Distillation 2

Distillation Equilibrium (Review) Flash Distillation Multistage Distillation

07/03/2013

MRB

Single Equilibrium Stage –

Ethanol-Water, P = 1 atm

Vapor

Liquid

F, zEtOH

V, yEtOH

L, xEtOH

F is the total moles of ethanol and water fed to the stage. V is the total moles in the vapor stream exiting the stage. L is the total moles in the liquid stream exiting the stage. zEtOH is the mole fraction of ethanol in the feed. yEtOH is the mole fraction of ethanol in the vapor stream. xEtOH is the mole fraction of ethanol in the liquid stream.

Feed Mole-Fraction Relationships

• Note that a feed mole-fraction, zF,can be a

subcooled liquid, a saturated liquid, a two-phase

mixture, a saturated vapor, or a superheated vapor.

• The feed phase is dependent upon the temperature,

pressure, and the composition (mole fraction).

zF and x,y Relationships

• Assuming that the equilibrium stage is at the same temperature and pressure of the feed:

• If zF is a subcooled liquid, then zF is simply xF and there is no y.

• If zF is a superheated vapor, zF is yF and there is no x.

• If zF is a saturated liquid, zF is essentially xF with a single vapor bubble formed of new mole fraction y.

• If zF is a saturated vapor, zF is essentially yF with a single liquid drop formed of new mole fraction x.

• If zF is in the two-phase region, the system will separate into a liquid and vapor of new mole fractions x and y, respectively. zF is not equal to either x or y, but x and y be determined from the T vs. x,y data or plot.

Mass Balance – Lever Rule

Vapor

Liquid

F, zA

V, yC

L, xB


Let

F = the moles of feed of composition zA

L = the moles of liquid of composition xB

V = the moles of vapor of composition yC

Then the mass balances before and after separation are

CBA VyLxFz Eq. (2-6)

and

VLF Eq. (2-7)


Substituting Eq. (2-7) into Eq. (2-6) and rearranging yields

BA

AC

xz

zy

V

L

Eq. (2-8)

where L/V is the ratio of liquid to vapor.

Comparing the numerator and denominator with the two-

phase diagram indicates that the distance between points A

and C and points A and B are equivalent to the magnitudes

of the liquid-phase and vapor-phase quantities,

respectively.

Graphically, this is BA

AC

V

L :


Temperature-Composition Diagram

for Two-Phase System

75

80

85

90

95

100

0.0 0.2 0.4 0.6 0.8 1.0

x or y

T(o

C)

Superheated Vapor Phase

Subcooled Liquid Phase

Isotherm

yCxB

Two Phase

Tsy s

B A C

zA

L

V

Mass Balance – Further Relationships

From inspection, other useful relationships can be

determined:

Fraction feed remaining as liquid

BC

AC

xy

zy

F

L

VL

Lq

Fraction feed vaporized

BC

BA

xy

x

F

V

VL

Vf

z

Note for a Two-Phase Mixture…

• At vapor-liquid equilibrium, the temperatures of the vapor and liquid are equal.

• When a two-phase mixture separates at vapor-liquid equilibrium conditions, the vapor phase will be at saturated vapor conditions and the liquid phase will be at saturated liquid conditions.

• We will use this assumption when we do our multi-stage solutions – the vapor and liquid streams exiting a stage will be assumed to be at saturated conditions.

• Thus, the liquid fed from one stage to another stage can be assumed to be a saturated liquid and the vapor feed to another stage can be assumed to be a saturated vapor.

Enthalpy vs. Composition –

Ponchon-Savarit Plot

• Presents the temperature equilibrium relationship for enthalpy vs. x and y.

• Pressure is constant.

• Enthalpy will be required in future problems utilizing energy balances.

• Note the units of concentration!

• For a non-ideal system, where the molar latent heat is no longer constant and where

there is a substantial heat of mixing, the calculations become much more tedious.

• For binary mixtures of this kind a graphical model has been developed by RUHEMANN, PONCHON, and SAVARIT, based on the use of an enthalpy-composition chart.

• It is necessary to construct an enthalpy-composition diagram for particular binary system over a temperature range covering the two-phase vapor-liquid region at the pressure of the distillation.

Enthalpy vs. Composition –Ponchon-Savarit Plot

What is the enthalpy of a (two phase) feed stream at 1 kg/cm2 pressure, 82°C, 0.6 wt% ethanol?


Enthalpy Determination

• The major purpose of an enthalpy diagram is to determine enthalpies.

• We will use enthalpies in energy balances later.

