Current Status of CAS Team on Task A Step 0: Model Inception

– two-phase flowtwo-phase flow modeling for the laboratory drying testmodeling for the laboratory drying test

By Xiaoyan Liu, Chengyuan Zhang and Quansheng Liu

Wuhan Institute of Rock and Soil MechanicsChinese Academy of Sciences (CAS)

October 20-23, 2008Wakkannai, Japan

DECOVALEX 2011

2nd workshop & Task A Force Meeting

Step 0: Identification of relevant processes and of Opalinus Clay

parameters. Modelling of the laboratory drying test.

Step 1: Hydromechanical modelling up to the end of Phase 1.

Step 2: Hydromechanical modelling up to the end of Phase 2 using

parameters backcalculated from step 1. Advanced features as permeability

anisotropy, rock damage and permeability increase in the damaged zone

may be considered.

Step 3: Hydromechanical and geochemical modelling of the full test.

Conservative transport and one species considered.

Step 4: Hydromechanical and geochemical modelling of the full test.

Reactive transport and full geochemical model (optional).

Task A Research programme

Step 0General model

description

Impermeable lateral boundaries

10cm

28cm

2/1.1

/51.0

%33

30

cmdaygpev

scmV

RH

CT

air

o

General model description

Governing Equations

Code developement

Simulation results

Discussion

Conclusion

Next steps

OutlineOutline

Based on three interacting continua

General model description multiphase system:General model description multiphase system:

Capillarity

Two-phase-flow

Liquid phase

Gas phaseVapour

Dry air

Phase exchange

Water

)(Kelg eej s

Governing Equations Governing Equations

For liquidFor liquid

phase exchangeevaporation or precipitation

lgjg

x

pkk

xt

ppp

s

Sil

j

l

l

lijrl

i

lavl

2/1 ))1(1( SSk rl

volume change changeretention curveretention curve

advection

Governing Equations Governing Equations

For vapourFor vapour

volume change change

j

aavv

vv

j x

MPMPMP

x

v

aavv

vv

av

v

MPMP

MP

mm

m

v

)( lg

gv

vatm

jgx

pkk

xDS

xt

ppp

s

S

t

p

pp

S

v

liv

j

v

v

vijr

jg

i

lavgvg

j

a

aavv

avv

j

v

aavv

vv

aavv

v

x

p

MPMP

MMP

x

p

MPMP

MP

MPMP

M

22

2

v0 p

1b

kk ijvij

v

3.212109.5p

TD

grg Sk

Klinkenberg parameter

phase exchange

ordinary diffusion

SlipKnudsen

effect

advectioncompressibilitycompressibility retention curveretention curve

0a

aagaa

aatm

ijv

ijr

jg

i

lavgg gx

pkk

xDS

xt

ppp

s

S

t

p

pp

S

Governing Equations Governing Equations

For dry airFor dry air

No phase exchange

CouplingCoupling schemescheme

(1) Phase exchange

(2) Saturation-Suction

(3) Different mobility (advection and diffusion effects) of two gas

Code DevelopmentCode Development

FEM solver FEM solver :: FRT-THMFRT-THM

(Developed for Task D of Decovalex-THMC)

FEBEX conception modelFEBEX conception model

Bentonitebuffer

Bentonitebuffer

Thermalexpansion

Thermalexpansion

Permeabilitychange

Permeabilitychange

SwellingSwelling

No boilingNo boiling

Unsaturated / Saturated

volcanic rock / crystalline

boiling / no boiling

no buffer / buffered

YMP DST / FEBEX

YMP DST conception modelYMP DST conception model

Permeabilitychange

Permeabilitychange

Drift with airDrift with airBoilingBoiling

Thermalexpansion

Thermalexpansion

Dry-outDry-out

(for Task A of Decovalex-2011)Modified FRT-THMModified FRT-THM

0.1m0.1m

D=0.1mD=0.1m

Step 0 Inception simulationStep 0 Inception simulation

Boundary conditionsBoundary conditions

FEM meshes: 3206 304FEM meshes: 3206 304

Geometry, Grid Design and Boundary Conditions

H=0.28mH=0.28m

Top

Bottom

Lateral

no flux

no flux

lp

vp

ap

freeseRH *

vatm pp

0.28m0.28m

vapour & air, no watervapour & air, no water

No-flux bNo-flux boundary oundary

forforwaterwater

vapourvapourdry airdry air

3D3D 2D2D

Variables & ParametersStep 0 Inception simulationStep 0 Inception simulation

(Munoz, 2001)

0.40 (in our work)

0.165

0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60%

time /hour

B ExpGro1 fit of Data1_B

Boundary conditionRH = -20.06*exp(day*24/-686.624)+39.59

Step 0 Simulation resultsStep 0 Simulation results

pv time= 21 99 142 days

Dry air pressure pa

Vapour pressure pv

Total gas pressure pv+pa

142 days99

21

142 days

99

21

142 days

99 21

142 days99

21

Water pressure pl

Pressures profile

0 20 40 60 80 100 120 140 160

0.00

0.03

0.06

0.09

0.12

0.15

0.18

Wa

ter

loss

[K

g]

Time [days]

Sample A Sample B Sample C Calculated

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.00

0.05

0.10

0.15

0.20

0.25

0.30

dis

tan

ce to

ba

se [m

]

Saturation

Comparison with Measured Data Step 0 Simulation resultsStep 0 Simulation results

0 1 2 3 4 5 6 7 8 9

0.00

0.05

0.10

0.15

0.20

0.25

0.30

dis

tan

ce

to

ba

se

[m

]

Water content [%]

time (d) 21 99 142

0 1 2 3 4 5 6 7 8 9

0.00

0.05

0.10

0.15

0.20

0.25

dist

ance

to b

ase

[m]

Water content [%]

time (d) 21 99 142

Comparison with calculation by (Munoz, 2001)

Step 0 Simulation resultsStep 0 Simulation results

by (Munoz, 2001)Our work

Comparison with calculation by (Munoz, 2001)

Step 0 Simulation resultsStep 0 Simulation results

0 20 40 60 80 100 120 140 1600.00

0.03

0.06

0.09

0.12

0.15

0.18

Wat

er lo

ss [K

g]

Time [days]

Sample A Sample B Sample C Calculated

by (Munoz, 2001)

Our work

Discussion (1) Discussion (1) Influence of relative permeability kInfluence of relative permeability krlrl

142 days

21 days

99 days

0.6 0.4 0.3 0.135

Discussion (2) Discussion (2) Influence ofInfluence of Relative Humidity (RH)

0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

%

time /hour

B ExpGro1 fit of Data1_B

0 20 40 60 80 100 120 140 160

0.00

0.05

0.10

0.15

0.20W

ate

r lo

ss [

Kg

]

Time [days]

RH slightly varying 33% constant

ConclusionConclusion

Simulation on the laboratory drying test seems good. Preliminary compare to test data and the calculation using code_bright show that they match well.

We must do more calibration and benchmark test on our model, especially to make sure the parameters are correct and model work well.

Next stepNext step

1. To consider coupled mechanical processes (swell & shrinkage effect; Damage of the material)

2. Step from 0 to 1.

Thank you for your attention