12. kesetimbangan uap cair 2014

Kesetimbangan uap cair(V Li id E ilib i VLE)(Vapor-Liquid Equilibrium-VLE)

Volatilitas (volatility)

Ukuran kemampuan (mudah atau tidaknya) suatu zat cair (liquid) untuk berubahmenjadi uap (vapor)menjadi uap (vapor)

Setiap jenis zat cair memiliki volatilitasberbeda

Ethanol & air: ethanol lebih volatil (boiling point: 78 C) dibanding air (bp: 100C)

Kit d t l k k i h Kita dapat melakukan pemisahandengan mengambil keuntungan dariperbdedaan volatilitas antarperbdedaan volatilitas antarkomponen

Komponen yang lebih volatil akan Komponen yang lebih volatil akanbanyak berada di fase uap, yang kurang volatil ada di fase cairkurang volatil ada di fase cair

Uap (V) dan cairan (L) dapatdipisahkandipisahkan

Binary Separation A Single StageBinary Separation A Single Stage

VInitial

Final Concentrations

Liquid Feed A and B

VaporVapor Product A and B

Concentrations

Liquid Product A and B

Liquid

What we need Bagaimana menghubungkan konsentrasi (fraksi mol) Bagaimana menghubungkan konsentrasi (fraksi mol)

komponen di fase uap dengan konsentrasi di fase cair

Dilakukan dengan asumsi standard condition darigsistem yang dikenal dengan vapor-liquid equilibrium condition (kondisi kesetimbangan uap-cair).

Dengan mengasumsikan vapor liquid equilibrium Dengan mengasumsikan vapor-liquid equilibrium, dapat diketahui hubungan antara konsentrasi di faseuap dan cair

Memanfaatkan equilibrium curve (kurvakesetimbangan).

Vapor-Liquid Equilibrium Thermal Equilibrium there is no net heat L VT T Thermal Equilibrium there is no net heat transfer and the temperature of the vapor

and liquid phases are equal.

L VT T

Mechanical Equilibrium the forces between vapor and liquid are balanced and the pressure of vapor and liquid phases are equal.

L VP Pq

Chemical Equilibrium the rates of vaporization of liquid and the condensation of vapor are equal and the chemical potentials ;L Vi i p q pbetween the vapor and liquid and phases are equal; thus, the compositions of the vapor and liquid phases do not change at a given temperature and pressure.

;1,...,

i i

i C

Two Component System o Co po SysThe Binary System

Suppose that we add two components to a container, seal the container, and a container, seal the container, and place it in a constant temperature bath.

The system can be represented by a two-component mixture, a binary system in the closed container at a system, in the closed container at a particular temperature and pressure:

Two Component System Two Component System The Binary System

P TVapor Phase Pvap, TvapVapor Phase

A BrA vap rB vap

A BrA con rB con

Pliq, TliqLiquid Phase liq, liqq

Thermal and Mechanical Equilibrium

After a suitable period of time the system will reach After a suitable period of time, the system will reach equilibrium, and the temperature and pressure of the system cease to change. Thus, we have:

1.) Temperature (Thermal) Equilibrium

T = TTliq = Tvap

2.) Pressure (Mechanical) Equilibrium

Pliq = Pvap

Thermal and Mechanical Equilibrium

P TVapor Phase Pvap, Tvap

A B

Vapor Phase

r rA B

rA

rA vap rB vap

rBA BrA con rB con

T = T and P = P

Pliq, TliqLiquid Phase

Tvap = Tliq and Pvap = Pliq

Chemical Equilibrium

Lets assume component A is more l til th t Bvolatile than component B.

Over a suitable period of time, one will reach equilibrium in the distribution between the vapor and liquid phase of each component...

Phase Equilibrium Overall Overall at equilibrium one will have more of Overall, at equilibrium, one will have more of

component A than B in the vapor phase and more of B than A in the liquid phase:

Pvap, Tvap

A B

Vapor Phase

A

A B

BrA con

rA vap rB vap

rB conA B


Phase Equilibrium Chemical Potentials

At equilibrium, these rates, and, thus the vapor and liquid concentrations of each component, are governed by the minimum thermodynamic free ene g of tem the minim m Gibb F ee Ene genergy of system the minimum Gibbs Free Energy.

