Lattice Boltzmann Simulations of Supercritical CO2–Water Drainage

Nov 26, 2014 - ... Supercritical CO2–Water Drainage Displacement in Porous Media: CO2 ... For a more comprehensive list of citations to this article...
0 downloads 0 Views 1MB Size
Subscriber access provided by UNIV OF UTAH

Article 2

Lattice Boltzmann Simulations of Supercritical CO-Water Drainage Displacement in Porous Media: CO Saturation and Displacement Mechanism 2

Hirotatsu Yamabe, Takeshi Tsuji, Yunfeng Liang, and Toshifumi Matsuoka Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/es504510y • Publication Date (Web): 26 Nov 2014 Downloaded from http://pubs.acs.org on December 2, 2014

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Environmental Science & Technology is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 25

Environmental Science & Technology

1

Lattice Boltzmann Simulations of Supercritical CO2-

2

Water Drainage Displacement in Porous Media:

3

CO2 Saturation and Displacement Mechanism

4

Hirotatsu Yamabe†*, Takeshi Tsuji††, Yunfeng Liang†, and Toshifumi Matsuoka†

5



6

††

7

University, Fukuoka 819-0395, Japan

Environment and Resource System Engineering, Kyoto University, Kyoto 615-8540, Japan International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu

8 9 10

Conflicts of Interest The authors declare no competing financial interest.

11 12

TOC/Abstract Graphic

13

ACS Paragon Plus Environment

1

Environmental Science & Technology

Page 2 of 25

14

ABSTRACT

15

CO2 geosequestration in deep aquifers requires the displacement of water (wetting phase) from

16

the porous media by supercritical CO2 (non-wetting phase). However, the interfacial instabilities,

17

such as viscous and capillary fingerings, develop during the drainage displacement. Moreover,

18

the burst-like Haines jump often occurs under conditions of low capillary number. To study these

19

interfacial instabilities, we performed lattice Boltzmann simulations of CO2-water drainage

20

displacement in a 3D synthetic granular rock model at a fixed viscous ratio and at various

21

capillary numbers. The capillary numbers are varied by changing injection pressure, which

22

induces changes in flow velocity. It was observed that the viscous fingering was dominant at

23

high injection pressures, whereas the crossover of viscous and capillary fingerings was observed,

24

accompanied by Haines jumps, at low injection pressures. The Haines jumps flowing forward

25

caused significant drop of CO2 saturation, whereas Haines jumps flowing backward caused

26

increase of CO2 saturation (per injection depth). We demonstrated that the pore-scale Haines

27

jumps remarkably influenced the flow path and therefore equilibrium CO2 saturation in crossover

28

domain, which is in turn related to the storage efficiency in the field-scale geosequestration. The

29

results can improve our understandings of the storage efficiency by the effects of pore-scale

30

displacement phenomena.

31 32 33

ACS Paragon Plus Environment

2

Page 3 of 25

34

Environmental Science & Technology

INTRODUCTION

35

CO2 geosequestration is one of the promising solutions for reducing carbon emissions

36

and global warming.1-3 The estimation of geological CO2 storage capacity, evaluation of leakage

37

risk, and enhancement of storage efficiency are current focuses and require understanding of

38

microscopic CO2 flow in porous media, such as the fingering phenomenon.

39

To examine CO2 flow in porous media, a number of experimental studies have been conducted.

40

The preceding experiments can be divided into two approaches: core-flooding experiments using

41

magnetic resonance imaging (MRI) or X-ray computed tomography (CT)4-9 and the observation

42

of fluid displacement in fabricated micromodels.10-14 With X-ray CT scanners or MRI, we can

43

measure the saturation and fluid distribution changes during core flood experiments with CO2.4-8

44

However, the microscopic fluid state cannot be detected with medical CT scanners due to not

45

high resolution (millimeter scale) compared with pore sizes. The resolution of microfuocus CTs

46

are high, but it takes a long time to take one image unless fast synchrotron-based sources are

47

used.9 Recent advances in microfabrication have enabled us to create arbitrary micropore

