1

Modelling of Dispersion from Direct Injection of Carbon Dioxide in the Water Column

Baixin Chen and Makoto AkaiNational Institute of Advanced Industrial Science

and Technology (AIST), Japan

2

Turbulent Multiphase Mixing and Interactions: (Mass, Momentum,Energy Exchanging and Phase Changing)

Droplet- seawater interactions: drag, deformation, raisingDroplets interaction (collision, coalescence, second breakup)CO2 dissolution or shrinkingCO2 hydrate dynamics; gasificationLocal turbulent flow, wake, and mixingChemical reactions of dissolved CO2 and seawaterBiological Impacts

CO2 injection:

Droplets formation; Hydrate;Distributions of Initial Diameter and Number Density; Towering pipe wakes…..

Mesoscale Eddies

Ocean Currents

Bottom Boundary Layer

100~1000 m

Ocean Surface

• Small-scale ocean turbulence and turbulent wakes

• Two-fluid modeling

• Biological Impact Modeling

CO2

10 ~100 KmHorizontal 2-D modeling of CO2 dispersion

2000m

What must be handled!

3

Models developed

Alendal et al. (NERSC Technical Report,1998; JGR-ocean, 2002)

Sato et al. (RITE report, 1998;ASME,2000; GHGT-6, 2002)

Chen et al.(RITE report, 1999; ASME,2000; Tellus, 2003)

4

Outline

Introduction of the model developed

Case investigation:

Release of CO2 from fixed port

Release of CO2 from a towered pipe

Conclusions

5

A Near-field Physical & biological impact model of CO2 Ocean Sequestration

1. Modeling of Small scale ocean turbulent flow (Re-construction)

Forced-dissipative ocean turbulent flow model

CO2 enrich-seawater dynamic model

2. Modeling of momentum and mass transfer between CO2 droplets and seawater

Sub-model of CO2 droplet drag coefficient

Sub-model of CO2 droplet deformation

Sub-model of CO2 solubility

Supported by Lab. and field Exp.

3. Modeling of biological impacts of floating-orgms.

Conservative variables:Mass or Number density of organism k

Non-conservative variables: Degree of Damage/Activity Index, Ak.

Sub-models of Damage Degree /Activity Index

6

Part – I : Reconstruction of small scale turbulent ocean with basis on observation

data

Theories and physical model

Observation data analysis and implement

7

Turbulent kinetic energy spectrum in the ocean (J. D. Wood in Nature 1985 and CREIPI at Keahole

Pt. Offing,1999)

Eddy resolving truncation scale (10 km) by Earth

Simulator (0.1deg.) in Japan

Eddy resolving truncation scale (1 m) by Small-scale

two-phase model

Small-scale two-phase model

Eddy resolving truncation scale (100km) by year 2000 estimated by Wood in 1985

Forced-dissipative and kinetic energy cascade theories applied?

N-S

B-230m

Frequency (CPs)

Horizontal

Vertical

E (c

m3 /s

2 )

CREIPI at Keahole Pt. Offing,1999

Meso-scale ocean model

8

Theories and Techniques Applied

Inside of the ocean:

• N-S based 3-D unsteady Governing Eq.s

• Forced-dissipative Energy cascade theories

• Adjusted by observation spectrum

Large-scale information from Boundaries :

•Mean properties (X,t)

•Turbulent properties at K > Kf

Field Obs. Data

Data analysis

9

ijfF)F(g)(x

D

x

p

x

uu

t

udi0

j

ij

ij

jii

 

a. Forced-dissipative system of small-scale ocean:

Forced term:

Dissipative term:

ikkt S0.2D

ik

b. Structure-function Turbulent viscosity model:

)]x,x(F[xC.)xx( kkk

k/

kk,kk

t

2

23150

22 ))()((25.0 kkkkkk xxuxuF

Governing Equations for simulating small-scale ocean turbulence

fkk 000f kk)t,k(u)t,k(u/)t,k(uFf

10

1-4. Example: Hawaiian Case (small-scale): Computational domain, initial &boundary conditions

)t,X(u)t,X(U)t,X(U m

X1 = 500 m; N1 = 256

X2

= 3

00m

; N

2 =

128

X3 = 3

00 m

;

N3=12

8; P

erio

dic

cond

ition

s

)0tX(U ,3m1

Inlet

output0.0)0tX(U ,3m3

0.0)0tX(U ,3m2

solid wall

ρ0= f(T0,S0)

U1m(x3), T0(x3) S0 (x3)are the observation data

VLx2

2U

Lx2

1C

x

U;C

x

U

2222

11

-1.0

0.0

1.0

2.0

3.0

4.0

-5.5 -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 Log10 (K) (1/cm)

Lo

g1

0 (E

u(K

)) (

cm3/s

2 )

Observation data

Simulation with Plume

Simulation without Plume

Simulations of small-scale ocean turbulence

Instantaneous velocities and temperature T

0.0

0.1

0.2

0.3

0.0 1.0 2.0 3.0

u1mx100

x 2

Simulation

Initial & data

12

Part-II: CO2 droplet dynamicsExperimental Observations and Modeling

Assumptions

• Assumption:CO2 droplet with hydrate covered is a Deformable rigid droplet with Permeable Surface

• Experimental data adopted are those from Stewart(1970) and Kimuro (1994) for CO2 solubility, and from Ohgaki (1993) for phase diagram.