Another way to express this is by the chemical potentials of each component i in the vapor and liquid potentials, of each component i in the vapor and liquid phases, or:

(i)liq = (i)vap

ll b d l h h d h We will not be dealing with how to determine these chemical potentials in this course we will use equilibrium data and analytical expressions representing the equilibrium curve in the design of p g q gseparation processes.

Vapor-Liquid Phase Equilibrium Summarizing the definition of equilibrium: Summarizing the definition of equilibrium:

1.) Temperature (Thermal) Equilibrium

Tliq = Tvap Eq. (2-1)

2.) Pressure (Mechanical) Equilibrium

Pliq = Pvap Eq. (2-2)

3 ) Chemical Equilibrium3.) Chemical Equilibrium

(i)liq = (i)vap Eq. (2-3)

When can we assume equilibrium?

We assume that the vapor-liquid equilibrium system is well mixed and that there is a great amount of contact between the vapor and liquid phases this promotes between the vapor and liquid phases this promotes thermal and mechanical equilibrium between the vapor and liquid with no mass transfer limitations, which promotes phase equilibrium.

We assume that the time to reach equilibrium is almost instantaneous relative to the other times involved in the system we thus have temperature and pressure equilibrium, as well phase equilibrium.

Staged Separations Distillation

Separations Distillation

Separations Distillation Design

Equilibrium Summary

We assume thermodynamic equilibrium for a given temperature and pressure.

This sets the equilibrium relationship between the components in each phase.

The distribution between phase for each component will be different, with one component enriched in the vapor phase and the other in the liquid phase.

The next task is to determine what the equilibrium relationships are and how to handle them

Data Kesetimbangn

Equilibrium Mole-Fraction Relationship qu b u o a o a o s pBinary System

We will start by considering the concentrations of the components in the vapor and liquid phase for a binary system.

However, it is convenient to use mole fractions, instead of t ti i th f th l f ti i tl l concentrations, since the sum of the mole fractions conveniently equals

one. For a binary system comprised of component A and B, this can be written as:

xA + xB = 1 0xA + xB 1.0and Eq. (2-4)

yA + yB = 1.0

wherewherexA = mole fraction of component A in the liquid phasexB = mole fraction of component B in the liquid phaseyA = mole fraction of component A in the gas phaseyB = mole fraction of component B in the gas phaseyB mole fraction of component B in the gas phase

Equilibrium Mole-Fraction Relationship qu b u o a o a o s pBinary System

Pvap, TvapVapor Phase vap, vapp

yA + yB = 1.0

A BrA vap rB vap

A BrA con rB con

1 0


xA + xB = 1.0


Equilibrium Mole-Fraction Relationship qu b u o a o a o s pMulti-Component System

We can also extend this analysis to We can also extend this analysis to multi-component systems containing an i number of components:p

0.1x iEq. (2-4)

01y 0.1y i

Equilibrium Mole-Fraction Relationship

We now have a method to conveniently relate the We now have a method to conveniently relate the concentrations (as mole fractions) in the liquid and vapor phases we now need a relationships between the mole fractions in the liquid and vapor phases

We can do this via phase equilibrium relationships which tie the mole fractions in the liquid together with those in the vapor.

Phase equilibrium is dependent upon the temperature and pressure of the system, the mole fractions of the components, as well as the components of the system.components, as well as the components of the system.

Where do we get this equilibrium information or how do we determine it?

Equilibrium Data Where to Find?

Available from many sources including: Perrys Handbook (all editions) Literature (see Table 2 3 p 14 Wankat) Literature (see Table 2-3, p. 14, Wankat) Industry monographs (often hard to obtain)

Th d i th d b d Thermodynamic methods based upon vapor pressures, activity coefficients, etc. (such as the methods available in Aspen).

