Modeling Mass Transfer Performance of Packings

Di Song

Gary Rochelle & Frank Seibert

University of Texas at Austin

Contents

Introduction

Model of ae

Model of kL

Model of kG

Conclusions

2

• Mass transfer & Packings

• Why is µL important

• Methods & SRP database

• Scale-up: secondary area

• Effect of µL

• Scale up: packing height

• Effect of µL

• Significance of this work

• Recommendations

Introduction

3

Two-film theory 4

CO2

Bulk liquidLiquid filmGas filmBulk gas

PCO2

PiCO2

[CO2]i

[CO2] or P*CO2

Liquid-phase resistance = HA/EkL

Rxn. film

Gas-phase resistance = 1/kg

Overall resistance = 1/Kg = 1/kg + HA/EkL = 1/kg + 1/kg’

NCO2 = Kg · ae · ΔPCO2

Both K (kL & kG) and ae is important to predict capture rate

Packings5

Random Structured Hybrid

Since 1890s 1960s >2000

Cost Low High High

Efficiency Moderate High High

Capacity Moderate High Medium

Shape

Mass transfer in amine

capture process

6

Flue Gas

DCC (kGae)

Absorber(kL & ae)

WW(kGae)

Stripper (kLae)

C Free Gas

CO2 for Compr.

Amine

Reliable packing model is critical for design

μL is critical to solvent selection

Heat transfer

• h Q

Mass transfer

• Diffusion of CO2 through reactive layer

• Diffusion of free amine to L-G interface (surface depletion)

• Diffusion of loaded amine back to bulk liquid (P*CO2)

• Liquid turbulence

7

µSolvent ≫ µH2O

8

Amine soln.(α = 0.4)

H2O 7m MEA 11m MEA 5m PZ 8m PZ

μ @ 40 C̊(cP)

0.65 2.4 4.0 3.6 11.4

Water lean solvent.

Alkylcarbonates: IPADM-BOL

Switchable Carbamates:

TESA

Aminosilicones: GAP-0/TEG

Nonaqueous organic amine blends: AMP/PZ + EGME + 15 wt % H2O

μ @ 40 ̊C(cP)

~ 130 cP ~800 cP ~1300 cP ~30 cP

μL affects kL in two ways (how much?)9

α – Direct influence via the turbulence of liquid

βγ – Indirect influence via D of mass transfer species

kL = C1· μα·Dβ

D = C2· μγkL (kLa) = C3· μα+βγ

μL affects ae?

Pilot packed column10

Blower180-450 ACFM

Storage Tank250 gal

Pump 2.5-30 gpm/ft2

Liquid Outlet

Liquid Inlet

Bypass

Air Inlet

Air Outlet

H: 25 ft

Zmax: 10 ft

I.D.: 16.8 in

F40 DistributorTrutna Collector

Chemical systems11

kG: Trace SO2/NaOH/H2O

kL: Air/Toluene/H2O

ae: Ambient CO2/NaOH/H2O

Kinetic model based on WWC exp.

+ glycerol

+ glycerol (1–70 cP)

SRP database12

21 Structured Packings

MellaPak®, Montz-Pak®, GT-Pak®, Flexipac®, etc

12 Random Packings

Pall Ring, IMTP®, Raschig-SuperRing®, etc

4 Hybrid Packings

Raschig-SuperPak®, Hiflow Plus®

1 Gauze Packing

ae model

13

Effective mass transfer area: ae14

0

100

200

300

400

500

0 100 200 300 400 500

ae,

tota

l(m

2/m

3)

aP (m2/m3)

Plastic

Fractional area Φ = 1

M 252Y

M 250YS

Gauze

Structured Y

Structured X/Z

Random

Hybrid

Secondary ae

15

aWall

aTop

Gas

Liquid

5 in.

10 ft.