48

network models. The experimental studies with two-dimensional microporous media have been

49

conducted to reveal the mechanisms of immiscible fluid displacement. Despite the use of simple

50

two-dimensional porous media, the contributions of these experimental studies to knowledge of

51

fluid dynamics are considerable.10-14

52

In general, understanding the flow of multiphase fluids in porous media has been a

53

subject of great interest over a wide range of scientific and engineering disciplines.11,

14-20

54

Lenormand et al. have discussed the pore-scale displacement mechanism of the drainage process

55

from the standpoint of viscous and capillary forces.21 The effects of these forces on drainage

56

displacement processes can be characterized by two dimensionless numbers: the capillary

ACS Paragon Plus Environment

3

Environmental Science & Technology

Page 4 of 25

57

number (Ca), which is defined as Ca = µinUin/σ, where µin, Uin, and σ are the viscosity of injected

58

fluid, velocity of the injected fluid, and interfacial tension, respectively; and the viscosity ratio

59

(M), defined as the ratio of viscosities of the non-wetting and wetting fluids. In subsurface rocks,

60

CO2 phase usually behaves as non-wetting phase, thus the displacement process in CCS can be

61

considered as drainage.. These phenomena have been studied in core-scale. When we consider

62

the CO2 injection in subsurface rocks, the flow speed is slow (Ca > Scrossover. However, the displacement process in the crossover region has

78

not been revealed in detail.

ACS Paragon Plus Environment

4

Page 5 of 25

Environmental Science & Technology

79

In summary, CO2 saturation in subsurface rocks is a significant factor influencing storage

80

efficiency. We need to understand CO2 displacement mechanisms and its effect on saturation in

81

reservoir conditions. To achieve that, we conducted simulation studies with the lattice Boltzmann

82

(LB) method, which enables us to simulate multiphase fluid flow in complex pore structures.

83

Drainage displacement of a water phase by CO2 is simulated in a “granular model,” which is a

84

3D rock model constructed by the packing of numerous spherical grains. In this paper, we

85

discussed the displacement mechanisms in pore-scale and its effect on core-scale CO2 saturation

86

which is related to storage efficiency.

87

METHODOLOGIES

88

Lattice Boltzmann Method

89

The lattice Boltzmann (LB) method26 has been explored as a numerical method for simulating

90

viscous fluid flow in complicated porous media because the LB method can easily handle

91

complex solid boundaries and is suitable for parallel computation.27-28 For a more detailed

92

description of the LB method, see reviews of the LB method by Succi (2001), Rothman and

93

Zaleski (1997), and Wolf-Gladrow (2000).29-31For multiphase flow simulations, various LB

94

models have been developed28, 36: the color-fluid,32 Shan-Chen,33 free-energy34 and mean-field35

95

models. In this work we used a color-fluid model because the model requires fewer grids for

96

representing interfaces and results in a reduction of computational cost. The color-fluid model

97

has a potentially serious drawback; perturbations can cause spurious fluid velocities at an

98

interface. Such a spurious velocity disturbs the fluid flow when the flow is very slow. In this

99

work, we applied a modification suggested by Latva-Kokko and Rothmann (2005) to reduce the

ACS Paragon Plus Environment

5

Environmental Science & Technology

Page 6 of 25

100

magnitude of spurious velocities.37 See the Supporting Information for a detailed LB method use

101

in this paper.

102 103

Rock Model and Simulation Conditions

104

We used a synthetic granular rock model to provide the LB simulation with a pore-

105

geometry. This model is constructed by a random packing process38 with a number of spherical

106

grains. We assumed the grain-size distribution to be “well-sorted”.39 The most important

107

parameter in the well-sorted distribution is the “sorting” parameter.40-41 Here, simulation studies

108

were conducted for a granular rock model with a sorting parameter of 0.50 and dimensions of

109

100 × 100 × 100 lattice units. Because the realistic scale of one lattice unit is configured as 10

110

µm in the present study, the size of a rock model is 1 mm × 1 mm × 1 mm. See Supporting

111

Information for the detailed description about the rock model.

