4.3 Gas Liquid Separation - Integrated Approachjojoj

CHG 3111

Unit Operation

Chapter 10

Gas-Liquid Separation and Operations

4.3 Integrated Approach

CHG 3111/B. Kruczek 2

Design of Packed Towers Integrated Approach Absorption and Stripping

Thus far the height of the packed tower (Z) was estimated using:

where: N = the number of theoretical equilibrium contacts and HEPT = the height of the theoretical stage

Equilibrium Relationship

Mass Transfer

Operating Conditions


Mass Balance

Equilibrium Relationship N HEPT x

Z

In the integrated approach

Equilibrium Relationship

Mass Balance

Mass Transfer


Z For dilute solutions it will simplify to:


Absorption/Stripping in Packed Towers

moles of A leaving gas = moles of A entering liquid

Application of integrated approach for determination of Z:

Material balance on solute in a differential height (dz) of the tower:

or: A AG ALn d Vy d Lx

Both V and yAG as well as L and xAL change along the tower, but if liquid is not volatile and inert gas not soluble

in liquid, then:

1 1' constant and ' constantAG ALV V y L L x

Thus:

21 1 11

' ''AG AG AG AGA

AG AG AGAG

V y y V dy Vdyn d V d

y y yy

Similarly:

21 1 11

' ''AL AL AL ALA

AL AL ALAL

L x x L dx Ldxn d L d

x x xx



1

y

A A AG Ai

A iM

k an N dA y y Sdz

y

Application of integrated approach for determination of Z:

Combining mass balance with the rate equations:

Application of rate equation for a differential height (dz) of the tower:

where: dA aSdz

Tower Height

1

xA A Ai AL

A iM

k an N dA x x Sdz

x

or:

1 1

yAGAG Ai

AG A iM

k aVdyy y Sdz

y y

1 1

xALAi AL

AL A iM

k aLdxx x Sdz

x x

1

0 2 11

yZ

y y

i

iM

Vdydz Z

k aSy y y

y

yAG = y

Tower Height

1

0 2 11

xZ

x xi

iM

Ldxdz Z

k aSx x x

x

xAL = x


Absorption/Stripping in Packed Towers Application of integrated approach for determination of Z:

Dropping the subscripts, i.e. xAL = x and yAG = y

Integrated approach can be used with the overall mass transfer coefficients

1

0 2 11

*

'*

yZ

y y

M

Vdydz Z

K aSy y y

y

1

0 2 11

*

'*

xZ

x xi

M

Ldxdz Z

K aSx x x

x

x*A

y*A

Slope = m''

E

D

Slope = m'

1 1

1 1 1*y A y A x A iMM iM

m

K a y k a y k a x

AGA

AGA

MAyy

yyy

11ln

111

*

*

*

1 1 1

1 1 1*x A y A x AM iMiM

K a x m k a y k a x

*

*

*11ln

111

AAL

AAL

MAxx

xxx

where:

and

NB1: The integrated approach allows the design of the tower in the case when the mass transfer coefficients and the total flow of phases vary along the column, which occurs for the concentrated solution(s)

NB2: Evaluation of the height of tower requires graphical or numerical integration of derived equations


Absorption/Stripping in Packed Towers Simplifications for dilute solutions

Consider application of the integrated approach for the determination of Z based on ky

NB 1: The above analysis provides justification from the HEPT approach

1

2 11

y

G Gy y

i

iM

VdyZ H N

k aSy y y

y

1

2

1

1av

yiM

G Gyy i

y dyVZ H N

k aS y y y

where: is the arithmetic average at the top and the bottom of the tower

1

1av

iMG

y

yVH

k aS y

11 2

2

y

Gy i i M

dy y yN

y y y y

and :

Furthermore, for dilute solutions:

11 0

1.iM

y

y

av av

G

y y

V VH

k aS k aS

thus

NB 2: The above expression provides an alternative to graphical and analytical methods for the

estimation of theoretical equilibrium contacts

1 11 1 2 22 2

where: ln ii i iMi

y yy y y y y y

y y


Absorption/Stripping in Packed Towers Simplifications for dilute solutions

Summary of other expressions for height of the transfer towers for dilute solutions

Liquid-phase film coefficient

1

2 11

x

L Lx x

i

iM

LdxZ H N

k aSx x x

x

av av

L

x x

L LH

k aS k aS

1 2

L

i M

x xN

x x

where and

Gas-phase overall coefficient

1

2 11

*

'*

y

OG OGy y

M

VdyZ H N

K aSy y y

y

1 2

*OG

M

y yN

y y

where

av av'