6 ft.

aBot

aSecondary = aTop + aWall + aBot

aTotal = ae,packing + aSecondary

Sec. ae is critical to scaling up16

0%

5%

10%

15%

20%

5 10 20 40 80 160

Rat

io t

o t

ota

l are

a

DColumn (in)

Wall area

Bottom area

Top area

Avg. value @ G = 300 ACFM, L = 10, 15, 20 gpm/ft2

M 250Y (10 ft)

M 250Y

ae Model17

𝑎𝑒,𝑝𝑎𝑐𝑘𝑖𝑛𝑔

𝑎𝑃= 1.16 ∙ 𝜂 ∙ 𝑊𝑒 ∙ 𝐹𝑟−

1

2

0.138

= 1.16 ∙ 𝜂𝑡𝑦𝑝𝑒 ∙ 𝜂𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 ∙ 𝜂𝑙𝑜𝑎𝑑𝑖𝑛𝑔 ∙𝜌𝐿𝜎

∙ 𝑔 Τ1 2 ∙ 𝑢𝐿 ∙ 𝑎𝑃Τ−3 2

0.138

∙ 𝜇𝐿0

Random/hybrid:

𝜂𝑡𝑦𝑝𝑒 = 1.34 − 0.26𝑎𝑃250

Plastic:

𝜂𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 = 0.62

Loading zone (ΔP ≥ 400 Pa/m):

𝜂𝑙𝑜𝑎𝑑𝑖𝑛𝑔 = 1.15

ae Model18

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

50 100 150 200 250 300 350 400

Cal

cula

ted

/me

asu

red

ae,

tota

l

Measured ae,total (m2/m3)

-20%

+20%

σ~72 mN/m, µ~1 cP

G = 300 ACFM

AAD = 8.9%

ae model w/ viscosity 19

-20%

-10%

0%

10%

20%

0.5 2 8 32

Rel

ativ

e er

ror

µL (cp)

Avg. value @ G = 300 ACFM, L = 10, 15, 20 gpm/ft2

PEG (Tsai)

Glycerol

kL model

20

Liquid film mass transfer coefficient: kL21

1

2

3

4

5

0 100 200 300 400 500

avg.

k L·µ

0.4

/D0

.5

aP (m2/m3)

Avg. value @ G = 300 ACFM, L = 10, 15, 20 gpm/ft2

Structured Y

Structured X/Z

Random

Hybrid

GTP 350 Y/Z

M 250 X/Y

Scaling packing height (kL)22

0

1

2

3

4

5

0 1 2 3 4 5

k L·µ

L0.4

/D0

.5(6

ft

pac

kin

g)

kL·µL0.4/D0.5 (10 ft packing)

6-10 ft Ratio

Structured 1.29

Hybrid 1.39

Random 1.54

Overall 1.32

Maldistribution is

worse for taller bed

Correction = ln Τ1.32 1

ln Τ6 10= −0.54

kL Model

23

𝑆ℎ𝐿 = 0.12 ∙ 𝑆𝑐𝐿0.5 ∙ 𝑅𝑒𝐿

0.565 ∙ 𝐺𝑎𝐿Τ1 6 ∙

𝑍

1.8

−0.54

𝑘𝐿 = 0.12 ∙ 𝑢𝐿0.565 ∙

𝜇𝐿𝜌𝐿

−0.4

∙ 𝐷𝐿0.5 ∙ 𝑔 Τ1 6 ∙ 𝑎𝑃

−0.065 ∙𝑍

1.8

−0.54

Dependence on µL of kL24

1.E-06

1.E-05

1.E-04

0.5 5 50

k L·a

P0

.06

5/(

uL0

.56

5 ·g

1/6

·ρL0

.4)

µL (cP)

Hybrid

Structured

Random

-0.75 predicted in model

G = 300 ACFM

Direct = -0.40

Indirect = -0.35

Universally applicable

System-specific based on D-µ relationship

Comparison to other work: µL25

-100%

0%

100%

200%

300%

400%

500%

0.5 1 2 4 8 16 32 64

Rel

ativ

e er

ror

= (k

Lam

od

el-k

Laex

p)/

k Laex

p

µL (cP)

This work

Billet

Rocha

DelftValenz

M 250Y

kG model

26

Gas film mass transfer coefficient: kG27

0

4

8

12

0 100 200 300 400 500

avg.