112

The fluid properties used in the study are shown in Table 1. The values in Table 1

113

simulate the properties of supercritical CO2 and water at 13.8 MPa (2000 psi) and 50 °C,42-43

114

which is close to the conditions at the pilot carbon capture and storage (CCS) site in Nagaoka,

115

Japan.44 The surface of solid grains in the media was configured to be completely hydrophilic. It

116

should be noted that the dissolution and mineralization is not considered in this study, thus the

117

flow is under the condition of immiscible flow. We set identical densities for both fluids (994

118

kg/m3), and the viscosities of both fluids were configured as 10 times the realistic viscosities

119

because the multiphase LB model used in this study cannot deal with density contrasts and small

120

viscosities. The effects of these assumptions are discussed in the last section in this paper.

ACS Paragon Plus Environment

6

Page 7 of 25

Environmental Science & Technology

121

We conducted 6 case studies, designated “Case 1” to “Case 6,” by changing the injection

122

pressure. Differences in injection pressure alter the fluid velocity and capillary number. In the

123

present study, the capillary number was calculated by using the average fluid velocity until the

124

CO2 front reached the outlet (breakthrough). The fluid velocity (UCO2) was calculated from the

125

CO2 flux (QCO2), which can be defined as the rate of CO2 volume change; QCO2 = dVCO2/dt,

126

where VCO2 is the volume of CO2 at each time step. The fluid velocity is obtained by dividing the

127

CO2 flux by the cross-sectional area of the rock model (A), i.e. UCO2 = QCO2/A. The calculated

128

capillary numbers for the case studies were 1.21×10−3, 6.35×10−4, 3.42×10−4, 1.07×10−4,

129

5.13×10−4, and 2.90×10−5 for Cases 1–6. The conditions simulated in the present study are

130

plotted on the phase diagram in Figure 1. The capillary numbers in this study varied by two

131

orders of magnitude, this is the limitation of current lattice Boltzmann model. When the capillary

132

number is lower than the limit, i.e. the flow speed is slow, fluids cannot flow due to the

133

prevention by spurious velocity.

134 135

NUMERICAL RESULTS AND DISCUSSION

136

In the simulation studies, CO2 was injected into a synthetic granular medium saturated

137

with water. The injection direction was defined as the x-direction. The simulation continued until

138

the distributions and saturation of fluids reached an equilibrium state. Simulated CO2

139

distributions in six case studies are shown in Figure 2.

140

Displacement Mechanism

ACS Paragon Plus Environment

7

Environmental Science & Technology

Page 8 of 25

141

For the purpose of discussing the displacement mechanism, we focused on Cases 2 and 5.

142

Figure 3 shows the time series of CO2 flow in Cases 2 and 5. Clear differences in migration

143

patterns between the two cases are associated with altered displacement mechanisms imposed by

144

different capillary numbers (6.35×10−4 in Case 2, 5.13×10−5 in Case 5). The simulation results

145

shown in Figure 3 indicate characteristics of viscous and capillary fingering. In Case 2, the

146

invading CO2 flows via many fingers toward the outlet (clearly observed in Case 2-b, c and d),

147

passing through many pore spaces despite the narrow size of some pores (i.e., high capillarity).

148

This is the characteristic of viscous fingering and we can conclude that viscous fingering is the

149

dominant displacement mechanism in Case 2. In contrast, the invading CO2 in Case 5 had only a

150

few fingers passing through large pores selectively. The front of the fingers in Case 5 moved not

151

only in the direction of injection (along the x-axis) but also in the vertical direction and even

152

toward the inlet (backwards), as shown in Case 5-d in Figure 3. The movement of fingers toward

153

the inlet is characteristic of capillary fingering. Nevertheless, the front moved toward the outlet

154

(shown in the change of CO2 distribution from Case 5-d to Case 5-e) in the same time, despite

155

narrower pores. We can conclude that both viscous and capillary fingering occurred in Case 5

156

and that the crossover of viscous and capillary fingering is the dominant displacement

157

mechanism in this case.