• For example, if one were given a feed mixture of 35% ethanol (weight %) at T = 92oC and P = 1 kg/cm2 and the mixture was allowed to separate into vapor and liquid, what would be the enthalpies of the feed, vapor, and liquid?

Lecture 5 14


Enthalpy Determination

425

295

90

Equilibrium Data – How to Handle?

• Tabular Data • Generate graphical plots

• Generate analytical expressions (curve fit)

• Graphical • y vs. x (P constant) – McCabe-Theile Pot

• T vs. x,y (P constant) – Saturated Liquid, Vapor Plot

• Enthalpy vs. composition (P constant, T) – Ponchon-Savarit Plot

• Analytical expressions • Thermodynamics: Equations of state/Gibbs free energy models

• Distribution coefficients, K values

• Relative volatility

• DePreister charts

• Curve fit of data

Analytical Expressions for Equilibrium

• There are several disadvantages to using graphical techniques: • One cannot readily plot multi-component systems graphically

(maximum is typically three).

• Separator design often has to be done using numerical methods; thus, analytical expressions for equilibrium behavior are needed.

• We will now look at other representations for handling equilibrium data analytically…

Other Equilibrium Relationships –

Distribution Coefficient

Another method of representing equilibrium data is to

define a distribution coefficient or K value as:

AAA

/ xyK Eq. (2-10)

KA is typically a function of temperature, pressure, and

composition.

The distribution coefficient K is dependent upon

temperature, pressure, and composition. However, for a

few systems K is independent of composition, to a good

approximation, which greatly simplifies the problem.

p)K(T,KA Eq. (2-11)


DePriester Charts

• One convenient source of K values for

hydrocarbons, as a function of temperature and

pressure (watch units), are the DePriester charts

• The DePriester plots are presented over two

different temperature ranges.

Using DePriester Charts –

Boiling Temperatures of Pure Components

• One can determine the boiling point for a given component and pressure directly from the DePriester Charts – one can then determine which component in a mixture is the more volatile – the lower the boiling point, the more volatile a component is.

• For a pure component, K = 1.0.

• Assume one wishes to determine the boiling point temperature of ethylene at a pressure of P = 3000 kPa…

Lecture 5

Tbp = - 9.5 oC

Question – DePriester Charts

• What are the equilibrium distribution coefficients, K,

for a mixture containing:

Ethylene

n-Pentane

n-Heptane

at T = 120 oC and P =1500 kPa?

Lecture 5

Answer – DePriester Charts

• The equilibrium distribution coefficients, K, are:

K

Ethylene 8.5

n-Pentane 0.64

n-Heptane 0.17

at T = 120 oC and P =1500 kPa.

Question – Volatility

• What can one say about the volatility of

each component from the K values?

K

Ethylene 8.5

n-Pentane 0.64

n-Heptane 0.17

Answer – Volatility

• What can one say about the volatility of each component from the K values?

K T boiling

Ethylene 8.5 -35.5 oC

n-Pentane 0.64 153 oC

n-Heptane 0.17 >200 oC

• The boiling point temperatures of the pure components at P = 1500 kPa have also been determined from the DePriester charts for K = 1.0 for each component (n-heptane’s is off the chart).

• From the K values and the boiling point temperature of each pure component, one can say that the volatility follows the trend that ethylene>n-pentane>n-heptane.

AAA / xyK


DePriester Equation

While the DePreister charts may be used directly, they have

been conveniently fit as a function of temperature and

pressure:

p

a

p

aaa

T

a

T

a2

p3

2

p2p1T6

T2

2

T1 plnKln Eq. (2-12)

where T is in oR and p is in psia. Table 2.4 (p. 26, Wankat)

contains the K fit constants along with their mean errors

(again, watch units!).

Eq. (2-12) provides an analytical expression which can be

used in numerical analyses. We will use this later for

bubble and dew-point temperature calculations.


Mole Fraction – Vapor Pressure Relationship

If one does not have equilibrium data, K can be approximated

using other more common thermodynamic data quantities such as

vapor pressures.

From Raoult’s law for ideal systems:

AAA (VP)xp Eq. (2-14)

where pA is the pressure due to component A in the mixture and

(VP)A is the vapor pressure of pure component A, which is

temperature dependent.

