W11 W12 Multiphase Systems

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BKF2343 Chap 5 Multiphase System FKKSA, UMP

Multiphase Systems


Objectives

At the end of this chapter, the students will have:

! Ability to describe physical properties and laws that governthe behavior of two-phase systems.

! Ability to show that these laws must be included in theformulation of material balances on separation process units.

! Ability to describe the concept of phase rules.! Ability to predict physical properties for multi-component

systems, solutions of solids in liquids, and systemscontaining two immiscible or partially miscible liquids.


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Introduction

! Complete chemical plants normally will be comprised of twoimportant sections:

1. Chemical reaction, followed by2. Separation of chemical species

! Separation of chemical species can be done physically.! How to separate physically?

Through creating Multiphase Systems


Separation Processes

! Multiphase systems Mainly involved in separation process! Distillation !"vapor-liquid

!Driving force of separation : Vapor pressure

! Crystallization !"liquid solid! Driving force of separation : solubility

! Extraction !"liquid liquid! Driving force of separation : distribution co efficient.


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Single Component Phase EquilibriumPhase Diagram

A phase diagram of a pure substance is a plot of pressure vs

temperature that shows the conditions at which the substanceexists as solid, liquid and gas.


Phase Diagram

! Phase diagram shows that equilibrium not only existbetween liquid and gas phase, but also between the solidand liquid phases, and the solid and gas phases of asubstance.

! IfTand Pcorrespond to a point on the vapor-liquidequilibrium curve for a substance, Pis the vapor pressureof the substance at temperature T, and Tis the boilingpoint temperature of the substance at pressure P.

! The boiling point of a substance at P= 1 atm is the normalboiling point of that substance.


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Phase Diagram

! If (T, P) falls on the solid-vapor equilibrium curve, then Pisthe vapor pressure of the solid at temperature T, and T isthe sublimation point at pressure P.

! If (T, P) falls on the solid-liquid equilibrium curve, then Tisthe melting point or freezing point at pressure P.

! The point (T, P) at which solid, liquid and vapor phases canall coexist is called the triple point of the substance


Estimation of Vapor Pressure

! Volatility- degree a to which the species tends to transfer from theliquids 9or solid) state to the vapor state.

! Source of Vapor Pressure Data! Experimental Data from Literature

! Perrys Handbook! Journals ( J.Chem.Eng.Data, Fluid Phase Equilibria, )

! Equations and Coefficients : Antoine Equation,! Perrys Handbook! Data Books, Databases ,

! From Cox chart (Fig. 6.1-4)! Estimation from Clausius Clapeyron Equation


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Clausius-Clapeyron Equation

! Clausius-Clapeyron Equation is derived from Clapeyron Eqn by assumingthat the specific volume of liquid is negligible relative to that of vapor and

heat of vaporization is independent of temperature.

! According to this equation, a plot of ln p* vs 1/T should be a straight line,with slope !Hv/R and intercept B.

! If you know !Hv/R and p* at a single temperature To, you can solve theconstant in Clausius-Clapeyron Eqn. and thereafter use this equation toestimate p* at any temperature close to To.

! If you have p* vs T data, you can plot ln p* vs 1/T and determine !Hv/Rand B graphically or by method of least squares

Heat of Vaporization

Constant


Cox Chart and Antoine Equation

! Cox Chart is a straight line graph of logarithm of thevapor pressure plotted against a non uniform temperaturescale. (* Refer to textbook for a glimpse on Cox Chart)

! Antoine Equation is a relatively simple empirical equationthat correlates very well vapor pressure-temperature.

! A, B and C are Antoine constants (Table B.4) and havespecific values for each substances. Antoine Eqn. onlyapplicable in certain temperature limits.


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Gibbs Phase Rule

! Why Gibbs Phase Rule is important? So that we will be able to know thedegree of freedom for that particular system and hence the number of

intensive variables that can be specified independently for a system thatremains at phase equilibrium.

! Extensive variables: Depend on the size of system (e.g. mass andvolume)

! Intensive variables: Independent of size (e.g. T, P, y, x)! the number of degrees of freedom (the number of intensive variables such

as temp, pres, or mol frac that can be changed without disturbing the

number of phases in equilibrium)

! The number of intensive parameters that must be specified in order tocompletely determine the system

F = 2 + m -

! = the number of phases in a systemm = the number of chemical species presentF = the number of degrees of freedomFor a reactive system, if r independent reactions occuramong the system components and the reactions proceedto equilibrium, then the value of m in this equation mustbe reduced by r.


Gibbs Phase Rule- Example 6.2-1

1. Pure liquid water (F = 2) T & P2. A mixture of liquid, solid and vapor water (F = 0)- no

further information about the system may be specified,triple point at only one temperature and pressure

3. A vapor liquid mixture of acetone and methyl ethyl ketone(F = 2)- set T&P, then mole frac will be fixed; or set T &mole frac, then P will be fixed


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Gas Liquid System:One Condensable Component

! Processes involving gas-liquid systems!

