CHEN 4470 – Process Design Practice

Dr. Mario Richard EdenDepartment of Chemical Engineering

Auburn University

Lecture No. 7 – Overview of Mass Exchange Operations

January 31, 2013

Mass Integration

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 Exchanger– A mass exchanger is any direct-contact mass-

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

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

• Generalized Description– The composition of the rich stream (yi) is a

function of the composition of the lean phase (xj)

• Dilute Systems– For some applications the equilibrium functions

may be linearized over the operating range

Equilibrium 1:4

* *( )i j jy f x

*i j j jy m x b

• Special Cases– Raoult’s law for absorption

– Henry’s law for stripping

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 Cases– Distribution function used in solvent extraction

• Interphase Mass Transfer– For linear equilibrium the pollutant composition

in the lean phase in equilibrium with yi can be calculated as:

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)– For linear equilibrium the pollutant composition

in the rich phase in equilibrium with xj can be calculated as:

• Rate of Mass Transfer

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 Contactors– Multistage 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 Mixer-Settler System

Mass Exchangers – I 2:2

MSA out

Waste in MSA

in

Waste out

• Stagewise Columns– A generic mass exchanger

– Schematic 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)– Operating line (material balance)

– The 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)– The Kremser equation

• Isothermal• Dilute• Linear equilibrium

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)– Other forms of the Kremser equation

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)– Number of actual plates

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

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) Contactors– Countercurrent 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 (Continued)

– Spray column

Mass Exchangers – II 2:3

Light Phase Out

Heavy Phase In

Light Phase In

Heavy Phase Out

Shell

• Differential (Continuous) Contactors (Continued)

– Mechanically agitated mass exchanger

Mass Exchangers – II 3:3

Light Phase Out

Heavy Phase In

Light Phase In

Heavy Phase Out

Shell

Mixer

• Continuous Mass Exchangers– Height of a differential contactor

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 jout 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?– Fixed cost: The car itself, i.e. body, engine,

tires, etc.

Crash Course in Economics 1:5

$500 $21,000

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

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)– Annualized Fixed Cost (AFC)

– Total Annualized Cost (TAC)

Crash Course in Economics 3:5

Initial Fixed Cost Salvage or Resale ValueAFC

Useful Life Period

T AC Annualized Fixed C ost Annual O perating C ost

• 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)

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 System

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

heating/cooling, etc.

• Driving Force– Minimum allowable composition

difference– Must stay to the left of

equilibrium 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)– Minimum allowable composition difference at

rich 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 (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,

OPTIMUM

Trade-off between reducing fixed cost

and increasing operating cost

Composition driving force, becomes a

optimization variable

• Next Lecture – February 5– Synthesis of mass exchange networks part I– SSLW pp. 297-308

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