OG

y y

V VH

K aS K aS

and

Liquid-phase overall coefficient

where

av av'

OL

x x

L LH

K aS K aS

and

1

2 11

*

'*

x

OL OLx x

M

LdxZ H N

K aSx x x

x

1 2

*OL

M

x xN

x x



A gas stream contains 4.0 mol % NH3 and its ammonia content is reduced to 0.5 mol % in

a packed absorption tower at 293 K and 1.013x105 Pa. The inlet pure water flow is 68.0 kg

mol/h and the total inlet gas flow is 57.8 kg mol/h. The tower diameter is 0.747 m. The film

mass-transfer coefficients are kya = 0.0739 kg mol/s m3 mol frac. and kxa = 0.169 kg mol/s

m3 mol frac.

(a) Calculate the tower height using kya

(b) Calculate the tower height using Kya

Use equilibrium data from Appendix A.3.

Example 5: Design of Packed Tower using Integrated Approach


Continuous

Humidification/Dehumidification General information

Parameter Absorption Humidification

Number of phases two liquid and gas two liquid and gas

Solute component soluble in both phases

water vapor and heat

Heat effects negligible purpose of the process

Contact of phases packed, tray, spray, bubble towers

packed and spray towers

Operation countercurrent, liquid on top countercurrent, liquid on top

Method: direct contact of dry (not necessarily) cold air and water

Purpose: cooling of hot water by water evaporation, and thus air humidification, but also removal of water vapor from moist cold air (dehumidification)

Comparison of absorption and humidification processes

CHG 3111/B. Kruczek

Continuous Humidification - Approach

10

Heat and Mass Transfer

Rate Equations Thermodynamics

(Equilibrium Relation)

Mass and Energy

Balances

Integrated Approach Complete Design

Height of Tower = Height of Transfer Unit x Number of Equilibrium Contacts

CHG 3111/B. Kruczek

Continuous Humidification

11

Rate Equations for Heat and Mass Transfer

Consider a single point close to the top of a humidification tower

Liquid phase:

Heat transfer: " L L iq q A h T T Mass transfer: there is no mass transfer in the liquid phase because liquid is pure water

Gas phase:

Mass transfer: A A c G B i GN M R k PM H H

Heat transfer: " G i G c o G i G G B i G oq q A h T T R h T T k PM H H

Combining on the basis of heat transfer: L L i G i G G B i G ih T T h T T k PM H H

Rc in terms of DH was derived in Chapter 9

Why we do not express Rc in terms of DT?

CHG 3111/B. Kruczek


12

Rate Equations for Heat and Mass Transfer

Consider a single point close to the bottom of a humidification tower

Question: What is the effect of humidification on air temperature?

At the bottom of the tower, liquid is already cooled down, but dry air is still at relatively

high temperature

Therefore, it is possible that close to the bottom of the tower TG > TL

Regardless of the relationship between TG and TL in humidification: TL > Ti = interface

temperature

Recall Humidity Chart:

Since TL > Ti , water loses heat, humidification is always associated with cooling of water

The net effect of humidification is cooling of air In adiabatic process, TG decreases along the

adiabatic saturation line.

TG1 TG2

NB: Humidification is a unique heat transfer process

in which temperature of both streams decrease

CHG 3111/B. Kruczek


13

Equilibrium Considerations

Conditions at the interface

Hyi and Hy are the total enthalpies of air at interface and bulk

Bulk air phase and bulk water phase are not in equilibrium, but at the interface the air and water are in equilibrium

The air is in equilibrium with water when for a given temperature the partial pressure of water in air (pA) equals to the vapor pressure of water (pAs).

yi iH f T

Criterion for the humidification: yi yH H

1 005 1 88 2501 4kJ kg dry air . . .y s oH c T H H T Recall from Chapter 9, that taking

reference temperature, To = 0oC:

0

100

200

300

400

500

15 25 35 45 55 65

Hy [

kJ/

kg

dry] a

ir]

Water Temperature, TL [oC]

Equilibrium Relationship:

Generation of equilibrium data:

NB: Evaluation of Hyi requires Hi = Hs = saturation humidity at Ti

1. Vapor pressure (pAs ) at given T from Steam Tables or:

20 386 5132mmHg exp . KASp T

2. Saturated humidity:

18 02

28 97

.

