An Overview of Mass Exchange An Overview of Mass Exchange OperationsOperations

Dr. Mario Richard EdenDr. Mario Richard EdenDepartment of Chemical EngineeringDepartment of Chemical Engineering

Auburn UniversityAuburn University

Lecture No. 2Lecture No. 2

August 30, 2004August 30, 2004

CHEN 4460

What is a Mass Exchanger?

Mass Exchanger

Outlet Composition: yi

out

Lean Stream (MSA) Flowrate:Lj Inlet Composition: xj

in

Outlet Composition: xj

out

Rich (Waste) StreamFlowrate:Gi Inlet Composition: yi

in

• Mass ExchangerMass Exchanger– A mass exchanger is any direct-contact mass-A mass exchanger is any direct-contact mass-

transfer unit which employs a transfer unit which employs a Mass Separating Mass Separating AgentAgent (or a lean phase) to selectively remove (or a lean phase) to selectively remove certain components (e.g. pollutants) from a rich certain components (e.g. pollutants) from a rich phase (e.g. a waste stream). phase (e.g. a waste stream).

– Absorption, Adsorption, Extraction, Ion Absorption, Adsorption, Extraction, Ion Exchange, ….Exchange, ….

• Generalized DescriptionGeneralized Description– The composition of the rich stream (yThe composition of the rich stream (yii) is a ) is a

function of the composition of the lean phase (xfunction of the composition of the lean phase (xjj))

(2.1)(2.1)

• Dilute SystemsDilute Systems– For some applications the equilibrium functions For some applications the equilibrium functions

may be linearized over the operating rangemay be linearized over the operating range

(2.2)(2.2)

Equilibrium 1:4

* *( )i j jy f x

*i j j jy m x b

• Special CasesSpecial Cases– Raoult’s law for absorptionRaoult’s law for absorption

(2.3)(2.3)

– Henry’s law for strippingHenry’s law for stripping

(2.4)(2.4)

(2.5)(2.5)

Equilibrium 2:4

0*( )solute

i jTotal

p Ty x

P

*i j jy H x

• Mole fraction of solute in gas

• Vapor pressure of solute at T

• Mole fraction of solute in liquid

• Total pressure of gas

solubility0

( )( )

Totalj i

solute

PH y T

p T

• Mole fraction of solute in gas

• Mole fraction of solute in liquid

• Henry’s coefficient

• Liquid-phase solubility of the pollutant at temperature T

• Special CasesSpecial Cases– Distribution function used in solvent extractionDistribution function used in solvent extraction

(2.6)(2.6)

• Interphase Mass TransferInterphase Mass Transfer– For linear equilibrium the pollutant composition For linear equilibrium the pollutant composition

in the lean phase in equilibrium with yin the lean phase in equilibrium with yii can be can be calculated as:calculated as:

(2.7)(2.7)

Equilibrium 3:4

*i j jy K x

• Solute composition in liquid

• Solute composition in solvent

• Distribution coefficient

* i jj

j

y bx

m

• Interphase Mass Transfer (Continued)Interphase Mass Transfer (Continued)– For linear equilibrium the pollutant composition For linear equilibrium the pollutant composition

in the rich phase in equilibrium with xin the rich phase in equilibrium with x jj can be can be calculated as:calculated as:

(2.8)(2.8)

• Rate of Mass TransferRate of Mass Transfer

(2.9)(2.9)

Equilibrium 4:4

*i j j jy m x b

*

pollutant *

y i i

x j j

K y yN

K x x

• Overall mass transfer coefficient for rich phase

• Overall mass transfer coefficient for lean phase

Correlations for estimating overall mass transfer coefficients can be found in McCabe et al. (1993), Perry and Green (1984), King (1980) and Treybal (1980).