Actually perform the experiment and determine the equilibrium data.

Equilibrium Data How to Handle?

Tabular Data Generate graphical plots Generate analytical expressions (curve fit)

Graphical y vs. x (P constant) McCabe-Thiele Pot T vs. x,y (P constant) Saturated Liquid, Vapor Plot Enthalpy vs. composition (P constant, T) Ponchon-Savarit Plot

Analytical expressions Distribution coefficient Distribution coefficient Relative volatility DePriester charts Curve fit of data

Vapor-Liquid Equilibrium Data apo qu d qu b u a aEthanol-Water, P =1 atm

DData: From Table 2-1, Wankat, p. 11

Vapor-Liquid Equilibrium Data for Ethanol and Water at 1 atm.xEtOH xw yEtOH yw T (

oC)0 1 0 0 1 0 1000 1,0 0 1,0 100

0,019 0,981 0,170 0,830 95,50,0721 0,9279 0,3891 0,6109 89,00,0966 0,9034 0,4375 0,5625 86,70 1238 0 8762 0 4704 0 5296 85 30,1238 0,8762 0,4704 0,5296 85,30,1661 0,8339 0,5089 0,4911 84,10,2377 0,7623 0,5445 0,4555 82,70,2608 0,7392 0,5580 0,4420 82,30,3273 0,6727 0,5826 0,4174 81,50,3965 0,6035 0,6122 0,3878 80,70,5079 0,4921 0,6564 0,3436 79,80,5198 0,4802 0,6599 0,3401 79,70,5732 0,4268 0,6841 0,3159 79,30,6763 0,3237 0,7385 0,2615 78,740,7472 0,2528 0,7815 0,2185 78,410,8943 0,1057 0,8943 0,1057 78,15

1,0 0 1,0 0 78,30

Binary Separation by Phase Creationy p y A Single Stage

VInitial

Final Concentrations

T P

Liquid Feed

VaporVapor Product yEtOH and yW

Initial Concentrations

yEtOH+yW = 1.0

Tvap, Pvap

EtOH and Water Liquid Product xEtOH and xW

Liquid

xEtOH+xW = 1.0

Tliq, Pliq

Lets Assume Equilibrium atP = 1 atm and T = 82.3 oC

What is the mole fraction of ethanol in the liquid phase?

What is the mole fraction of ethanol in the vapor phase?

What is the mole fraction of water in the liquid phase?

Wh t i th l f ti f t i th h ? What is the mole fraction of water in the vapor phase?

Other Important Information

One can determine from the data alone what the boiling points are of each pure what the boiling points are of each pure component

What are the boiling points of each pure component from the data?

Which is the more volatile component?

Graphical Plots of Equilibrium Data

L t l k t t l t thi Lets now look at a way to plot this equilibrium data

One usually plots the more volatile component in this case it is ethanol component in this case it is ethanol.

y vs. x y sMcCabe-Thiele Plot

Eth l W t E ilib i D t P 1 tEthanol-Water Equilibrium Data, P = 1 atmyEtOH vs xEtOH

0.9

1.0

0.6

0.7

0.8

H

0.2

0.3

0.4

0.5

y

E

t

O

0.0

0.1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

xEtOH

More Important Points

Note that the more volatile component ethanol generally has a component, ethanol, generally has a higher mole fraction, yEtOH, in the vapor phase for a given liquid phase p p g q pmole fraction, xEtOH.

What would this plot look like if one plotted the less volatile component?

y vs. x yMcCabe-Thiele Plot

Pressure is constant.

One normally plots the more volatile component.y p p

Points on the curve represent two phases in equilibrium.

Any point not on the curve may indicate both liquid and vapor phase are present, but they are not in equilibrium.

The auxiliary line x = y is often indicated on the The auxiliary line, x = y, is often indicated on the McCabe-Thiele plot. It has no physical meaning other than to indicate on the plot where x = y for reference. It is convenient to us as we shall see.