k G/D

0.5

aP (m2/m3)

Avg. value @ L = 15 gpm/ft2, G = 180, 300, 450 ACFM

Structured Y

Structured X/Z

Random

Hybrid

GTP 350 Y/Z

M 250 X/Y

Model of kG

28

𝑆ℎ𝐺 = 0.28 ∙ 𝑆𝑐𝐺0.5 ∙ 𝑅𝑒𝐺

0.62 ∙sin 2𝛼

sin 2 × 45°

0.65

𝑘𝐺 = 0.28 ∙ 𝑢𝐺0.62 ∙

𝜇𝐺𝜌𝐺

−0.12

∙ 𝐷𝐺0.5 ∙ 𝑎𝑃

0.38 ∙ sin 2𝛼 0.65

aeffective = 45° (for random/hybrid packings)

Finer packings are more controlled by kL29

0.001

0.002

0.004

0.008

50 100 200 400

Avg

. kL/

k G@

25

°C

aP (m2/m3)

Baseline: σ ~ 72 mN/m, µ ~ 1 cP

Structured Y

Structured X/Z

Random

Hybrid

Conclusions

30

Significance of this work

Reliable & simple mass transfer models

• Large database & column size, variance of µL

• No packing-specific parameter

•

•

•

31

𝑎𝑒,𝑝𝑎𝑐𝑘𝑖𝑛𝑔

𝑎𝑃= 1.16 ∙ 𝜂 ∙ 𝑊𝑒 ∙ 𝐹𝑟−

12

0.138

𝑆ℎ𝐿 = 0.12 ∙ 𝑆𝑐𝐿0.5 ∙ 𝑅𝑒𝐿

0.565 ∙ 𝐺𝑎𝐿Τ1 6 ∙

𝑍

1.8

−0.54

𝑆ℎ𝐺 = 0.28 ∙ 𝑆𝑐𝐺0.5 ∙ 𝑅𝑒𝐺

0.62 ∙ sin 2𝛼 0.65

Selection of packing

• aP, α, material, type

Selection of solvent

• µL, σ, ρL

Selection of operating condition

• L, G

Scale-up of column design

• Secondary effect, liquid maldistribution

Conclusions

kL ∝ µL-0.75 (-0.4 & -0.35)

ae ≠ f (µL)

All types of packings have similar behavior in ΔµL

Z (or L/D) may strongly affect mass transfer

32

Recommendations

Avoid finest packings

Use low µL solvent

Use reliable models (developed in this work)

Thanks!

33

University of Texas at Austin

Di Song (Graduating 10/2017)

dsong@utexas.edu

512-750-1480

Back-up slides

34

Why glycerol?35

Structure Mw

wt % to 100 cP(20 ˚C)

Tested?

Dissolve in H2O

Newtonian ?

Affect D?Affect

kinetics?Hazardous?

PEG 0.4 M 2.2 Yes Hard No No No No

Glycerol 92.1 88 No Easy Yes Yes Yes No

Blue – preferable; Red – undesirable

Henry constant of CO236

0

20

40

60

80

100

0 0.2 0.4 0.6 0.8 1

HC

O2

(atm

·L/m

ol)

Glycerol (wt. fraction)

60 ˚C

40 ˚C

15 ˚C

30 ˚C25 ˚C20 ˚C

log𝐻𝐶𝑂2,𝑔−𝑤

𝐻𝐶𝑂2,𝑤= (𝐴𝑤𝑔 + 𝐵 ln 𝑤𝑔 + 1 + 𝐶𝑙𝑛2 𝑤𝑔 + 1 )

×𝐷

𝑇+ 𝐸 + 𝐹𝑇 + 𝐺 ln 𝑇

log𝐻𝐶𝑂2,𝑤 = −7.89 × 10−5𝑇2 + 5.90 × 10−2𝑇 − 9.12

Diffusivity in aqueous glycerol 37

0.01

0.1

1

10

0.1 1 10 100 1000

Dif

fusi

vity

in a

qu

eou

s gl

ycer

ol (

10

-9m

2/s

)

Viscosity (cP)