.AS

s

As

pH

P p

Dehumidification

Humidification

3 20 0035 0 2 7 2897 34 303o oAlternatively, for 15 C <

CHG 3111/B. Kruczek


14

Material and Energy Balances

Consider material and energy balances on the entire tower

2 1 1 2 and L L L G G G

Material balance mass of liquid water decrease due to evaporation, but the loss of liquid water is typically less than 1.5%, thus:

where cL = 4.187 J/kg K

Energy balance

2 1 1 2y y L L LG H H Lc T T

Operating line Energy balance on the bottom (top) part of the

tower:

1 1L L

y L y L

Lc LcH T H T

G G

1 1y y L L LG H H Lc T T

0

100

200

300

400

500

15 25 35 45 55 65

Hy [

kJ/

kg

dry] a

ir]


Intercept Slope

Top

Bottom

Where on the Hy-TL diagram would be the top of a dehumidification tower?

CHG 3111/B. Kruczek


15

Integrated Approach

Consider a differential element of tower of height dz Enthalpy balance: "y L LGdH Lc dT q

Focusing on the air-side of the interface: z

dz

At the same time, q can be expressed using heat balance at the interface:

" L L i G i G G B i G iq h a T T dz h a T T dz k aPM H H dz

NB: Since the contact area is unknown, hL, hG, and kG are replaced by hLa, hGa, and kGa

y G i G G B i G iGdH h a T T dz k aPM H H dz

Considering that, , the above equation becomes: G G sB y B G

h a h ac

M k a M Pk a

y B G s i i i s G G iGdH M k aPdz c T H c T H

Adding and subtracting csTG inside the brackets :

y B G s i o i o s G o G i B G yi yGdH M k aPdz c T T H c T T H M k aPdz H H

NB: Do not confuse Hy = enthalpy with H = humidity

CHG 3111/B. Kruczek


16

Integrated Approach Height of Tower

The combined material and energy and heat balances along with application of rate equations on dz of the tower lead to:

Integrating above equation leads to the final design equation:

z

dz

y B G yi yGdH M k aPdz H H

2

0 1

HyZy

G GHyB G yi y

dHGdz Z H N

M k aP H H

Connection between operating and equilibrium lines

40

80

120

160

200

15 20 25 30 35 40 45

Hy [

kJ/

kg

dry] a

ir]


Consider different ways of expressing GdHy

y L L iGdH h a T T dz

y B G yi yGdH M k aPdz H H

yi yL

B G i L

H Hh a

M k aP T T

(Ti, Hyi)

(TL, Hy)

slope = L

B G

h a

M k aP


Continuous Humidification Integrated Approach Overall Mass Transfer Coefficient

Design equation in terms of the overall mass transfer coefficient (KG) Analogy with the analysis of absorption/stripping processes

2

0 1*

HyZy

OG OGHyB G y y

dHGdz Z H N

M K aP H H

Where: H*y is the enthalpy air water vapor mixture

in contact with water at TL

Often only the overall coefficient KGa is known while hLa and kGa are not available,

but the resistance to heat transfer in the

liquid phase is negligible, i.e.:

large number, and P RL

B G

h a

M k aP

Design using HOG is limited to the cases when the equilibrium line is approximately

straight over the range used.

Question: What is the physical meaning of the triangle SMP ?


Continuous Humidification Operation Constrains

Minimum air flow For a given water flow, what is the minimum air flow to cool water from TL2 to TL1? Constrain: the operating line cannot cross the

equilibrium line. Why?

Line MN has the maximum possible slope.

max min

min max

slope =slope

L LLc LcGG

The actual air flow rate should be 1.3 1.5 Gmin

NB: because of the shape of the equilibrium line,

the operating line may touch the equilibrium

line below the top of the tower

The slopemax can also be determined analytically. How?

Dehumidification operations Questions: 1) How a dehumidification operation is represented on Hy-TL diagram?

2) What is the constrain corresponding to the minimum air flow in dehumidification?



A forced draft counter-current water cooling tower is to cool water from 43.3C to 26.7 C. the air enters the bottom of the tower at 29.3 C with a wet bulb temperature of 21.1C. The value of

HG for the flow conditions is HOG = 0.533 m. The heat transfer resistance in the liquid phase will

be neglected, that is hL is very large. Hence, values of H*y should be used.

Calculate the tower height needed if 1.5 times the minimum air rate is used.

Example 6: Design of Packed Cooling Tower

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4.3 Gas Liquid Separation - Integrated Approachjojoj

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