Evaluation of oil contamination in porous media by X-ray CT image analysis and LBM

simulation

Kumamoto Univ. X-Earth CenterToshifumi Mukunoki

Chiaki Nagai

1

BASICS OF X-RAY CT METHOD

GENERAL PRINCIPLE, VOXEL AND CT VALUE

n voxels

n voxels

thickness of the slice

CT image is a digital image.

Figure 17

Bulk density (t/m3)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

CT

valu

e

-1000

-500

0

500

1000CT value = 943.2 - 987.18AirWaterRatio of fine grains: 0 %Ratio of fine grains: 30 %Ratio of fine grains: 50 %Ratio of fine grains: 70 %Ratio of fine grains: 100 %Equation [4]

10001000 dvalueCT

…………

Reconstruction of 3-D CT image

IMPORTANT FEATURES IN IMAGE ANALYSIS

•THRESHOLD VALUE•BEAM HARDENING EFFECT•PARTIAL VOLUME EFFECT

THRESHOLDING VALUE

(a) 0<CT-value<500

(b) –1000<CT-value<500(II) CT image

Figure 3

(I) Histogram of CT value

0

3000

6000

9000

-1500 -1000 -500 0 500 1000 1500CT-values

Freq

uenc

y

(b) 256levels

WW

WL

(a) 256levels

PARTIAL VOLUME EFFECT

The size of all particles is greater than a voxel dimension

Baseline

X-ray beamSoil particle

CASE1

BaselineThe size of some particles is greater or smaller than a voxel dimension

CASE2

BaselineThe size of all particles is smaller than a voxel dimension

CASE3

(a)

Figure 14

Location along the diameter of spesimen (mm)

-30 -20 -10 0 10 20 30C

T-va

lue

-1500

-1000

-500

0

500

1000

1500

2000

(b)

CASE1

CT-value for air

(a)

CASE3

Location along a diameter of image (mm)

CT-

valu

e

Figure 15

(b)

-2000

-1000

0

1000

2000

-40 -20 0 20 40

IMAGE PROCESSING ANALYSIS TO X-RAY CT

IMAGE

12

X-ray source

Detectors

Specimen table

①

②

③ ④

⑤⑥

⑦

⑧ ⑨

scan area

100

300

840

Fig. 4

⑩

⑪⑫

⑬

Initial step B step C step D step Estep A

70mm

55mm

40mm

25mm

10mm

Hei

ght f

rom

the

botto

m o

f spe

cim

en

Strain level

Specimen

SMOOTHING TECHNIQUE

Basic analysis of X-ray CT image(2) 11pixel

11pi

xel

(a) (b) (c)

Fig. 15

0

200

400

600

800

1000

-40 -20 0 20 40

step Astep F

CT-

valu

e

Location of a voxel from the center of the specimen

25mm

500

550

600

650

700

750

800

-30 -25 -20 -15 -10 -5 0location along radius(mm)

CT-

valu

e

initialstep Astep Bstep Cstep Dstep E

MAIN TOPIC

Introduction

It is important to know the mechanism of LNAPL migration

ＬＮＡＰＬ：Light- non aqueous phase liquids (gasoline, diesel, etc)

Residual LNAPL causes long-term pollution

Ground contamination

Source

Vadoze zone

Saturated zone

Soil particlesResidualLNAPL

pore waterPore scale

17 Motivation

(～1μm)

Grain

Water

LNAPL

Air

Pore-Scale

Core-Scale

Small-size blockLarge-size block

(1cm～)

(1m～) (10m～)Representative

parameter

Ex.Pore-Scale

（C. Pan et al,2004)

Numerical Analysis for Micro scale

Avergae

0)( gpKk

tS r

Numerical Analysis for Macro scale

Introduction

Soil Particles ResidualLNAPL

Pore waterPore scale

19

Transfer mechanism of oil flow

Pore structure

Pore Pore size

Pore Pore shape Connectivity

Fluid Fluid distribution

Velocity and

distribution

Velocity and Pressure

distribution

Image analysis

CFD analysis

Objective

To clarify the transfer mechanism of oil and water in pore structure of sandy soil using Image analysis and CFD analysis

Image analysisGeneration mechanism of blobs in sandy soils

ＬＢＭ analysisLBM simulation can be performed using MXCT image

MXCT image

20

APPLICATION OF M-FOCUSED X-RAY CT SCANNER FOR THIS

STUDY

M-FOCUSED X-RAY CT SCANNER GIVES THE SPATIAL DISTRIBUTION OF MATERIAL DENSITY. A CT IMAGE IS NOT A

MICROSCOPE PHOTOGRAPH BUT A DIGITAL IMAGE.