• Experiment data dealing with momentum transfer between droplets and seawater are from the experiments of Dr. Ozaki (1999)

13

Sub-models of drag coefficient and terminal velocities

Re10)Re104596.1

Re103484.86419.5(0.1)A/A(

)2(Re/)Re125.01(24Cd

)1()A/A(CdCd

426

3Cdeqeff

72.0r

Cdeqeffrd

1.0 1.5 2.0 2.5 3.0 3.5 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

O: P=10.1MPa;T=275K O: P=15.1MPa;T=278K O: P=20.1MPa;T=278K Exp data (Ozaki et al)

: Cdr Rigid spheres Eq. (2) : Cdd Rigid spheres with deformation Eq.(1)

Logarithmic Reynolds Number

Dra

g C

oeff

icie

nt C

dr a

nd C

d d

0 5 10 15 20 25 0

5

10

15

20

CO2 Droplets Diameter (mm)

O: P=10.1MPa;T=275K O: P=15.1MPa;T=278K O: P=20.1MPa;T=278K

Exp Data (Ozaki et al)

: Cdr Rigid spheres Eq. (2)

:Cdd Rigid spheres with deformation Eq.(1) Ter

min

al v

eloc

ity

of C

O2

drop

let

(cm

s-1

)

14

900

800

700

600

500

400

300

200

5 15 25 35 45 55 65 75

Elapsed Time (min)

Dep

th o

f D

ropl

et R

ose

(m

)

Modeling Prediction (Droplet A)

Modeling Prediction (Droplet B)

: Observation Data (P.Brewer et al)

Model prediction of an individual

droplet dissolution (model

calibration)(CO2 droplet Diameter vs Exp

data by P. Brewer et al)

0.00

0.20

0.40

0.60

0.80

1.00

10 25 40 55 70

Elapsed Time (min)

Dro

plet

Dia

met

er (

cm)

Modeling Prediction (Droplet A)

Modeling Prediction (Droplet B)

:Observation Data of Droplet A (P. Brewer et al)

:Observation Data of Droplet B (P. Brewer et al)

dt

)mln(du)C

D

ug).((

dt

du cd

s

c

c

s 4

301

2

)D

CDSh2

dt

d

3

D(

1

dt

dD sfc

c

Key Parameters:Cd: Drag coefficientSh: Sherwood NumberCs: The solubilityα : The effective area coefficient

15

CO2 droplet dissolution at variant depth

Release depth(m)

Density Ratio

Elapsed time(min)

Release depth (m)

Density Ratio

Elapsed time(min)

1000 0.93144 84.5 2900 1.0001 240.0 1500 0.95462 113.0 3500 1.0164 180.2 2000 0.97233 142.0 4000 1.0287 151.7 2500 0.98832 187.0 5000 1.0503 122.6 2890 0.99997 240.0 5500 1.0597 113.8

-6500

-5500

-4500

-3500

-2500

-1500

-500

-5.0 -4.0 -3.0 -2.0 -1.0 0.0

CO2 Droplet Shrinking Rate (10-4cm s-1)

Dep

th (

m)

D0= 2.0 cm

16

Ascending /Descending of CO2 droplet

-800

-600

-400

-200

0

200

400

600

800

0 3 6 9 12 15 18 21 24

Initial Diameter of CO2 Droplet (mm)

Asc

endi

ng /

desc

endi

ng

Dis

tanc

es (

m) Release depth: 1000m

Release depth: 2000m

Release depth: 2895m

Release depth: 2900m

Release depth: 3000m

17

cicj

djdicdic Fgx

uu

t

u

)(ˆˆˆˆˆˆ

Governing Equations of Seawater

Governing Equations of LCO2

cwx

u

t i

i

ˆ

)()(ˆˆˆˆˆ

0 ci

j

ij

ij

jii

Fgxx

p

x

uu

t

u

i

ii

gx

P

x

p0

klc

j

k

j

k

k

jj

jkk

wx

q

xD

xx

u

t

ˆ

)ˆ

(ˆˆˆ

Two-fluid ocean turbulent flow model

ninjinjj

dj wx

un

t

n

ˆˆˆ

injinjccj

dj wwx

u

t

/ˆˆˆ

18

Density change of CO2 enriched seawater

1.000

1.005

1.010

1.015

1.020

1.025

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Density change of CO2 seawater solution (3℃)

CO2 Concentration (wt)

Den

sity

rat

io o

f C

O2

Sea

wat

er S

olut

ion

to S

eaw

ater

(g

/cm

3 )

s =w (1.0 + )

s : CO2 solution density

w : seawater density

: CO2 mass fraction

=0.273 by Exp (Song et al. 2003)

19

Part – III : Dispersion from Direct Injection of Carbon Dioxide in the Water Column