From Dalton’s law of partial pressures:

p

py A

A Eq. (2-15)

Combining Eqs. (2-15) and (2-14) and rearranging yields:

p

(VP)

x

y A

A

A Eq. (2-16)


Distribution Coefficient – Vapor Pressure Relationship

The left-hand side of Eq. (2-16) is the definition of the distribution coefficient K; thus,

p

(VP)K A

A Eq. (2-17)

Eq. (2-17) allows one to obtain K’s from the vapor pressures of the pure components, which can be

readily found for many chemical species using the Antoine equation:

CT

BAln(VP)A

Eq. (2-18)

where A, B, and C are constants, which can be found in many thermodynamic texts for many

chemical species. Vapor pressure correlations can also be found in “The Properties of Gases and

Liquids” (5th

Ed. Poling, Prausnitz, O’Connell)

Caution must be used when applying this K relationship since many systems are non-ideal.

Actually, systems are often less ideal in the liquid phase because of the intimate contact of the

chemical species, and these are handled by the liquid-phase activity coefficient, γA:

p

(VP)K AA

A

Eq. (2-19)

The activity coefficient can be obtained from correlations, e.g, Van Laar, Wilson, etc. (see

thermodynamic texts).


Relative Volatility

K values are strongly dependent on temperature; however, this temperature behavior maybe

somewhat similar, especially for similar chemical species, over certain temperature ranges.

Consequently, if one takes the ratio of the K’s for two components, the temperature dependence

will be less (see HW problem 2-D5).

This ratio, defined as the relative volatility, αAB, for a binary system is:

BB

AA

B

AAB

/xy

/xy

K

K Eq. (2-20)

If the temperature dependence for the K values is identical, then αAB will be independent of

temperature. However, for all but the most ideal situations, αAB will have some temperature

dependence.

Why is it termed relative volatility? Because, if Raoult’s law is valid:

B

AAB

(VP)

(VP) Eq. (2-21)

Thus, if (VP)A > (VP)B, component A is the more volatile and αAB > 1. Likewise, KA > KB; thus,

one can determine the more volatile component by comparing K’s. If A is more volatile, its K

value will be greater than B’s K value.


Relative Volatility

It will be convenient later on in separation problems to express the relative volatility in terms of the

mole fractions and vice-versa

For binary systems, the mole fractions are related by

AB y1y and AB x1x Eq. (2-4)

and substituting these into Eq. (2-20) yields:

AA

AAAB

)xy(1

)x(1y

Eq. (2-22)

or A

AAAB

y1

x1K

Solving Eq. (2-22) for yA and xA yields:

AAB

AABA

x)1(1

xy

Eq. (2-23)

and

AABAB

AA

y)1(

yx

Flash Distillation

• Flash distillation is the simplest method of separation.

• A feed stream is “flashed” into a chamber or “flash drum” and the liquid and vapor are allowed to separate under equilibrium.

• It is “flashed” by throttling the feed stream through a nozzle or valve into the chamber – the pressure drops through the valve.

• The more volatile component will be concentrated in the vapor stream – the less volatile in the liquid stream.

• The system is very close to a single “equilibrium stage”.

• Separation is usually not very high for a single equilibrium stage.

Flash Distillation – Solution

• Flash distillation problems can be solved using

three sets of equations:

–Equilibrium relationship

–Mass balance

–Energy balance

Flash Distillation –

Equilibrium Parameters

• Feed Composition – z

• Vapor-Phase Composition – y

• Liquid-Phase Composition – x

• Upstream Feed Temperature – T1

• Feed Temperature – TF

• Drum Temperature – Td

• Upstream Feed Pressure – P1

• Feed Pressure – PF

• Drum Pressure – Pd


Mass Parameters

• Feed Flow Rate – F

• Vapor Flow Rate – V

• Liquid Flow Rate – L

• Feed Composition – z

• Vapor-Phase Composition – y

• Liquid-Phase Composition – x


Energy Parameters

• Heater Input – QH

• Flash Drum Heat Input – Qflash

• Feed Enthalpy– hF

• Vapor Enthalpy – HV

• Liquid Enthalpy – hL

• Upstream Feed Temperature – T1

• Feed Temperature – TF

• Drum Temperature – Td

Flash Distillation – Mass Balances

• Overall mass balance

• Component mass balance

LVF

LxVyFz

Flash Distillation – Operating Line

Solving the overall mass balance for y yields

which is termed the operating line. It relates the

composition of the streams leaving the stage or

drum.

zV

Fx

V

Ly

Common problem specifications.

• Liquid to vapor ratio

L/V

• Fraction of feed vaporized

f = V/F

• Fraction of feed remaining as liquid

q = L/F

Operating Line Form –

Fraction Vaporized

From the overall mass balance

then

f

f1

V/F

V/F1

V

VF

V

L

zf

1x

f

f-1y

Operating Line Form –

Fraction Remaining as Liquid

or

and

q-1

q

L/F-1

L/F

L-F

L

V

L

zq1

1x

q-1

qy

Operating Lines – Linear!