Evaporation, drying, humidification! Condensation, dehumidification

! Example

! The gas in GLE is called noncondensable .! The gas phase is saturated with water

Gas (Water + Nitrogen)

Liquid (Water)


Gas Liquid System:One Condensable Component

! For this type of system which has water and gascomponents coexist in 2 phases, Gibbs Rule follows that

! Only two of three intensive variable, T, P and yH2O can bespecified arbitrarily and that some relationship must existthat uniquely determines the value of the third variableonce the first two have been fixed.

F = 2 + 2 -2 = 2


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Behavior of Gas Liquid System

! The behavior of gas-liquid systems can be described byfollowing the following Law:

! If a gas at temperature Tand pressure Pcontains asaturated vapor whose mole fraction is yv (moles vapor/mole total gas), and if this vapor is the only species thatwould condense if the temperature were slightly lowered,then the partial pressure of the vapor in the gas equals thepure component vapor pressure pv* (T) at the systemtemperature.


Behavior of Gas Liquid System

! A gas in equilibrium with a liquid must be saturated with thatliquid.

! The partial pressure of a vapor at equilibrium in a gas mixturecontaining a single condensable component cannot exceed thevapor pressure of the pure component at the system temperature.

Ifpv = pv*, the vapor is saturated; any attempt to increase pvmust instead lead to condensation (pi>p*(T))

! A vapor present in a gas in less than its saturation amount isreferred to as a superheated vapor.

! If a gas containing a single superheated vapor is cooled atconstant pressure, the temperature at which the vapor becomessaturated is referred to as the dew point of the gas.

! The difference between the temperature of a gas and its dewpoint is called the degrees of superheat of the gas.


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Example 6.3-1

Air and liquid water are contained at equilibrium in a closed

chamber at 75C and 760mmHg. Calculate the molarcomposition of the gas phase


Example 6.3-2

A stream of air at 100C and 5260mmHg contains 10% water by

volume.

1. Calculate the dew point and degrees of superheat of the air2. Calculate the percentage of the vapor that condenses and the

final composition of the gas phase if the air is cooled to80C atconstant pressure

3. Calculate the percentage condensation and the final gas phasecomposition if instead of being cooled, the air is compressed

isothermally to 8500 mmHg.


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Terminology for GLE System

! Saturation refers to any gas-vapor combination.!

Humidity refers specifically to an air-water system! Relative Saturation (Relative Humidity):

! Molal Saturation (Molal Humidity):


Terminology for GLE System

! Absolute Saturation (Absolute Humidity):

! Percentage saturation (Percentage Humidity):


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Example 6.3-3

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

process unit at rate of 1000 m3/h. Determine

1. Molar flow rate of water, dry air and oxygen entering theprocess unit

2. The molal humidity, absolute humidity and percentagehumidity of air

3. The dew point


Multicomponent Gas-Liquid Systems

! There are several ways to evaluate equilibriumcompositions for multicomponent gas-liquid systems:

! From tabulated VLE data! Raoults Law and Henrys Law! VLE calculation assuming ideal solution! Graphical Representations of VLE! Rigorous VLE calculation using model equations


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Example 6.4-1

A gas stream consisting of 100 lbmole/h of an SO2-air mixture

containing 45mole% SO2 in contacted with liquid water in acontinuous absorber at 30C. The liquid leaving the absorberanalyzed and found to contain 2 g of SO2 per 100g of H2O.Assuming that the gas and liquid streams leaving the absorber in

equilibrium at 30C and 1 atm, calculate the fraction of the

entering SO2 absorbed in the water and the required water feedrate.

From Perrys Handbook, the partial pressure of SO2 and H2O at 45

mole% SO2 are:pH2O = 31.6 mmHg

pSO2 = 176n mmHg


Raoults Law and Henrys Law

! Raoults Law is an approximation that is generally valid when xAis close to 1 that is when the liquid phase is almost pure A.Sometimes, it is valid over the entire range of compositions formixtures of similar substances, such as straight-chainhydrocarbons of similar molecular weights.

! Henrys Law is valid for solutions in which xA is close to 0 (dilutesolutions of A) provided that A does not dissociate, ionize, or reactin the liquid phase. The law is often applied to solutions of non-condensable gases.

pA = yAP = xA p*A(T)

pA is partial pressure of A in gas phase

xA is the mole fraction of A in liquid phaseyA is the mole fraction of A in gas phase

pA = yAP = xA HA(T)HA(T) is the Henrys Law constant

for A in specific solvent. Look upfrom Tables.


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Example 6.4-2

Use either Raoults law or Henry law to solve the following problems

1.A gas containing 1 mole% ethane is in contact with water at20C and 20 atm. Estimate the mole fraction of dissolvedethane.

2. An equimolar liquid mixture benzene and toluene is inequilibrium with vapor at 30C. What is the system pressureand composition of vapor?