Injection of CO2 from fixed ports

Injection of CO2 from towered pipe

A shear ocean current Um=2.3cm/sec

Towered pipe

10 m

Mc = 100 kg/sec Nzl = 100 D0 = 20 mm

-135

0m

Vship = 3.0m

10 m

10 m

H= 10m ; 100m

Nozzle port: Mc = 100kg/sec Nzl= 100 D0 = 10.0 mm

A shear ocean current Um=2.03 cm/sec

-110

0m

/sec

20

Dispersion from a fixed port release

T=32 min T=32 min

T=93 min T=93 min

CO2 droplet plume CO2 enriched water plume

21

Plume characters from a fixed port

0.0

0.3 0.0

0.2

0.2

0.0

0

50

100

150

200

0 50 100 150

Elapsed Time (min)

Vert

ical p

osi

tion o

f dro

ple

t (Y

d)

and

CR

wate

r part

icle

s (Y

c)

(m)

Yc=0.1 kg m-3 Yc =0.8 kg m-3 Yd=0.93 kg m-3 Yd = 0.083 kg m-3 T=93 min

22

Lower Injection rate (pH plume at middle depth)

Mc=0.6kg/s; D0 =8.0mm

T=100.3 min

Mc=0.1kg/s; D0 =8.0mm

23

O u t l i n e o f C O 2 D r o p l e t P l u m e

C O 2 R i c h - w a t e r P l u m e

1 . 3 4 1 . 2 6 1 . 1 7 0 . 8 9 0 . 6 5 0 . 0 0

Dispersion from a towered pipe release

0.00 0.50

0.00

0.60

0.00

0.15

T=1.0 min

T=23 min

T=70 min

X=180 mX=10 m

T=70 min

Yc=0.01kg m-3

24

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5pH changes

Per

cent

age

of v

olum

e w

ith re

spec

t to

pH

cha

nges

T = 58 min; H = 100m

T = 116 min ; H = 100 m

T = 175 min; H = 100m

T = 175 min; H = 10m

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5pH Changes

Per

cent

age

of th

e vo

ume

with

re

spct

to th

e pH

cha

nges

e

T = 23 min T = 46 min T = 70 min

Towered pipe

Fixed ports

tot

k

iXX

XX V

V

)V(Pk

k

1

pHX

0.0E+00

2.0E+06

4.0E+06

6.0E+06

8.0E+06

1.0E+07

1.2E+07

1.4E+07

0 50 100 150 200

Elapsed Time (min)

Tota

l Vol

ume

of C

O2 e

nric

hed

seaw

ater

plu

me

(m3)

Fixed port releaseH= 10mFixed port release H= 100mTowered piperelease

Statistical characteristics of CO2 enriched seawater plume

25

0.0

0.1

0.2

0.3

0.40.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0

Delta pH

Per

cent

age

of C

O2

enric

hed

wat

er v

olum

e w

ith re

spec

t to

Del

t pH

M=0.6;D0=8.0;Uc=2.5

M=0.1;D0=8.0;Uc=2.5

Statistical characteristics of CO2 enriched seawater plume

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0

Delta pH

Pe

rce

nta

ge

of C

O2

en

rich

ed

wa

ter

volu

me

with

re

spe

ct to

de

ltp

H

M=0.6;D0=8.0;Uc=2.5M=0.1;D0=8.0;Uc=25.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0

Delta pH

Per

cent

age

of C

O2

enric

hed

wat

er v

olum

e w

ith r

espe

ct t

oD

elt

pH

M=0.6;D0=8.0;Uc=2.5

M=0.6;D0=5.0;Uc=2.5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0

Delta pH

Per

cent

age

of C

O2

enric

hed

wat

er v

olum

e w

ith re

spec

t del

pH

M=0.6;D0=8.0;Uc=2.5

M=0.6;D0=8.0;Uc=25.0

26

Conclusions

Near-filed physical and chemical process created by directly injected LCO2 into the ocean waters could be reasonably simulated.

To engineering application, injection of LCO2 from fixed ports should be

carefully arranged to limit the local injection rate associated with the selection of an incline seafloor.

In case of large injection rate (100kg/s) from fixed port on a flat seafloor, injected LCO2 could yield a large pH change and an unsteady waving double-plume.

Alternatively, release of LCO2 from a towered pipe at middle-depth with a relatively large size droplets is an expectable option to practically performance of CO2 ocean sequestration, which could be adjusted with the limitation of biological impact.

Understanding of the effect of dissolved CO2 on oceanic bio-organisms appeared to be urgently necessary for assessing the oceanic environmental impacts.

…. We still have more works to be done .

27

Acknowledgements

This study is a part of the investigation of two projects: A research Project on Accounting Rules on CO2 Sequestration for National GHG Inventories (ARCS) managed by National Institute of Advanced Industrial Science and Technology (AIST) and The CO2 Ocean Sequestration Project managed by Research Institute of Innovative Technology for the Earth (RITE). New Energy and Industrial Technology Development Organization (NEDO), Japan, fund both projects.