the first n stages,La HL,a + Vn+1 Hv, n+1 = Ln HL, n + Va, Hv,a (5)where HL and HV are the enthalpies per mole of the L phase and V phase, respectively. For the entire cascade, La HL,a + Vb Hv, b = Lb HL, b + Va HV, a (6)

17problem#1- Boiling Point Diagram & Equilibrium CurveThe vapor pressure of benzen & toulene are given in the following table. Assuming that the mixture of these materials follows Roults law. Calculate & plot the boiling point diagram & the equilibrium curve. For the system Benzene-Toulene at the total pressure of 01 atmosphere.18Vapor pressure dataS#Temp, CVap. Press (Benzene), mmHgVap. Press. (Toul). mmHg180.1760-285877345390101640549511684755100134455761051532654711017487438110.6180076019Solution:Suppose that benzene is represented by A & toulene is by B

According to Roults Law

Xe = (P- pb)/ (pa-pb)

Ye= xe (pa/P)20Problem#2Draw the equilibrium curve of SO2, water & air system at 2 atmospheric pressure & temperature of 30 degree celcius. Keeping the range of SO2 solubility maximum 6%

CaPa, mmHgxeye1852176327343765482658821Xe = pa/ Pt

Ye = (Ca/ M.Wt. of solute) / (Ca/M.Wt of solute) + (Ca/ mol. Wt. of solvent) 22IDEAL CONTACT STAGESThe ideal stage is a standard to which an actual stage may be comparedIn an ideal stage, the V phase leaving the stage is in equilibrium with the L phase leaving the same stageE.g., if plate n in Fig. 17.4 is an ideal stage, concentrations xn and yn are coordinates of a point on the curve of xe vs. ye showing the equilibrium between the phasesIn a plate column ideal stages are also called perfect stagesTo use ideal stages in design it is necessary to apply a correction factor, called the stage efficiency or plate efficiency, which relates the ideal stage to an actual one

23DETERMINING THE NUMBER OF IDEAL STAGESA problem of general importance is that offinding the number of ideal stages required in an actual cascade to cover a desired range of concentration xa to xb or ya to ybIf this number can be determined, and if information on stage efficiencies is available, the number of actual stages can be calculatedThis is the usual method of designing cascadesA 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. Figure 17.6 shows the operating line and the equilibrium curve for a typical gas absorber

24The ends of the operating line are point a, having coordinates (xa, ya), and point b, having coordinates (xb, yb)The problem of determining the number of ideal stages needed to accomplish the gas-phase concentration change yb to ya and the liquid-phase concentration change xa to xb is solved as followsThe concentration of the gas leaving the top stage, which is stage 1, is ya or y1If the stage is ideal, the liquid leaving is equilibrium with the vapor leaving, so the point (x1,y1) must lie on the equilibrium curve

This fact fixes point m, found by moving horizontally from point a to the equilibrium curveThe abscissa of point m is x1The operating line is now usedIt passes through all points having coordinates of the type (xn, yn+1), and since x1 is known, y2 is found by moving vertically from point m to the operating line at point n, the coordinates of which are (x1, y2)The step, or triangle, denned by points a, m, and n represents ONE ideal stage, the first one in this column

The second stage is located graphically on the diagram by repeating the same construction, passing horizontally to the equilibrium curve at point O, having coordinates (x2, y2) and vertically to the operating line again at point p, having coordinates (x2, y3) Figure 17.6: operating line diagram for the gs absorber

The third stage is found by again repeating the construction, giving triangle pqb

For the situation shown in Fig. 17.6, the third stage is the last, as theconcentration of the gas leaving that stage is yb and the liquid leaving it is xb which are the desired terminal concentrationTHREE ideal stages are required for this separationThe same construction can be used for determining the number of ideal stages needed in any cascade, whether it is used for gas absorption, rectification, leaching, or liquid extraction

The graphical step-by-step construction utilizing alternately the operating and equilibrium lines to find the number of ideal stages was first applied to the design of rectifying columns, and is known as the McCabe-Thiele methodThe construction can be started at either end of the column, and in general the last step will not exactly meet the terminal concentrations, as was the case in Fig. 17.6A fractional step may be assigned, or the number of ideal stages may be rounded up to the nearest whole number.

EXAMPLE

By means of a plate column, acetone is absorbed from its mixture with air in nonvolatile absorption oil. The entering gas contains 30 mole percent acetone, and the entering oil is acetone free. Of the acetone in the air 97 percent is to be absorbed, and the concentrated liquor at the bottom of the tower is to contain 10 mole percent acetone. The equilibrium relationship is ye = 1.9 xe Plot the operating line and determine the number of ideal stages.