VLE Equilibrium Calculations for Ideal Solution

! Consider a multi-component mixture in liquid phase with differentboiling points.

! As heat being applied, a temperature is reached at which the firstbubble of vapor forms. The composition of vapor generated, yA will

generally have a composition different from that of the liquidmixture, xA.

! As vaporization proceeds, therefore, the composition of remainingliquid mixture continuously changes as a result of differentvolatility, and hence so does its vaporization temperature.

! A similar phenomenon occurs if a mixture of vapors is subjectedto a condensation process at constant pressure. At some

temperature the first droplet of liquid forms, and thereafter thecomposition of the vapor and the condensation temperature both

changes.


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! The temperature at which the first bubble of vapor forms when aliquid is heated slowly at constant pressure is the bubble point ofthe liquid at the given pressure.

! If a gas-vapor mixture is slowly cooled at constant pressure, thetemperature at which the first droplet of liquid forms is the dewpoint of the gas at the given pressure.

How to calculate bubble point and dew point for a mixture?

! If the liquid phase mixture behaves as an ideal solution, we canemploy Raoults Law and Henrys Law

pi = xip*i (Tbp)

P= #xip*i (Tbp)

i = A, B, ..P= Total pressureEqn. 6.13

Eqn. 6.12


Bubble Point and Dew Point Calculation

! Bubble Point temperaturecalculation

! Given P,x " calculate T,y

! Dew point temperaturecalculation

! Given P,y" calculate T,x

VLE Calculation

! Bubble T : P,x " T,y! Bubble P : T,x " P,y! Dew T : P,y " T,x! Dew P : T,y " P,x


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BUBBLE POINT CALCULATION: GivenP & xi

Evaluate vapor pressure for each speciesusing Antoine Eqn

Choose a temperature

Compare this calc P with

actual P given in statement

Calc partial pressure and

calculate the overall P system

Contradict

COMPLY! Proceed to calculate yi= pi/P

HINT:Toch

ooseaBASETEMPERATURE,

youcancheckthemaincomponentinthemixture

andusethe

boilingpointofthatcomponen

t


Evaluate vapor pressure for each species

using Antoine Eqn

Choose a temperature

#xi = 1 ???

Subs intoxi = yiP/pi*(Tdp)

Contradict

DEW POINT CALCULATION: GIVENP & yi

COMPLY! xi=yiP/pi*(Tdp)


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Example 6.4-3

1. Calculate the temperature and composition of a vapor inequilibrium with a liquid that is 40 mole% benzene-60 mole%toluene at 1 atm. Is the calculated temperature a bubble point ordew point temperature?

2. Calculate the temperature and composition of liquid in equilibriumwith a gas mixture containing 10 mole% benzene, 10 mole%

toluene and balance nitrogen (which may be considerednoncondensable) at 1 atm. Is the calculated temperature a bubble

point or dew point temperature?

3. A gas mixture consisting of 15 mole% benzene, 10 mole% tolueneand 75 mole% nitrogen is compressed isothermally at 80C untill

condensation occurs. At what pressure will condensation begin?

What will be the composition of the initial condensate?


Immiscible and Partially Miscible Liquids

! A mixture of two different solution is termed miscible if asingle phase results from the mixing at all concentrations.

! A system is partially miscible if the two different liquidsform a single phase at certain composition and form two

liquid phases at other concentrations.! A system is immiscible if it forms two liquid phases even

at lean concentration of other component.

! If a third substance is added to a two-phase liquid mixture,it distributes itself according to its relative solubility in eachphase.

! What is distribution coefficient?! Liquid extraction is a common chemical separation

process employed in industry that is based on miscibilityconcept.


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Immiscible and Partially Miscible Liquids

Water Rich Phase

MIKB Rich Phase

Acetone

Distribution Coefficient

Partially miscible liquidsImmiscible SystemLiquid-Liquid Extraction


Ternary Diagram

! A system which contains 3 components with differentsolubility affinity is termed as Ternary System.

! In a system composed ofA and S that are nearlyimmiscible liquids, and B is a solute distributed between the

phases of anA-S mixture, the distribution coefficient forcomponent B is the ratio of the mass fraction ofB in the Sphase to that in theA phase.

! The behavior of this partially miscible ternary systemsystems is frequently represented on a Triangular PhaseDiagram (TPD).

! Lever rule is needed to perform mass balance calculationbased on this TPD.


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Ternary Diagram



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Example 6.6-2

1000 kg of a 30 wt% solution of acetone in water and a second

stream of pure methyl isobutyl ketone (MIBK) id fed to a mixer.The mixture is then fed to a settler where two phases form andare withdrawn separately at 25C. How much MIBK must be fed tothe process to reduce the acetone concentration in the water-rich

phase to 5 wt%, assuming that the fluids remain in the settler

long enough for equilibrium to be achieved?


AnyQuestion??

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W11 W12 Multiphase Systems