• Multistage ContactorsMultistage Contactors– Multistage countercurrent tray columnMultistage countercurrent tray column

Mass Exchangers – I 1:2

Light Phase Out

Heavy Phase In

Light Phase In

Heavy Phase Out

Shell

PerforatedPlate (Tray)

Weir

Downcomer

• Multistage Contactors (Continued)Multistage Contactors (Continued)– Multistage Mixer-Settler SystemMultistage Mixer-Settler System

Mass Exchangers – I 2:2

MSA out

Waste in MSA

in

Waste out

• Stagewise ColumnsStagewise Columns– A generic mass exchangerA generic mass exchanger

– Schematic of a multistage mass exchangerSchematic of a multistage mass exchanger

Modeling – I 1:5

Mass Exchanger

Outlet Composition: yi

out

Lean Stream (MSA) Flowrate:Lj Inlet Composition: xj

in

Outlet Composition: xj

out

Rich (Waste) StreamFlowrate:Gi Inlet Composition: yi

in

1 2 n N-1 N

yi,1=yiout

xj,0=xjin xj,1

xj,2

yi,2 yi,3 yi,n

xj,n.1xj,n

yi,n+1 yi,N-1 yi,N

xj,N-2xj,N-1 xj,N=xj

out

yi,N+1=yiin

• Stagewise Columns (Continued)Stagewise Columns (Continued)– Operating line (material balanceOperating line (material balance

(2.10)(2.10)

– The McCabe-Thiele diagramThe McCabe-Thiele diagram

Modeling – I 2:5

yout xin

yin xout

L

G

in out out ini i i j j jG y y L x x

yiin

yiout

xjin xj

out

xj

yi

Operating Line

Equilibrium Line

Lj/Gi

• Stagewise Columns (Continued)Stagewise Columns (Continued)– The Kremser equationThe Kremser equation

• IsothermalIsothermal• DiluteDilute• Linear equilibriumLinear equilibrium

(2.11)(2.11)

Modeling – I 3:5

ln 1

ln

in inj i i j j j j i

out inj i j j j j

j

j i

m G y m x b m G

L y m x b LNTP

L

m G

• Stagewise Columns (Continued)Stagewise Columns (Continued)– Other forms of the Kremser equationOther forms of the Kremser equation

(2.12)(2.12)

(2.13)(2.13)

(2.14)(2.14)

Modeling – I 4:5

,*

,*ln 1

ln

in outj i j i

out outj i j j j i

j i

j

L x x L

m G x x m GNTP

m G

L

,*ini jout

jj

y bx

m

NTPin outi j j j j

out ini j j j j i

y m x b L

y m x b m G

• Stagewise Columns (Continued)Stagewise Columns (Continued)– Number of actual platesNumber of actual plates

(2.15)(2.15)

– Stage efficiency can be based on either the rich Stage efficiency can be based on either the rich or the lean phase. If based on the rich phase, the or the lean phase. If based on the rich phase, the Kremser equation can be rewritten as:Kremser equation can be rewritten as:

(2.16)(2.16)

Modeling – I 5:5

o

NTPNAP

ln 1

ln 1 1

in inj i i j j j j i

out inj i j j j j

j iy

j

m G y m x b m G

L y m x b LNTP

m G

L

• Differential (Continuous) ContactorsDifferential (Continuous) Contactors– Countercurrent packed columnCountercurrent packed column

Mass Exchangers – II 1:3

Light Phase in

Heavy Phase In

Packing Restrainer

Random Packing

Heavy-Phase Re-Distributor

Heavy Phase Out

Packing Support

Shell

Light Phase Out

Random Packing

• Differential (Continuous) Contactors Differential (Continuous) Contactors (Continued)(Continued)

– Spray columnSpray column

Mass Exchangers – II 2:3

Light Phase Out

Heavy Phase In

Light Phase In

Heavy Phase Out

Shell

• Differential (Continuous) Contactors Differential (Continuous) Contactors (Continued)(Continued)