Power of voltage (kV) 150Current (mA) 180

Numver of views 1500Number of integration

treatment10

Voxel dimension (mm) 4.43 x 4.43 x5.0Number of voxel 1024 x 1024 x 1000

Imgae processing

23

NOWADAYS, SO MANY USEFUL APPLICATIONS ARE DISTRIBUTED IN THE

IMAGE ENGINEERING• IMAGE J (ONE OF POPULAR APPLICATION FOR CT USERS)

• ITK (IMAGE TOOL KIT: LANGUAGE IS C++

• MOST OF CASE, WE DON’T NEED TO DEVELOP VERY NEW ALGORISM WHICH WE WANT TO DO IMAGE ANALYSIS.

24

Decision of analyzing area

100voxels 200voxels 300voxels

400voxels 500voxels 600voxels 700voxels

25

Decision of analyzing area Porosity

38.63

37.65

38.7138.82

39.1439.30 39.26

37.5

38

38.5

39

39.5

0 100 200 300 400 500 600 700

poro

sity

(%)

range of analysis (voxel)

試料作製時

の間隙率

39.40

The are for evaluation of porosity is changed and then, 500 voxels should be enough dimensions because errors are within 1 %.

26

27

100 190200 195～200300 200～205400 200～205500 200～205600 200～205700 200～205

試料作製時の平均粒径

200

一辺のサイズ(voxel)

平均粒径(μm)

Grain size distribution

Image J has the option called “3D object counter” and then, its data can be output as text data, such as number of particles, long and short diameter. We analyze those value using Excel, whatever.

As for grain size distribution, dimension of 300 cubic voxel is enough for evaluation of grain size distribution.

0102030405060708090

100

0.025 0.050 0.100 0.200 0.400

Pass

mas

s per

cent

age (

%)

Diameter(mm)

100200300400500600700Sieving test

When 1voxel =5μmWe concluded that we should use 500 cubic voxels for image analysis and numerical analysis.

28

3D distribution of pore size

XBBX XXX

B |Mathematical Morphology: Opening and Closing

3D binary image

Pore

Sphere element

1 5

10 15

Pore sizeParticles Large pore It is possible to extract pore structure and

pore size

3D distribution of pore size

Toyoura sand

Glass beads

29

Small

Large

Pore size

02468

1012141618

5 15 25 35 45 55 65 75 85 95 105

115

125

135

145

155

165

175

185

195

205

215

225

Freq

uenc

y, %

Pore diameter, μm

02468

1012141618

5 15 25 35 45 55 65 75 85 95 105

115

125

135

145

155

165

175

185

195

205

215

225

Freq

uenc

y, %

Pore diameter, μm

Toyoura sand

Glass beads

NAPL INJECTION TEST

30

1D INJECTION TEST

Water or NAPL is injected1㎝

ParticlesResidualLNAPL

Pore water

Particles

Pore water

Particles

Pore water

LNAPL

20cm

31

Sample Mean diameter (mm)

Particle density (t/m3)

Porosity (%)

Case 1 Glass beads 300 2.45 36.0

Case 2 Toyoura sands 200 2.65 39.4

Test Method

土粒子密度 乾燥密度

(t/m3) (t/m

3)

CASE1 ガラスビーズ 250-350 2.45 1.57 0.89

CASE2 ガラスビーズ2種 250-350と1000の混合 2.45 1.75 0.89

CASE3 ガラスパウダー 250-450 2.45 1.49 0.89

CASE4 豊浦砂 200 2.64 1.6 0.87

試料 粒径(μm) 相対密度

Injection test apparatus Illustration

Flow

Sample should be fully

saturatedLNAPL was

injectedKI solution was

injected CT scan

Precision balance

200mm

Syringe pump

Pressure sensor10mm

KI solution was used.For saturation, we injected CO2 gas using 120 kPa pressure.