158

Pore-Scale Displacement Event: Observation of Haines Jump

159

Figure 4 gives the plots of CO2 saturation versus the normalized position of CO2 front

160

from the inlet at each time step. Note that the plotted points show the data from injection through

161

to breakthrough. In Cases 1–3, CO2 saturation increased smoothly with increasing front position,

162

whereas the curves for Cases 4–6 are not smooth. To study the different flow characteristics and

163

the pore-scale displacement event in detail, we have investigated three particular stages of the

ACS Paragon Plus Environment

8

Page 9 of 25

Environmental Science & Technology

164

flow, as shown in Figure 4 by the vertical dashed lines. The first typical behavior is observed

165

when the normalized distance from the inlet is between 0.3 and 0.55 (labeled (i) in Figure 4). In

166

this range, the gradients of plots for low capillary numbers (Cases 4–6) are smaller than those

167

with high capillary numbers (Cases 1–3). A small gradient indicates that CO2 saturation does not

168

increase rapidly during CO2 migration toward the outlet. The small incremental increase in CO2

169

saturation is due to the presence of only a few fingers. Because the fingers of CO2 selectively

170

pass through large pores when the capillary number is low, only a few fingers grow, which cause

171

a small increment in CO2 saturation in Cases 4–6.

172

The second behavior is the most typical one; the plots for lower capillary numbers have a

173

CO2 increment without front migration in the x-direction at a normalized distance of 0.57 (range

174

(ii)). The cause of this phenomenon may be explained by a Haines jump backward. In Figure 5,

175

we focused on two sub-units (a) and (b) for Case 5 at different times. From (1) and (2), we can

176

confirm the occurrence of CO2 flow back to the inlet, which is one of the characteristics of

177

capillary fingering. By this phenomenon, two CO2 fingers coalesce. Figure 6 represents the CO2

178

pressure inside each sub-unit in Case 5. It can be observed from the plot of sub-unit (a) that the

179

back flow and coalescence of the two fingers occurred in a short time. After CO2 reached sub-

180

unit (a) at a normalized time of around 0.11, the CO2 pressure increased because of the local

181

pressure concentration. The pressure concentration caused a “burst-like flow” backward and the

182

coalescence of two CO2 fingers. This flow caused a sudden pressure drop. The phenomena

183

observed here for the flow and corresponding local pressure are characteristic of a Haines jump.9,

184

23

185

in the sub-unit had locally reached equilibrium. The CO2 cluster in the sub-unit could not migrate

186

further, and the CO2 front stopped momentarily, as shown in range (ii) in Figure 4. Note that

After the pressure drop, there was no further increase in the local pressure, indicating that CO2

ACS Paragon Plus Environment

9

Environmental Science & Technology

Page 10 of 25

187

fingers elsewhere from the sub-unit grew and migrated toward the outlet while the CO2 front

188

locally stopped in the sub-unit; these fingers are the reason for an incremental change in CO2

189

saturation without advancement of the CO2 front.

190

The third behavior is observed in range (iii) in Figure 4. As was observed in range (i), the

191

slopes for Cases 4–6 are much smaller than those for Cases 1–3 in this range. The lower slopes

192

are attributed to the fewer numbers of fingers, which is evident from the CO2 distribution at

193

breakthrough in Figure 2. Fewer fingers in this range were a result of Haines jumps. These

194

Haines jumps in the range (iii) can be observed in sub-unit (b). The flow from (3) to (4) in Figure

195

5 occurred in a short time, which can be confirmed in the graph in Figure 6, and the jump

196

decreased the CO2 pressure in sub-unit (b). In contrast to the backward Haines jump in sub-unit

197

(a), this jump occurred in the forward direction. Because of this Haines jump, breakthrough of

198

the CO2 phase occurred with only one finger around the outlet of our model.

199

Equilibrium CO2 Saturation

200

The saturation of CO2 at an equilibrium state is of great concern in the CCS project

201

because equilibrium saturation is one of the most important factors affecting storage efficiency.