– Mechanically agitated mass exchangerMechanically agitated mass exchanger

Mass Exchangers – II 3:3

Light Phase Out

Heavy Phase In

Light Phase In

Heavy Phase Out

Shell

Mixer

• Continuous Mass ExchangersContinuous Mass Exchangers– Height of a differential contactorHeight of a differential contactor

(2.17a)(2.17a) (2.17b) (2.17b)

(2.18a)(2.18a)

(2.18b)(2.18b)

Modeling – II

y yH HTU NTU x xH HTU NTU

*log( )

in outi i

yi i mean

y yNTU

y y

*

log

ln

in out out ini j j j i j j j

i i in outmeani j j j

out ini j j j

y m x b y m x by y

y m x b

y m x b

• Which Car is Cheaper?Which Car is Cheaper?– Fixed cost:Fixed cost: The car itself, i.e. body, engine, The car itself, i.e. body, engine,

tires, etc.tires, etc.

Crash Course in Economics 1:5

$500 $21,000

• Which Car is Cheaper? (Continued)Which Car is Cheaper? (Continued)– Annual Operating Cost (AOC): Annual Operating Cost (AOC): How much to How much to

run and maintain the car.run and maintain the car.

Crash Course in Economics 2:5

$4,000/year $700/year

$ vs. $/year ???

We need to annualize the fixed

cost of the car

• Which Car is Cheaper? (Continued)Which Car is Cheaper? (Continued)– Annualized Fixed Cost (AFC)Annualized Fixed Cost (AFC)

– Total Annualized Cost (TAC)Total Annualized Cost (TAC)

Crash Course in Economics 3:5

Initial Fixed Cost Salvage or Resale ValueAFC

Useful Life Period

TAC Annualized Fixed Cost Annual Operating Cost

• Which Car is Cheaper? (Continued)Which Car is Cheaper? (Continued)

Crash Course in Economics 4:5

Useful Life: 2 Years

Salvage Value: $200

AFC = ($500-$200)/2 yr = $150/yr

Useful Life: 20 Years

Salvage Value: $1000

AFC = ($21,000-$1,000)/20 yr = $1000/yr

• Which Car is Cheaper? (Continued)Which Car is Cheaper? (Continued)

Crash Course in Economics 5:5

TAC = $4,000 + $250 =

$4,250/yr

TAC = $1,000 +$700 =

$1,700/yr

• Total Annualized Cost of Mass Exchange Total Annualized Cost of Mass Exchange SystemSystem

– Fixed cost: Trays, shell, packing, etc.Fixed cost: Trays, shell, packing, etc.– Operating cost: solvent makeup, pumping, Operating cost: solvent makeup, pumping,

heating/cooling, etc.heating/cooling, etc.

(2.21)(2.21)

• Driving ForceDriving Force– Minimum allowable compositionMinimum allowable composition

differencedifference– Must stay to the left ofMust stay to the left of

equilibrium lineequilibrium line

Minimizing Cost of MENs 1:3

TAC AOC AFC

xj

EquilibriumLine

y

j

j

Practical Feasibility Region

Practical Feasibility Line

x*j = (y - bj )/mj

• Driving Force (Continued)Driving Force (Continued)– Minimum allowable composition difference at Minimum allowable composition difference at

rich end of mass exchangerrich end of mass exchanger

Minimizing Cost of MENs 2:3

Fig. 2.9. Minimum Allowable Composition Difference at the Rich End of a Mass Exchanger

xjout, max xj

out, *xjin

yiout

yiin

Operating Line

EquilibriumLine

xj

yi

j

When the minimum allowable composition difference εj increases,

then the ratio of L/G increases.

AOC increases, due to higher MSA flow

AFC decreases, due to smaller equipment, e.g.

fewer stages

• Driving Force Driving Force (Continued)(Continued)

Minimizing Cost of MENs 3:3

0.0020 0.0030 0.0040 0.0050

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

Fig2.13. Using Minimum Allowable Composition Difference to

Trade Off Fixed Versus Operating Costs

0.0000 0.0010

$/ye

ar

TAC

Annual Operating Cost

Annualized Fixed Cost

Minimum Allowable Composition Difference,

Trade-off between reducing fixed cost and

increasing operating cost

Composition driving force, becomes a

optimization variable

OPTIMUM

• General CommentsGeneral Comments– Explain the problem and the solution steps Explain the problem and the solution steps

taken.taken.