Remember McCabe-Thiele Method

Chapter 2

EquilibriumEquilibrium

x is the mole fraction of a

y is the mole fraction of a component in

component in the liquid phase

component in the vapor phase

Enthalpy vs. Composition P h S it Pl tPonchon-Savarit Plot

Lecture 5 36



0.9

1.0

0.6

0.7

0.8

H

0.2

0.3

0.4

0.5

y

E

t

O

0.0

0.1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

xEtOH

Question

Where does the equilibrium curve intersect x y and what are the intersect x = y and what are the equilibrium vapor and liquid ethanol mole fractions at this point?mole fractions at this point?



0.9

1.0

0.89

0.6

0.7

0.8

H

0.2

0.3

0.4

0.5

y

E

t

O

0.0

0.1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

xEtOH 0.89

Azeotropes

The equilibrium curve is, in general, above the x = y line when the more volatile component is plotted, in this case ethanol.

The point where the liquid and vapor mole fractions touch the x = y line indicates that they are equal this is termed the azeotropic point or azeotrope.

The initially more volatile component is no longer the more volatile component at the azeotrope.

For an ethanol-water mixture at P = 1 atm, this point is xEtOH = yEtOH = 0.8943, which from Table 2-1 occurs at T = 78.15oC.



0.9

1.0

Azeotrope

0.6

0.7

0.8

H

0.2

0.3

0.4

0.5

y

E

t

O

0.0

0.1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

xEtOH

Azeotropes The Problem

Azeotropes often present problems in equilibrium vapor-liquid phase separations since their presence means that one will not obtain enrichment between the vapor phase and the liquid phase above the azeotrope one cannot and the liquid phase above the azeotrope one cannot obtain separation greater than the azeotropic point for a given set of conditions.

F l thi li it i 0 8943 l f ti f th l For example, this limit is 0.8943 mole fraction of ethanol for an ethanol-water mixture at P = 1 atm.

If one wished to separate a mixture containing 0 9 If one wished to separate a mixture containing 0.9 ethanol liquid mole fraction at 1 atm, one would not obtain a greater concentration in the vapor phase than in the liquid phase.

Azeotropes Circumventing the Problem

Azeotropes are dependent upon pressures and one way to circumvent this problem is to vary the pressure.

For example under a vacuum (P = 70 mmHg) no azeotrope For example, under a vacuum (P = 70 mmHg), no azeotrope exists for the ethanol-water mixture. This is one reason that vacuum distillation is often done for many separations.

Azetropes are often also very component dependent Azetropes are often also very component dependent.

For example, the addition of a 3rd component to a binary system, may change or break the azeotrope.

We will discuss how to break the azeotrope later by varying the pressure and also adding additional components to the system.

Minimum Boiling Point Azeotropes

An azeotrope that occurs at a temperature that is less than either of the boiling points of the pure components is termed a minimum boiling point azeotrope.

For example, the azeotrope for ethanol-water is a minimum boiling azeotrope since it occurs at a temperature (T = 78.15oC) which is less than the boiling point of either ethanol or water (T =78 30oC and 100oC respectively) ethanol or water (T =78.30oC and 100oC, respectively) see Table 2-1, which indicates this more clearly.

Maximum boiling azeotropes also occur where the t t t t b b th th b ili azeotrope occurs at a temperature above both the boiling

points of the pure components well look at these a little later.

Vapor-Liquid Equilibrium p q qComponent Effect

One must remember that the equilibrium behavior is often very different for different systems of components.

The following are examples of binary mixtures of ethanol and other components.

Comment on the relative ease of separation for each and identify the azeotrope.

What does it mean when the equilibrium curve drops below x = y?

Vapor-Liquid Equilibrium ffComponent Effect

Question

From the y vs. x plot, what is temperature at P =1 atm and xEtOH = 0 6?0.6?

Answer

From the ethanol-water y vs. x plot, what is the temperature at P =1 atm and xEtOH = 0.6 at equilibrium?

One cannot tell from the plot. One must have additional data.p

The temperature is different at each point on the equilibrium curve although without the corresponding temperature data, one cannot tell directly what the temperature is from the plot y p palone.