202

Figure 7 shows plots of CO2 saturation versus capillary number for each case study. The highest

203

CO2 saturation was observed in Case 1 (95.87%) and the lowest in Case 6 (40.91%). Since the

204

rock model is homogeneous and isotropic, the CO2 phase can enter almost all the pore spaces

205

when the capillary number is high, thus the saturation in Case 1 is extremely high. Figure 7

206

shows that the saturation of CO2 drastically drops with decreasing capillary number. This is

207

because of crossover of capillary and viscous fingering. The decreasing trend in CO2 saturation

208

is considered reasonable when compared with preceding research.21

ACS Paragon Plus Environment

10

Page 11 of 25

Environmental Science & Technology

209

To further characterize the different behaviors, we divided the rock model into two half

210

sub-units: the inlet side of the sub-unit was denoted sub-unit 1 (x = 1–50 lattice units), and the

211

outlet side was denoted sub-unit 2 (x = 51–100 lattice units). The saturations in sub-unit 1 were

212

99.98% and 71.62% in Case 1 and Case 6, respectively; the corresponding saturations in sub-unit

213

2 were 91.72% and 9.964%, respectively. The difference in saturation between the two cases is

214

especially significant in sub-unit 2 (Figure 7). In sub-unit 1, CO2 was supplied to all pore spaces

215

because the sub-unit 1 is located on the border with the inlet boundary. However, in sub-unit 2,

216

CO2 was supplied only by the pore spaces where CO2 existed in sub-unit 1. Therefore, lower

217

capillary numbers caused larger differences in CO2 saturation between sub-units 1 and 2 because

218

CO2 selectively passed only through large pore spaces by capillary fingering.

219

The Haines jump can have a strong impact on CO2 saturation, and the impact can be

220

positive or negative. As discussed above, we observed two different types of Haines jumps,

221

going backward and forward, when the crossover of viscous and capillary fingering was

222

dominant. The “backward jump” caused the coalescence of two CO2 clusters and a decrease in

223

pressure toward equilibrium. As a result of this phenomenon, fingers in other pore spaces can

224

grow and effectively increase CO2 saturation (evident from range (ii) in Figure 4). Therefore, we

225

can conclude that the “backward jump” can have a positive impact on CO2 saturation.

226

Conversely, “forward jumps” posed fewer fingers than in cases with high capillary numbers.

227

Once the CO2 phase had reached the outlet (breakthrough), CO2 saturation could not increase

228

effectively when the capillary number was low because CO2 injected at low rates can only flow

229

along paths that had already been formed prior to breakthrough. By comparing CO2 distributions

230

at breakthrough and equilibrated states (Figure 2), we can confirm that there was little growth in

231

the CO2 fingers. This is also evident from the differences in CO2 saturation at equilibrium and

ACS Paragon Plus Environment

11

Environmental Science & Technology

Page 12 of 25

232

breakthrough. In Cases 1 and 2 (high capillary numbers), 131% and 108% increment of CO2

233

saturation after breakthrough was observed; whereas only 27.6% and 7.38% increment were

234

observed in Cases 5 and 6 (low capillary numbers), respectively. These data show that CO2

235

saturation does not significantly increase when “forward” Haines jumps occur at low capillary

236

numbers. For these reasons, the CO2 saturation in cases with lower capillary numbers was much

237

lower than in those with higher capillary numbers.

238

Implications

239

Our simulation studies demonstrated that pore-scale displacement phenomena have

240

strong effects on CO2 saturation. It was found that the existence of forward-going Haines jump

241

decreases equilibrium CO2 saturation. The typical capillary number at reservoir conditions is

242

generally believed to be at the order of 10-5.45 Our studies have shown that the CO2 saturation

243

becomes low when the capillary number is on the order of 10-5. It should be noted that the

244

relationship between the capillary number and displacement mechanisms is dependent on the

245

geometry of porous media. The granular rock model that we employed, according to us, is

246

relatively homogeneous. In addition, we have ignored the gravity effect intentionally. Even in

247

such simple case, we demonstrated that a non-uniform CO2 distribution develops as a

248

consequence of unstable displacement at pore-scale.