25 °C

O2

CO2

N2O

Sucrose

Urea

C2H4

NaCl

20 °C

22.5 °C

15 °C

Slope = -0.7

Wetted-wall column38

[CO2]WWC

N2

CO2 Analyzer

[CO2]Bypass

CO2 flux

kg’

(known ae)

CO2

Solv.Tank

1L

SS tube O.D.: 1.26 cm

SS tube L: 9.1 cm

Rxn chamber O.D.: 2.54 cm

Outer chamber O.D.: 10.2 cm

Non-monotonic trend of kg’39

0

4

8

12

0 20 40 60 80

k g'×

10

7

(mo

l/m

2·s

·Pa)

Glycerol (wt%)

calculated kg'

measured kg' for 0.1 N NaOH

measured kg' for 0.1 N NaOH w/ 0.05 N Na2CO3

measured kg' for 0.3 N NaOH

CO2 + NaOH/H2O/glycerol

20 °C

30 °C

40 °C

Equilibrium and Rxns for CO2/NaOH/H2O-Glycerol40

𝑘𝑔′ =

𝑘𝐴𝑙𝑘 𝐴𝑙𝑘 𝐷𝐶𝑂2,𝐿

𝐻𝐶𝑂2

𝑘𝐴𝑙𝑘 = 𝑘𝑂𝐻−𝑂𝐻−

𝐴𝑙𝑘+ 𝑘𝐺𝑙𝑦𝑐𝑒𝑟𝑜𝑙−

𝐺𝑙𝑦𝑐𝑒𝑟𝑜𝑙−

𝐴𝑙𝑘

Measured and calculated kAlk

41

8

16

32

64

128

256

0 0.1 0.2 0.3 0.4 0.5 0.6

k Alk

(10

3L/

mo

l·s)

Glycerol (mole fraction)

20 C̊

30 C̊

40 C̊

0.1 M NaOH 1st exp.

0.1 M NaOH 2nd exp.

0.1 M NaOH 3rd exp.

0.3 M NaOH exp.

Calculated kAlk

Surface depletion of alkalinity for WWC runs 42

0%

5%

10%

15%

20%

25%

0 20 40 60 80

Avg

. dep

leti

on

Glycerol (wt %)

0.1N NaOH

w/ 0.05N Na2CO3

0.3N NaOH

Blue = 20 C̊

Red = 30 C̊

Green = 40 C̊𝑘𝑔′ =

𝑘𝐴𝑙𝑘 𝐴𝑙𝑘 𝐷𝐶𝑂2,𝐿

𝐻𝐶𝑂2

𝑁𝐴𝑙𝑘𝑎𝑙𝑖𝑛𝑖𝑡𝑦 = 2𝑁𝐶𝑂2 = 𝑘𝐿0 𝐴𝑙𝑘 𝑏 − 𝐴𝑙𝑘 𝑖

𝐷𝑒𝑝𝑙𝑒𝑡𝑖𝑜𝑛% =𝐴𝑙𝑘 𝑏 − 𝐴𝑙𝑘 𝑖

𝐴𝑙𝑘 𝑏× 100%

Pressure drop 43

0.01

0.02

0.04

0.08

0.16

0.32

0 100 200 300 400 500

avg.

ΔP

(in

. H2O

/ft

pac

kin

g)

aP (m2/m3)

Avg. value @ G = 300 ACFM, L =10, 15, 20 gpm/ft2

Structured Y

Structured X/Z

Random

Hybrid

Effect of flow rate sequence on ae44

0.6

0.8

1

1.2

0 10 20 30

Frac

tio

nal

are

a (a

e/ap)

L (gpm/ft2)

10 ft GT-OPTIMPAK 250Y

G = 180 ACFM

System = Water

Different ae regimes45

0

0.25

0.5

0.75

1

1.25

1.5

0 10 20 30

Frac

tio

nal

are

a Φ

(ae/aP)

L (gpm/ft2)

Before end & wall effect correction

After correction

Metal surface area

Satellite droplets

MG 64Y

GC sampling technique46

AWC sample

Heptane Heptane w/ toluene

Internal standard

ShakeGC

(ATol, AStd)(mStd)(mHpt2)(mHpt1, mSample)