One can say that temperature decreases from left to right along the curve or decreases from bottom to top when one g pplots the more volatile component.

There is another way to plot the data that indicates equilibrium temperature behaviorp

T vs x,y ySaturated Liquid and Vapor Plot

The T vs x,y plot presents the temperature equilibrium relationship for temperature equilibrium relationship for x and y.

Pressure is constant.

One normally plots the more volatile component.

T vs x,y Saturated Liquid and Vapor Plot

Temperature-Composition Diagram for Ethanol-Water, P = 1 atm

100

90

95

C

)

Superheated Vapor PhaseTwo Phase

80

85

T

(

o

C

75

80

0.0 0.2 0.4 0.6 0.8 1.0

Subcooled Liquid Phase

xEtOH or yEtOH

What can the T vs. x,y plot tell one?

One now has two equilibrium curves a saturated liquid line and saturated vapor line.

Any point below the saturated liquid line is a single phase Any point below the saturated liquid line is a single-phasecomposition of a subcooled liquid no vapor exists.

Any point above the saturated vapor line is a single-phasecomposition of a superheated vapor no liquid existscomposition of a superheated vapor no liquid exists.

Any point between the saturated liquid and saturated vapor lines is a two- phase composition both vapor and liquid exist in equilibrium.equilibrium.

Thus, one can obtain a lot more information from the T vs. x,y plot than from the y vs. x

Question

What are the boiling point t t f th t temperatures of the pure components from the T vs. x,y plot?



100

90

95

C

)


80

85

T

(

o

C

75

80

0.0 0.2 0.4 0.6 0.8 1.0


xEtOH or yEtOH

Answer

What are the boiling point temperatures of the pure components, ethanol and water, from the T vs. x,y plot?plot?

If one has pure ethanol in the system, xEtOH = yEtOH = 1.0; thus, at xEtOH = 1.0, the boiling point of ethanol is 1.0; thus, at xEtOH 1.0, the boiling point of ethanol is 78.3oC at 1 atm from the plot.

If one has pure water in the system, xEtOH = yEtOH = 0.0 p y , EtOH yEtOHor xW = yW = 1.0 ; thus, at xEtOH = 0.0 the boiling point of water is 100oC at 1 atm from the plot.

Bubble and Dew Point Temperatures

Any point on the saturated liquid line is the point at which the liquid just begins to boil the first bubble of vapor is formed. This temperature, for a given of vapor is formed. This temperature, for a given composition and pressure, is the bubble-point temperature.

Any point on the saturated vapor line is the point at which the vapor just begins to condense the first drop of liquid is formed. This temperature, for a given composition and pressure, is the dew-point temperature.



100

90

95

C

)


80

85

T

(

o

C

75

80

0.0 0.2 0.4 0.6 0.8 1.0


xEtOH or yEtOH

Example using the T vs. x,ya p us g s ,ySaturated Liquid and Vapor Plot

Assume one is given an ethanol-water mixture with a concentration of 20% ethanol at P = 1 atm and T = 75oC.

Explain what happens as one heats the system to 80oC using the T vs. x,y plot.

By convention for a feed, designate the mole fraction as zEtOH on the diagram at 75oC and indicate heating to 80oC.

What is the phase of this mixture at 75oC and what is the phase at 80oC?

Saturated Liquid and Vapor Plot Sa u a d qu d a d apo oHeating, zEtOH = 0.2


100

90

95

C

)


80

85

T

(

o

C

75

80

0.0 0.2 0.4 0.6 0.8 1.0


zEtOH

xEtOH or yEtOH

Saturated Liquid and Vapor Plot Saturated Liquid and Vapor Plot Heating, zEtOH = 0.2

Starting with zEtOH = 0.2 at T = 75oC, one has a subcooled liquid.

As it is heated, this mixture remains a single-phase liquid until the saturated liquid line is reached.saturated liquid line is reached.

Once one reaches the saturated liquid line, the first vapor bubble appears.

This is known as the Bubble Point Temperature the temperature at which the mixture begins to boil.