• Slope

• y Intercept

• x intercept

q1

q

f

f1

V

L

zq-1

1z

f

1z

V

F

zq

1z

f-1

1z

L

F

So How Do Solve?

• We often know all of the system parameters except the compositions of the vapor and liquid leaving the stage or flash drum – two unknowns, y and x.

• We have two equations: – Equilibrium Relationship

– Mass Balance (Operating Line)

• With two equations and two unknowns we can solve the problem!

McCabe-Thiele Analysis


Typical Problem

• One will usually be given the feed stream, F, or it can be assumed.

• One will usually be given the feed composition, z, in mole or weight fraction.

• One will also typically be given one of the following: x, y, Td, f = V/F, q = L/F, L/V, or TF.

• One will usually be given the pressure, Pd, in the flash drum, or it will be chosen such that the feed is above its boiling point at Td, so that some of it vaporizes.

• What is given in the problem determines the type of problem and the method of solution.


Problem Type 1a: Sequential Solution

• If one of the equilibrium conditions – x, y, or Td – in the drum is specified, then the other two can be found from the equilibrium relationships using:

– Equilibrium data and plots or

– K values or

– Relative volatility relationships

• Once we have x and y, we can then solve for the streams – F, V, and L – using:

– Overall mass balance and

– Component mass balance

• We can then solve the energy balances to determine QH, TF, and T1 (Qflash = 0, since we typically assume an adiabatic drum) using enthalpies from:

– Heat capacities and latent heats of vaporization or

– Enthalpy-composition plots

• This method of solution is known as a sequential solution method since the energy balance is decoupled from the equilibrium and mass balances.


Problem Type 1b: Sequential Solution

• If the stream parameters are specified, usually as fraction of feed vaporized – f = V/F – or the fraction of feed remaining as liquid – q = L/F –, then the problem can be solved for x, y, Td, F, V, and L by a simultaneous solution using:

– Equilibrium relationships and

– Mass balances

• We can then solve the energy balances to determine QH, TF, and T1 using enthalpies from:

– Heat capacities and latent heats of vaporization or

– Enthalpy-composition plots

• This method of solution is also known as a sequential solution method since the energy balance is still decoupled from the equilibrium and mass balances.


Problem Type 2: Simultaneous Solution

• If the temperature, TF, of the feed is given, then the problem requires

a simultaneous solution for all of the other parameters using:

– Equilibrium relationship and

– Mass balance and

– Energy balance

• This method of solution is known as a simultaneous solution method

since the energy balance is not decoupled from the equilibrium and

mass balances.


Pressures

• The pressure, Pd, in the flash drum is chosen such that the feed is above its boiling point at Td, so that some of it vaporizes.

• The pressure, P1, is chosen such that the upstream feed is below its boiling point and remains liquid at T1.

• Likewise, the feed pressure, PF, must be chosen so that the feed is below its boiling point and remains liquid.

• The pump and heater assist in adjusting the required pressures and temperatures of the system.

• If the feed is already hot enough, the heater may not be needed, and if the pressure of the flash drum is low enough, the pump may not be needed.

Column Distillation

• Flash distillation provides a method of separation, but

the amount of separation obtained is limited.

• What if we need to have a greater separation to obtain

essentially pure components?

• We could place flash drums in series or as a cascade…

Lecture 9

Flash Drums in Cascade

Flash Drums in Cascade

• One can obtain a high level of separation using cascading flash drums.

• The problem with this arrangement is that we generate a large number of intermediate liquid and vapor streams, which would need to be separated.

• One could feed these intermediate streams to another flash drum cascade, but even more intermediate streams are formed, and so on and so on.

• Let’s look at what we can do with the intermediate streams…

Lecture 9

Flash Drums in Counter-Current Cascade –

Use of Intermediate Steams


Isobaric Operation

Lecture 9


Reflux and Boilup

Lecture 9


Intermediate Heat Exchange

Lecture 9

Distillation Column

Lecture 9

Distillation Column – External Balance

Column Distillation –

Typical Specified Variables

• Column pressure, Pc.

• Feed flow rate, F.

• Feed composition, z.

• Feed temperature, TF; enthalpy, hF; or quality, q = L/F.

• Reflux temperature,TR; or enthalpy, hD.

• Reflux ratio, L/D; or distillate composition, xD.

• Bottoms composition, xB.


Tools for Solution

• Equilibrium relationships

• Mass balances

• Energy balances


Methods of Solution

• External column balances

– Overall

– Condenser

– Reboiler

• Internal column balances

– Stage-by-stage calculations

Documents

Distillation 2