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CHE-201: Introduction to Chemical Engineering Chapter 6: Multiphase Systems By: Dr. Nabeel Salim Abo-Ghander

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CHE-201: Introduction to Chemical Engineering. Chapter 6: Multiphase Systems By: Dr. Nabeel Salim Abo-Ghander. Introductory Statement:. A Phase is a state of matter. Do you believe that: - PowerPoint PPT Presentation

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Page 1: CHE-201: Introduction to Chemical Engineering

CHE-201: Introduction to Chemical Engineering

Chapter 6: Multiphase SystemsBy:

Dr. Nabeel Salim Abo-Ghander

Page 2: CHE-201: Introduction to Chemical Engineering

Introductory Statement:

A Phase is a state of matter.

Do you believe that:All chemical processes involve operations in which material is transferred from one phase (gas, solid, liquid) to another.

Page 3: CHE-201: Introduction to Chemical Engineering

Examples on Multiphase Systems:

1. Brewing a cup of Coffee2. Removal of Sulfur dioxide from a gas stream.3. Recovery of Methanol from an aqueous Solution.4. Separation of paraffinic and aromatic compounds.

There are other systems which can be looked at!

Page 4: CHE-201: Introduction to Chemical Engineering

Brewing a cup of Coffee (leaching):

+ =

Page 7: CHE-201: Introduction to Chemical Engineering

Rate of transportation:

A species transfers from one phase to another until the second

phase is saturated, i.e. holding as much as it can hold at the

prevailing process condition. When the concentration of all species

in each phase no longer change with time, the phase are said to be

in phase equilibrium.

http://www.youtube.com/watch?v=gbUTffUsXOM

Page 8: CHE-201: Introduction to Chemical Engineering
Page 9: CHE-201: Introduction to Chemical Engineering

Phase Diagram:

Phase diagram of a pure species is defined as a plot of one system variable versus

another showing the conditions at which the substances exist as a solid, a liquid and a

gas.

Page 10: CHE-201: Introduction to Chemical Engineering

Phase Diagram:

Crossing Phases doesn’t occur instantaneously but gradually in which the

substance passes through three main stages, i.e. phase 1, phase 1 & 2, then

phase 2.

Solid

-Liq

uid

Equi

libriu

m C

urve

Liquid-Vapor Equilibrium Curve

Solid-Vapor

Equilibrium Curve

Page 11: CHE-201: Introduction to Chemical Engineering

Main points on the phase diagram:

Normal boiling point temperature is the point at which liquids

start to boil at one atmospheric pressure.

Triple point is the point at which the three phases, i.e. solid,

liquid and vapor coexist in equilibrium.

Critical temperature is the temperature at which a substances

can’t coexist in two phases whatever pressure is applied.

Sublimation points are located on solid-vapor equilibrium

curve.

Page 12: CHE-201: Introduction to Chemical Engineering

6.1b Estimation of Vapor Pressures:

Vapor pressure is the equilibrium pressure of the vapor above its liquid.

It indicates the tendency of a species to transfer from one phase to another.

Volatility of a species is the degree to which the species tends to transfer

from liquid (or solid) to state to the vapor state.

Four methods can be used to estimate the component vapor pressures:

1. Vapor pressure tables in references

2. Clapeyron equation.

3. Cox chart.

4. Antoine equation.

Page 13: CHE-201: Introduction to Chemical Engineering

Clapeyron equation:

It is an empirical equation given as:

Where: lg

v

VVTH

dTdp

ˆˆˆ

substancepureofpressurevaporp

etemperaturabsoluteT

liquidandvaporofvolumesmolarspecificˆ,ˆ lg VV

onvaporizatiofheatlatentˆ vH

Page 14: CHE-201: Introduction to Chemical Engineering

Clapeyron equation (Cont.):

At low pressure, and substituting for from ideal gas

low yields the Clausius-Clapeyron equation:

It is a straight line equations where a minimum of one point is needed to

obtain the value of “B”.

glgl VVVV ˆˆˆ0.0ˆ gV̂

2*

* ˆ

TdT

RH

pdp v

R

H

Tdpd v

ˆ1

ln *

BTR

Hp v

ln *

Page 15: CHE-201: Introduction to Chemical Engineering

Example 6.1-1: Vapor Pressure Using the Clausius-Clapeyron Equation:

The vapor pressure of benzene is measured at two temperatures, with the

following results:

Calculate the latent heat of vaporization and the parameter B in the Clausius-

Clapeyron equation and then estimate at 42.2oC using this equation.

mmHgpCT o 406.7 *11

mmHgpCT o 604.15 *22

*p

Page 16: CHE-201: Introduction to Chemical Engineering

Cox Plot:

Page 17: CHE-201: Introduction to Chemical Engineering

Antoine Equation:

It is an empirical equation expressed as:

where:

A, B, C are constant picked up from references

CT

BAp

*10log

Page 18: CHE-201: Introduction to Chemical Engineering

Table of Constant (Table B.4):

Page 19: CHE-201: Introduction to Chemical Engineering

6.2 The Gibbs Phase Rule:

V

L

A

A

A

A

A

A

V

L

A

A

AA

A

A

At the beginning of contact, different T, P, and mass or molar composition

At equilibrium, T, P, and no driving forces for mass or

molar between phases

Page 20: CHE-201: Introduction to Chemical Engineering

6.2 The Gibbs Phase Rule (Conti):

Variables can be divided into:

1. Extensive variables: depend on the system size.

Examples, mass and volume.

2. Intensive variables: don’t depend on the system size.

Example, temperature, pressure, density, mole

fractions, mass fractions.

Page 21: CHE-201: Introduction to Chemical Engineering

6.2 The Gibbs Phase Rule (Cont.):

To correctly specify a system, only intensive variables are

considered, mainly temperature, pressure and mole or mass fractions.

The number of intensive variables which should be specified for a

given system at equilibrium is calculated for nonreactive system by:

where:: Degree of freedom: Number of chemical species: Number of phases in a system at equilibrium

cDF 2

DFc

Page 22: CHE-201: Introduction to Chemical Engineering

Example 6.2-1: The Gibbs Phase Rule

Determine the degree of freedom for each of the following

systems at equilibrium. Specify a feasible set of

independent variables for each system.

1. Pure liquid water.

2. A mixture of liquid, solid, and vapor water.

3. A vapor-liquid mixture of acetone and methyl ethyl

ketone.

Page 23: CHE-201: Introduction to Chemical Engineering

6.3 GAS-LIQUID SYSTEMS: ONE CONDENSIBLE COMPONENT

Eventually equilibrium is established between the two phases.

Separation processes involving single condensable components are:

evaporation, drying, humidification, condensation, and dehumidification.

Dry Air at T=75oC and 760 mm Hg Dry Air at T=75oC and 760 mm HgIn contact with liquid water

w

w

w

w w

w

w w

w

w

w

w

w

2222 DF

Page 24: CHE-201: Introduction to Chemical Engineering

Separation Processes:

Evaporation:

Drying:

Humidification:

EvaporatorLiquid water

Liquid water

Water vapor

DryerWet solids

Dried solids

Water vapor

Humidifier

Dry air

Liquid water Humidified air

Transfer of Liquid into Gas

phase

Page 25: CHE-201: Introduction to Chemical Engineering

Separation Processes:

condensation and dehumidification:

Condenser or Dehumidifier

Wet airLiquid water

Air of less water

Transfer of component from Gas to Liquid phase

Page 26: CHE-201: Introduction to Chemical Engineering

Raoult’s Law, Single Condensable Species

If a gas at temperature T and pressure P contains vapor whose mole fraction is yi

(mol vapor/ mol total gas), and if this vapor is the only species that would condense

if the temperature were slightly lowered, then the partial pressure of the vapor in

the gas equals the pure-component vapor pressure at the system temperature:

Raoult’s Law, Single Condensable Species:

w

w

w

w w

w

w w

w

w

w

w

w

TpPyp iii*

Page 27: CHE-201: Introduction to Chemical Engineering

Example 6.3-1 Composition of a saturated Gas-Vapor System

Air and liquid water are contained at equilibrium in a

closed chamber at 75oC and 760 mm Hg, calculate

the molar composition of the gas phase.