– Explain your train of thought.Explain your train of thought.

– Don’t present values at the beginning that you Don’t present values at the beginning that you don’t calculate until later.don’t calculate until later.

– If you don’t write out the general form of an If you don’t write out the general form of an equation at least give a reference to which equation at least give a reference to which equation you are using.equation you are using.

Homework 1:5

• General Comments (Continued)General Comments (Continued)– Every value used, which is not given by the Every value used, which is not given by the

problem statement must be explained either by problem statement must be explained either by text or a calculation.text or a calculation.

– All values must be used with the corresponding All values must be used with the corresponding units in all calculations. This is also an additional units in all calculations. This is also an additional check for you.check for you.

– Always use the general equations. If you use an Always use the general equations. If you use an equation from an example in the book make sure equation from an example in the book make sure that it can be reused in the problem you’re that it can be reused in the problem you’re solving.solving.

– Don’t try to put 100 calculations on 1 page! Don’t try to put 100 calculations on 1 page! Make it easy to read and get the overview.Make it easy to read and get the overview.

Homework 2:5

• General Comments (Continued)General Comments (Continued)– Take the time to write up the answers nicely. It Take the time to write up the answers nicely. It

gives a bad impression if there are a lot of gives a bad impression if there are a lot of smudges and/or early calculations, which are smudges and/or early calculations, which are now crossed out.now crossed out.

– Check your results yourself when possible. If you Check your results yourself when possible. If you calculate a value by hand and subsequently you calculate a value by hand and subsequently you have to redo the calculations for a series of have to redo the calculations for a series of variables, check that your spreadsheet or solver variables, check that your spreadsheet or solver yields the same result as your initial calculation.yields the same result as your initial calculation.

– When presenting a graph, give some thought to When presenting a graph, give some thought to what the purpose of the graph is, i.e. what what the purpose of the graph is, i.e. what information is the reader supposed to obtain information is the reader supposed to obtain from this. from this.

Homework 3:5

• General Comments (Continued)General Comments (Continued)– Don’t plot series of data with different orders of Don’t plot series of data with different orders of

magnitude in the same diagram. Use a second y-magnitude in the same diagram. Use a second y-axis or plot the data sets separately.axis or plot the data sets separately.

– Use a consistent number of significant figures.Use a consistent number of significant figures.

– Avoid rounding off intermediate results.Avoid rounding off intermediate results.

Homework 4:5

• Problems 2.1, 2.2 and 2.5Problems 2.1, 2.2 and 2.5– Turn in at lecture on Monday September 13Turn in at lecture on Monday September 13

– Problem statements are handed out as Problem statements are handed out as photocopiesphotocopies

– A rough version of Chapter 2 of Dr. El-Halwagi’s A rough version of Chapter 2 of Dr. El-Halwagi’s book is placed on course webpage as a PDF file book is placed on course webpage as a PDF file in case they have not yet arrived at the in case they have not yet arrived at the bookstorebookstore

Homework 5:5

• Textile 228 and 230Textile 228 and 230– Computer systems are up and runningComputer systems are up and running– Networked with access to internet and H-driveNetworked with access to internet and H-drive– When starting Aspen, create a working folder on When starting Aspen, create a working folder on

your H-driveyour H-drive– Aspen lab notes available at Engineering Aspen lab notes available at Engineering

Duplicating Services in Ramsay HallDuplicating Services in Ramsay Hall– Labs start this weekLabs start this week– Although no lecture, there will be labs next weekAlthough no lecture, there will be labs next week– Check with Ahmed for schedule if you haven’t Check with Ahmed for schedule if you haven’t

yetyet

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