249

The studies were conducted by assuming different absolute viscosities of water and CO2.

250

However, the studies were conducted with fixed realistic viscosity ratio (M=1). Even though the

251

absolute values of viscosities would have influences on displacement patterns, the key of the

252

conclusion, the pore-scale phenomena (Haines jumps) have strong impact on core-scale CO2

253

saturation in porous media, would be guaranteed.

ACS Paragon Plus Environment

12

Page 13 of 25

Environmental Science & Technology

254

The results provided a fundamental understanding of CO2 behavior and its effect on

255

storage efficiency in homogeneous region in CCS site. The effect of strong heterogeneity of CCS

256

site (e.g. fractures) has not been explored in this study, however, it is important to consider the

257

possibility that typical capillary number (the order of 10-5) under reservoir conditions can make

258

the storage efficiency poor. Although the numerical studies were conducted with mm-scale, the

259

results can be upscaled by following consideration: CO2 displacement process with viscous

260

fingering will occur near an injection well where the capillary number is expected high.

261

Whenever the crossover of capillary and viscous fingering occurs, CO2 storage efficiency

262

becomes low. The latter will be observed far from an injection well where capillary number is

263

expected low.

264

ACS Paragon Plus Environment

13

Environmental Science & Technology

Page 14 of 25

265 266

Figure 1. Phase diagram showing each displacement pattern plotted in the log Ca–log M plane.

267

There exists a crossover zone among the displacement pattern zones. The boundaries described

268

with blue lines are noted by Lenormand et al. (1988)21 whereas those described with red lines are

269

results from Zhang et al. (2011).12 These boundaries are dependent on the system, especially on

270

the geometry of the porous media, therefore should be understood only as a qualitative

271

representation. The six plotted points indicated by circles represent the conditions simulated in

272

Cases 1–6, from top down.

ACS Paragon Plus Environment

14

Page 15 of 25

Environmental Science & Technology

273

ACS Paragon Plus Environment

15

Environmental Science & Technology

Page 16 of 25

274

Figure 2. CO2 distributions from the simulation results. Panels from top to bottom show

275

results of Cases 1–6. Note that the water phase is not visualized in these figures and that CO2 is

276

injected along the x-direction (from left to right). The six panels on the left show the CO2

277

distribution (red-colored parts) in the granular rock model (gray-colored) when the CO2 front

278

reached the outlet (breakthrough point); the right panels show the CO2 distribution in the

279

granular rock model when fluid flow had reached the equilibrium state.

280 281

Figure 3. Time series change of CO2 distribution in Case 2 (top) and Case 5 (bottom). From

282

left to right, the five snapshots are ordered chronologically. The last snapshots (Cases 2-e and 5-

283

e) show the equilibrated state (same as in the right panels in Figure 2).

ACS Paragon Plus Environment

16

Page 17 of 25

Environmental Science & Technology

284 285

Figure 4. Plots of evolutional CO2 saturation in a porous rock model versus distance of CO2

286

front from the inlet until breakthrough. Note that the distance is normalized by the size of the

287

porous medium.

288

ACS Paragon Plus Environment

17

Environmental Science & Technology

Page 18 of 25

289

Figure 5. CO2 distribution in Case 5 before (1) and immediately after (2) a burst-like flow

290

backward occurred, and before (3) and immediately after (4) a burst-like flow forward occurred.

291

(1-a) and (2-a) are focused CO2 distributions in sub-unit (a) shown in the white boxes identified

292

in (1) and (2); (3-b) and (4-b) show CO2 distributions in sub-unit (b) which is shown in (3) and

293

(4) as the white boxes.

294 295

Figure 6. Time series plots of CO2 pressure in the focused sub-units (a) and (b). (1), (2), (3),

296

and (4) correspond to the numbered images in Figure 5. Note that the simulation time is

297

normalized by the time at which the CO2 phase reached the outlet (breakthrough).