Page 28: CHE-201: Introduction to Chemical Engineering

Table B.3 in Appendix B: Vapor Pressure of Water

Page 29: CHE-201: Introduction to Chemical Engineering

Remarks on Equilibrium Concept:

A gas in equilibrium with a liquid must be saturated with the volatile components of that liquid.

The partial pressure of a vapor at equilibrium in a gas mixture containing a single component can’t exceed the vapor pressure of the pure component at the system temperature. If , the vapor is saturated; any attempt to increase either by adding more vapor to the gas phase or by increasing the total pressure of the system at constant temperature, will lead to condensation.

A vapor present in a gas in less than its saturation amount is referred to as a superheated vapor. For such a vapor,

Achieving the condensation required changing the system conditions till equilibrium is maintained, then either the pressure is increased at constant temperature or the temperature is lowered at constant pressure.

TpPyp iii*

Tpp ii*

Page 30: CHE-201: Introduction to Chemical Engineering

Remarks on Equilibrium Concept:

If a gas containing a single superheated vapor is cooled at constant pressure, the temperature at which the vapor becomes saturated is referred to as the dew point of the gas:

Degree of superheat of a gas is the deference between the temperature of the gas and the dew point.

dpiii TpPyp *

Page 31: CHE-201: Introduction to Chemical Engineering

Equilibrium Concept:

w

A

ww

w

w

w

ww

ww

ww w

ww

ww

ww

w w

w

w w

A

ww

ww

w

ww

ww

ww w

ww

ww

ww

w w

ww

AAA

A A

AAA

A A

w

w

w

w

A

ww

ww

w

ww

ww

ww w

ww

ww

ww

w w

ww

AAA

AA

w

w

w

A

w w

w w

w

w

w

w

ww

w

Beginning of contact between the Phases

Air with superheated vapor

Air saturated with vapor

Hgmmp OH 0.02

TpPyp OHOHOH*

222 TpPyp OHOHOH

*222

w

Page 32: CHE-201: Introduction to Chemical Engineering

Example 6.3-2 Material Balances Around a Condenser

A steam of air at 100oC and 5260 mm Hg contains 10.0% water by volume.

1. Calculate the dew point and degrees of superheat of the air.

2. Calculate the percentage of the vapor that condenses and the final composition

of the gas phase if the air is cooled to 80oC at constant pressure.

3. Calculate the percentage condensation and the final gas-phase composition if,

Instead of being cooled, the air is compressed isothermally to 8500 mm Hg.

4. Suppose the process of part 2 is run, the product gas is analyzed, and the mole

fraction of water differs considerably from the calculated value. What could be

the responsible for the disparity between calculated and measured values? (List

several possibilities).

Page 33: CHE-201: Introduction to Chemical Engineering

Table B.3 in Appendix B: Vapor Pressure of Water

Page 34: CHE-201: Introduction to Chemical Engineering

Terminologies in Humidification:

Relative Saturation (Relative Humidity):

Molal Saturation (Molal Humidity)

Absolute Saturation (Absolute Humidity):

Percentage Saturation (Percentage Humidity):

%100* Tpphsi

irr

gasdryfreevaporofmoles

vaporofmolespP

phsi

imm )(

gasdryofmassvaporofmass

MpPMphs

dryi

iiaa

%100%100 ***

ii

ii

m

mrr pPp

pPpsshs

Page 35: CHE-201: Introduction to Chemical Engineering

Example 6.3-3:

Humid air at 75oC, 1.1 bar, and 30% relative humidity is fed into a

process until at a rate of 1000 m3/h. Determine:

1. The molar flowrate of water, dry air, and oxygen entering

the process unit.

2. The molal humidity, absolute humidity, and percentage

humidity of the air.