What is the Bubble Point Temperature for a mixture containing What is the Bubble Point Temperature for a mixture containing mole fraction zEtOH = 0.2? Indicate the isotherm line on the plot.

Saturated Liquid and Vapor Plot Sa u a d qu d a d apo oBubble Point Temperature


100

90

95

C

)


80

85

T

(

o

C

83

75

80

0.0 0.2 0.4 0.6 0.8 1.0


zEtOH

xEtOH or yEtOH

Saturated Liquid and Vapor Plot Sa u a d qu d a d apo o1st Vapor Bubble Composition

What will be the vapor composition of this first bubble at equilibrium? Indicate this first bubble at equilibrium? Indicate the method of determination on the plotplot.

Remember that the temperature of the Remember that the temperature of the vapor and liquid phase are the same at equilibriumq

Saturated Liquid and Vapor Plot q p1st Vapor Bubble Composition


100

90

95

C

)


80

85

T

(

o

C

83 Isotherm

75

80

0.0 0.2 0.4 0.6 0.8 1.0


zEtOH yEtOH

xEtOH or yEtOH


Assume that the mixture is heated further to T = 89oC.

What is the phase of the mixture at T = 89oC?

What are the liquid and vapor phase compositions of the mixture at T = 89oC?

Indicate your method of determination on the plot.p



100

90

95

C

)


89 Isotherm

80

85

T

(

o

C

Isotherm

750.0 0.2 0.4 0.6 0.8 1.0

xEtOH or yEtOH


zEtOH yEtOHxEtOH

xEtOH or yEtOH


Assume that the mixture is heated further through the two phase g pregion.

Once one reaches the saturated vapor line, the last liquid drop disappears.

This is known as the Dew Point Temperature.

Why Dew Point? because the system is reversible. If one started in the superheated vapor region and cooled this would be the temperature the superheated vapor region and cooled, this would be the temperature at which the mixture begins to condense and the first liquid drop would form.

What is the Dew Point Temperature, and what will be the liquid p , qcomposition of the last liquid drop before it disappears?

Indicate your method of determination on the plot.

Saturated Liquid and Vapor Plot Sa u a d qu d a d apo oLast Liquid Drop Composition


100

90

95

C

)

Superheated Vapor Phase94.8

Isotherm

80

85

T

(

o

C

Two Phase

75

80

0.0 0.2 0.4 0.6 0.8 1.0


zEtOHxEtOH

xEtOH or yEtOH

Additional Problem

Using the equilibrium data for ethanol-water at P =1 atm (Table 2-1 Wankat), estimate the bubble point temperature and estimate the bubble point temperature and composition of the 1st vapor bubble formed for a feed mixture containing zEtOH = 0.508.

Estimate the dew point temperature and composition of the last liquid drop.

Use only the data table, do not plot.

T vs x,y Azeotrope The point where the saturated liquid line and the saturated vapor line touch p q p

is the azeotrope (x = y), which can be read directly from the T vs. x,y plot at T = 78.15oC.

Compare this to the azeotrope on the y vs. x plot of Figure 2-2, p. 15 in Wankat.Wankat.

This is a minimum boiling azeotrope as we previously determined the azeotrope occurs at a temperature (T = 78.15oC) which is less than the boiling point of either ethanol or water (T = 78.30 and 100oC, respectively).

One can also see this minimum boiling point behavior more clearly in Figure 2-3, p. 16 in Wankat. The azeotrope is the point where the saturated liquid line and the saturated vapor line touch.

Note that the equilibrium curves sweep up slightly past the azeotrope before reaching the boiling point of pure ethanol since this is a minimum boiling azeotrope.



100

90

95

C

)


80

85

T

(

o

C

Azeotrope

75

80

0.0 0.2 0.4 0.6 0.8 1.0


p

78.15

xEtOH or yEtOH

De Priester Chart

DePriester Charts: Low T

71

DePriester Charts: High T

72

DePriester: Low T

73

DePriester Charts: High T

74

12. kesetimbangan uap cair 2014

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