4. Test materials

2.5mm

ρ＝1.02t/m3 ρ＝1.05t/m3 ρ＝1.25t/m3

KI solution Water

Density (t/m3) 1.25 1.00

Surface tension (mN/m) 72.45 72.94

Interfacial tension withLNAPL (mN/m)

Contact angle (°) 61.5 53.7

Viscosity (mPa・sec） 0.966 1.002

KI ρ＝1.25t/m3 Main properties (18℃)

54.5 52.9

SoilKI solution

SoilKI solution

2.5mm

CT images of sample before and after KI solution injection10

CASE1( Ca = 1.57×10-6)

CASE2( Ca = 3.14×10-5)

5mm

5mm

Resolution：1024×1024×800

1voxel ： 5×5×5μm

Resolution：1024×1024×800

1voxel ： 5×5×5μm

3D pore distribution

Binary Image

Pore

Pore with residual LNAPL NAPL

3D pore structure

185μm

0μm

間隙径

35

Evaluation of residual LNAPL and KI solution

36

Residual LNAPL KI solution Residual LNAPL KI Solution

Glass beads Toyoura sand

Sample should be

fully saturatedLNAPL was

injectedKI solution

injected CT scan

ResidualLNAPL

KI solution

Conclusions

• Micro X-ray CT scanner is a powerfultool to evaluate pore structure ofsandy soil and its techniques can beapplied to the evaluation of porestructure with LNAPL．

37

Ongoing work• To perform LBM simulation using X-

ray CT image obtained from these test.

Lattice Boltzmann Method (LBM)

38

LBM - INTRODUCTIONLBM models the fluid consisting of fictive particles, and such particlesperform consecutive propagation and collision processes over adiscrete lattice mesh.

Advantages of LBM over traditional methods:Allows modelling of multi-phase behaviour at local scaleAllows dealing with complex boundariesAllows incorporation of microscopic interactionsAllows parallelization of algorithm (for example using GPU)

Disadvantages of LBM:Limited memory and mesh size (depends on efficiency ofparallelization modelling and hardware)Lack of use of classic physical parameters

LNAPL

Water

Glassbead

Wall

parameters LNAPL WaterDensity ratio Relaxation time (τ) 1.167 1fluid-fluid Interaction (gf)fluid-solid Interaction (gs) -0.020 0.020

1

0.0015

ρN=100

ρW=90

kk

kP7

3

λk：流体の圧縮性に関係するパラメータ

40

LBM simulation for two-phase flow in porous materials

33

0

20

Poresize(voxels)

LBM simulation 3D distribution of pore size

02468

1012141618

0.005 0.025 0.045 0.065 0.085 0.105 0.125 0.145 0.165

Nor

mal

izin

g va

lue(

％)

poresize(mm)

ALLLNAPLEntire pore size

Pore size with LNAPL

41

LBM simulation for two-phase flow in porous materials

Water

LNAPL

parameters LNAPL WaterDensity ratio Relaxation time (τ) 1.167 1fluid-fluid Interaction (gf)fluid-solid Interaction (gs) -0.020 0.020

1

0.0015k

kkP

73

λk：流体の圧縮性に関係するパラメータ

42

Pipe model for LBM simulation

Comparison porous material with pipe modelGlass beads Pipe model

43

Discussion of results for pipe model

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

AB C

D E FG H I

Definition of each areaPipe model

5

5

1nnX

Mean diameter along the flow direction =

X：location(A～I)

Aspect ratio along the flow direction =

4

4

11

nnn XX

X：場所(A～I)

44

db

ca

0

3

6

0.06 0.08 0.1

インクビン効果係数

平均間隙径(㎜)

a b

c d

45

Discussion of results for pipe model

5

5

1nnX

Mean diameter along the flow direction =

X：location(A～I)

Aspect ratio along the flow direction =

4

4

11

nnn XX

X：場所(A～I)0

3

6

0.06 0.08 0.1

インクビン

効果係数

平均間隙径(㎜)

ABCDEFGHI

0

50

100

150

200

250

300

A B C D E F G H I

Pene

tratio

n di

stan

ce (v

oxel

)

Area各領域(A～I)におけるLNAPLが浸透した距離

46

a

c d

b

a b

c dConnectivity of pore structure for LNAPL flow means the large mean diameter and less aspect ratio along flow direction.

Discussion of results for pipe model

47

Conclusions

poresmall large

X-ray CT image analysis and LBM simulationcan Evaluate LNAPL migration in porous media.

Conclusions

(～1μm)

Grain

Water

LNAPL

Air

Pore-Scale

Core-Scale

Small-size blockLarge-size block

(1cm～)

(1m～) (10m～)Representative

parameter

Average

0)( gpKk

tS r

We don’t say X-ray CT scanner can solve many geotechnical and geoenvironmental issues. X-ray CT scanner is a powerful tool to observe the inner condition of materials. Of course, the sample size is too small to evaluate real condition. Hence, we need to develop the model to connect micro observation and macro observation.