3. The dew point.

Page 36: CHE-201: Introduction to Chemical Engineering

6.4 MULTICOMPONENT GAS-LIQUID SYSTEMS

w

A

ww

ww

w

ww

ww

ww w

ww

ww

ww

w w

ww

AAA

AA

w

w

w

A

w w

w w

w

w

w

w

ww

ww

w

A

w

Cw

w

w

ww

wC

CC w

Cw

wC

ww

w w

ww

AAA

AA

w

w

w

A

w C

C w

C

w

w

w

ww

Cw

Already discussed in 6.3(Pure Liquid)

Will be discussed in 6.4(Liquid Mixtures)

TpPyp iii* TpxPyp iiii

*

Page 37: CHE-201: Introduction to Chemical Engineering

Remarks in Raoults Law:

General Raoult’s law for multicomponent mixtures is:

If the liquid mixture is a diluted one, i.e. , Raoult’s law can be

reduced to:

Henery’s Law:

Henery’s constant of i in a specific solvent

If the liquid phase is a pure one, Raoult’s law can be reduced into:

TpxPyp iiii*

THxPyp iiii

0.0ix

TpPyp iii*

TH i

Page 38: CHE-201: Introduction to Chemical Engineering

Example 6.4-2: Raoult’s and Henery’s Law

Use either Raoult’s law or Henry’s law to solve the following problems:

1. A gas containing 1.0 mol% ethane is in contact with water at 20oC and 20.0 atm.

Estimate the mole fraction of the disolved ethane.

2. An equimolar liquid mixture of benzene (B) and toluene (T) is in equilibrium

with its vapor at 30oC. What is the system pressure and the composition of the

vapor.

Page 39: CHE-201: Introduction to Chemical Engineering

Newton Method:

It is used to find zero(s) of nonlinear equation(s) starting from (an) initial guess(es).

The problem is: find the value(s) of x making equals to zero starting from

Any function can be expanded by Taylor’s series into:

Eventually, the value of should reach to zero.

the correction formula for the guess is obtained after cancelling the higher order

terms as:

..........21 2

111 nnnnnnnn xfxxxfxxxfxf

xf

1nxf

1nx

1nx

nnnn xfxfxx /1

Page 40: CHE-201: Introduction to Chemical Engineering

Newton Method Procedure:

1. Start with an initial guess

2. Evaluate the values of the function and the first derivative

3. Calculate the new updated value of using:

4. Check the value of the function at the new value “ “

5. If the value is within a certain tolerance, stop

6. If not, keep on iterating.

ox

xf

xf

x

1x

ooo xfxfxx /1

Page 41: CHE-201: Introduction to Chemical Engineering

Example on Newton Method:

Example: Find the value of ?Answer: we need to solve:Let’s start with 2.5 as an initial guess. Then, the update formula can be expressed as:

5 052 xxf

nn

nn xxxx2

52

1

x f(x) f’(x)xo 2.5 1.25 5.00

x1 2.25 0.0625 4.500

x2 2.236111111 0.0001929012 4.4722222222

x3 2.2360679779 0.00000018

I will stop here as the value of the function is small enough to accept the value of x. The value of from the calculator is 2.2360679775. 5

Page 42: CHE-201: Introduction to Chemical Engineering

6.4c Vapor-Liquid Equilibrium Calculations for Ideal Solutions

It is very important to know conditions at which condensation or evaporation occurs.

Bubble-point temperature is the temperature at which the first bubble is formed at constant pressure. Liquid phase composition is given.

Dew-point temperature is the temperature at which the first droplet of liquid is formed at a given pressure. Gas phase composition is given.

Dew-point pressure is the pressure at which condensation occurs at constant temperature

n

i dpi

i

TpPy

1* 1

PTpxn

ibpii

1

*

Page 43: CHE-201: Introduction to Chemical Engineering

Example 6.4-3 Bubble- and Dew-Point Calculations

1. Calculate the temperature and composition of a vapor in equilibrium with a liquid that is

40.0 mole% benzene-60 mole% toluene at 1 atm. It the calculated temperature a bubble-

point or dew-point temperature?

2. Calculate the temperature and composition of a liquid in equilibrium with a gas mixture

containing 10.0 mole% benzene., 10.0 mole% toluene, and the balance nitrogen (which may

be considered noncondensable) at 1.0 atm. Is the calculated temperture a bubble-point or

dew-point temperature?

3. A gas mixture consisting of 15.0 mole% benzene, 10.0 mole% toluene, and 75.0 mole %

nitrogen is compressed isothermally at 80oC until condensation occurs. At what pressure

will condensation begin? What will be the composition of the initial condensate?

Page 44: CHE-201: Introduction to Chemical Engineering

Problem 4.74