𝑤𝑇𝑜𝑙,𝐺𝐶

𝑤𝑆𝑡𝑑,𝐺𝐶=𝑅𝑇𝑜𝑙 × 𝐴𝑇𝑜𝑙𝑅𝑆𝑡𝑑 × 𝐴𝑆𝑡𝑑

𝑤𝑇𝑜𝑙,𝑆𝑎𝑚𝑝𝑙𝑒 =𝑤𝑇𝑜𝑙,𝐺𝐶 ×𝑚𝐻𝑝𝑡1

𝑚𝑆𝑎𝑚𝑝𝑙𝑒

𝑤𝑆𝑡𝑑,𝐺𝐶 =𝑚𝑆𝑡𝑑

𝑚𝐻𝑝𝑡2 +𝑚𝑆𝑡𝑑

kL reproducibility is good 47

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5 3 3.5

k L·µ

L0.4

/D0

.5(T

his

wo

rk)

kL·µL0.4/D0.5 (Previous work)

M 250X(avg. ratio = 2.0)

6 ft packing

10 ft packing

M 250Y(avg. ratio = 1.1)

GTP 350Y(avg. ratio = 0.9)

GTP 500Y(avg. ratio = 0.9)

RSP 250Y(avg. ratio = 0.9)

Outlier: M 250X 48

10

20

30

40

50

0 10 20 30 40 50

k L·µ

L0.4

/(D

0.5

·uL0

.57)

Outlet toluene (ppmW)

M 250X (this work)

M 250X (previous)

M 250Y

GTO 250Y

B1 250MN

RSP 250Y

RSR 0.5

Packing height: 6 ft or corrected 10 ft

Outlet toluene abnormally high

“Big rivulet” assumption49

Flow regimes Thin, spread film Thick, big rivulets

Contribute to ae ?

Yes Yes

Contribute to kL ?

No Yes

f (aP) Increase w/ aP Decrease w/ aP

Measured area > ae for kL

(underestimate kL)

Δa for finer packings

“No mixing” assumption50

Theoretical laminar falling film: kL ∝ L-1/2 (Q/W)1/3

“Mixing point”

Sketch

L𝑏

2∙sin 𝛼∙cos 𝛼

f (aP) aP L Q/W kL

“No mixing”

Helement/sinα

aP L Q/W kL

α

Helement

Helement/sinα

Compare measured kL w/ theory51

0.0E+00

4.0E-05

8.0E-05

1.2E-04

1.6E-04

2.0E-04

0 5 10 15 20 25

k L(m

/s)

Liquid Load (gpm/ft2)

GTP 500Y

Experimental

“Big Rivulet” assumption

“No mixing” assumption

Liquid film mass

transfer coefficient:

kL

52

0.05

0.5

5

50

0.5 5 50 500

Sh·Z

0.5

4/S

c0.5

Re·Ca1/5·Fr-1/3

-50%

+50%

AAD = 20 %

G = 300 ACFM

0.8-1 cp

3-5 cp

12-15 cp

35-70 cp

𝑆ℎ𝐿 = 0.12 ∙ 𝑆𝑐𝐿0.5 ∙ 𝑅𝑒𝐿

0.565 ∙ 𝐺𝑎𝐿Τ1 6 ∙

𝑍

1.8

−0.54

This work compared to literature

This work

• Greatly expand packing database

• Greatly expand µL variance

• Reliable ae (kinetic) data

• Relatively large column size

53

-1.2

-0.8

-0.4

0

0.4

0.8

0 20 40 60 80

α

Column I.D. (cm)

Random

Structured

Empty

Solid

μL < 5 cP

μL > 5 cP

This work

kL (kLa) = C·μα·Dβ

kG Model 54

2

4

8

16

32

50 100 200 400 800 1600

Sh/(

Sc0

.5· s

in0

.652

α)

Re

-50%

+50%

AAD = 21 %

1.5–3 ft packing

G = 180–750 ACFM

L = 10 or 15 gpm/ft2

kG model