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Distillation DesignThe McCabe Thiele Method

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Using rigorous tray-by-tray calculations is

time consuming, and is often unnecessary. One quick method of estimation for number

of plates and feed stage can be obtained

- . This eliminates the need for tedious,

understanding the Fenske-Underwood--

distillation

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yp ca y, t e n et ow to t e st at on co umn sknown, as well as mole percentages to feed plate,because these would be s ecified b lant conditions.

The desired composition of the bottoms and distillate

products will be specified, and the engineer will needto design a distillation column to produce theseesults

With the McCabe-Thiele Method, the total number of

necessary plates, as well as the feed plate locationcan be estimated, and some information can also bedetermined about the enthalpic condition of the feed

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This method assumes that the column is

operated under constant pressure, and theconstant molal overflow assumption isnecessary, which states that the flow rates of

liquid and vapor do not change throughoutthe column. To understand this method, it is necessary to

first elaborate on the subjects of the x-ydiagram, and the operating lines used tocreate the McCabe-Thiele diagram.

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- The x-y diagram depicts vapor-liquid

equilibrium data, where any point on theliquid that is in equilibrium with vapor at

. In a binary system containing substances A

,be separated into the mole percentage of theva or that is substance A on the axis andthe mole percentage of the liquid that issubstance A on the x axis.

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The relative volatility

can be consideredconstant and thefollowing equation

can be used. When considering a

binary system, the

previous equationcan be simplified.

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Knowing the relative volatility for a system is

separation possible.

components are equally volatile and no,

volatility is low, ( a < 1.05), separationbecomes difficult and ex ansive because alarge number of trays are required

The hi her the relative volatilit , or the lowerthe pressure, the more separable are the two

components; this connotes fewer stages in adistillation column in order to effect the sameseparation between the overhead and

.

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- Create the x-y diagram of the two-

component system and add the x=ydiagonal line. S ecif the urit of the to and

bottoms products, as well as the feed

respectively).

one of the following

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Operating line in rectifyingsection

ort on o t e st at on co umn a ove t e eeis called the rectifying section.

negligible and that the difference in the molarlatent heats of vaporization of the binary system

also differs by a negligible amount, then theobserved relationship between any two passingst eams is sim lified to:

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y = mole fraction of more volatile component in theva orx = mole fraction of more volatile component in theliquidxD = mole fraction of more volatile com onent in the distillate

D = Distillate product flow (mol/t)=section (mol/t)V = total flow rate of the vapor stream in the

This is known as the operating line for the rectifyingsect on, or t e upper operat ng ne, n s ort.Remembering that the x-y diagram is a plot of vapor(V) vs. liquid (L), it can be seen that the operatingline is a simple y=mx+b equation. Therefore, with thepoint (xD,y1) and the slope (L/V), this operating linecan be plotted.

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Portion of the distillation column below thefeed is called the stripping section. With thepreviously stated assumptions,

The observed relationship between any twopassing streams is simplified to:

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y = mole fraction of more volatile component in the

vaporx = mole fraction of more volatile component in theli uidxB = mole fraction of more volatile component in the

bottom product L = total flow rate of the liquid stream in the rectifyingsection (mol/t)

V = total flow rate of the vapor stream in therectifying section (mol/t)

section, or the lower operating line, in short. Again, it

can be seen that this is a simple line equation withthe slope (L/ V). With the slope and point where xDmeets the diagonal, the lower operating line can be

.

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Feed Line Equation

A third useful equation is the Feed-Line

Equation, commonly known as the q-line. q = mole fraction of saturated liquid infeed stream

the liquid

=the feed

It represents the intersection of the upperand lower o eratin lines. The sta e that

crosses the q-line is the optimum feedplate.

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Position A:q > 1.0subcooled liquid

Position B:

q = 1.0

Position C:0 < q

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Two possible feed conditions, saturated

liquid and saturated vapor. Notice how the slopes of the upper and loweroperating lines do not change, but the

feed conditions - ,

Direction of the q-line is horizontal-

infinity, Direction of the q-line is vertical

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If the slope of the q-line

is not directly known, itat the feed plateenthal ic conditions.

HV = enthalpy per molof vaporhl = enthalpy per mol ofliquid

= en a py per moof feed

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Slope of the q line and therectifying section

Draw the two known operating lines from the

known slopes. The stripping section line can be drawnbetween the points where the known

XBmeets the diagonal line.,

section operating line is red (upper section),-

green (lower section)

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Information about the reflux rationformation about the reflux ratio The use a limiting condition, there will be

two possibilities: only the slope of the q-line will be necessary, or no furtherinformation will be necessary.

The McCabe-Thiele method allows fullcontrol over reboiler duty, and it is notuncommon to first solve a problem

assuming minimum reflux ratio. Results canbe scaled to actual reflux ratio, typically R= 1.4*Rmin.

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Maximum Reflux The condition of total reflux implies that both

situated on the diagonal.

removed from the equilibrium curve, andtherefore the maximum se aration ossible

is occurring at each stage. Further this correlates to the minimum

number of equilibrium stages necessary to

reach the desired purity. The column is atmaximum diameter, but there is no productbecause all of the overhead product is beingre urne o e co umn as re ux.

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Minimum Reflux

This is a conceptual limit, as it implies thate en er ng an ex ng s reams o e s age

are in equilibrium, and it would take aninfinite number of stages to accomplish this. When a McCabe-Thiele dia ram is ra hed

using the condition of minimum reflux, theslo e of the u er o eratin line is no lon ernecessary.

,line between the point (xD,y1) and where the

- .condition, infinite stages are necessary.

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Shown in purple, starting at xD on the diagonal line,move or zon a o e equ r um ne, an envertically back to x-y line (see graph)Continue ocess towa d xB switchin the lowe

operating line after crossing the q-line, estimatingthe last stage if necessary.

- line. In the example, there are four stages, and theoptimum feed plate is number three.

s proce ure n s e eore ca num er o p a es,if all equipment was 100% efficient. In reality, an

efficiency factor should be specified to represent areal system.One efficiency factor is the overall efficiency, where

plates:

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