ACS Paragon Plus Environment

18

Page 19 of 25

Environmental Science & Technology

298 299

Figure 7. Plots of CO2 saturation versus capillary number on a logarithmic scale. The solid

300

line shows the saturation in the whole rock model and two types of dashed lines show the

301

saturation in sub-units 1 and 2. The exact value of CO2 saturation can be seen Table S2, in the

302

Supporting Information.

303 304

Table 1. Densities, viscosities, and interfacial tension used in simulations42-43. The values in

305

parentheses are the values configured in the LB simulations; the densities of both fluids are set identical,

306

and viscosities are 10 times the realistic ones.

Water (wetting)

CO2 (non-wetting)

Density (kg/m3)

994

994 (668)

Viscosity (cP)

5.51 (0.551)

0.521 (0.0521)

Interfacial Tension (mN/m)

35.0

307 308

ACS Paragon Plus Environment

19

Environmental Science & Technology

Page 20 of 25

309

Supporting Information.

310

The numerical method and synthetic rock model are detailed in the Supporting Information. The

311

CO2 saturation and its profiles in each case study are also described there. This material is

312

available free of charge via the Internet at http://pubs.acs.org.

313 314

Corresponding Author

315

*Hirotatsu Yamabe, E-mail: [email protected], TEL: +81-75-383-3206,

316

FAX: +81-75-383-3203

317 318 319

ACKNOWLEDGEMENTS

320

The authors acknowledge the financial support of the Japan Society for the Promotion of Science

321

(JSPS) through a Grant-in-Aid for Scientific Research A (no. 24246148) and JST/JICA-

322

SATREPS. H. Yamabe is grateful for the support provided by a Grant-in-Aid for JSPS 246048

323

Fellows. This research is partially supported by the Sumitomo Foundation. T. Tsuji gratefully

324

acknowledges the support of the I2CNER, sponsored by the World Premier International

325

Research Center Initiative (WPI), MEXT, Japan.

326

ACS Paragon Plus Environment

20

Page 21 of 25

Environmental Science & Technology

327

REFERENCES

328

1. Bachu, S.; Gunter, W.D.; Perkins, E.H. Aquifer disposal of CO2: hydrodynamic and mineral

329

trapping. Energy Convers. Manage. 1994, 35 (4), 269-279; DOI 10.1016/0196-8904(94)90060-4.

330

2. Metz, B.; Davidson, O.; Coninck, H.; Loos, M.; Meyer, L. IPCC Special Report on Carbon

331

Dioxide Capture and Storage; Cambridge University Press, Cambridge, U.K., 2005.

332

3. Michael, K.; Golab, A.; Shulakova, V.; Ennis-King, J.; Allinson, G.; Sharma, S.; Aiken, T.

333

Geological storage of CO2 in saline aquifers -A review of the experience from existing

334

operations. Int. J. Greenhouse Gas Control 2010, 4, 659-667; DOI 10.1016/j.ijggc.2009.12.011.

335

4. Shi, J.; Xue, Z.; Durucan, S. History matching of CO2 core flooding CT scan saturation

336

profiles with porosity dependent capillary pressure. Energy Procedia 2009, 1 (1), 3205-3211;

337

DOI 10.1016/j.egypro.2009.02.104.

338

5. Shi, J.; Xue, Z.; Durucan, S. Supercritical CO2 core flooding and imbibition in Berea

339

sandstone – CT imaging and numerical simulation. Energy Procedia 2011, 4, 5001-5008; DOI

340

10.1016/j.egypro.2011.02.471.

341

6. Shi, J.; Xue, Z.; Durucan, S. Supercritical CO2 core flooding and imbibition in Tako

342

sandstone—Influence of sub-core scale heterogeneity. Int. J. Greenhouse Gas Control 2011, 5

343

(1), 75-87; DOI 10.1016/j.ijggc.2010.07.003.

344

7. Zhao, Y.; Song, Y.; Liu, Y.; Liang, H; Dou, B. Visualization and measurement of CO2

345

flooding in porous media using MRI. Ind. Eng. Chem. Res. 2011. 50 (8), 4707-4715; DOI

346

10.1021/ie1013019.

347

8. Alemu, B.L.; Aker, E.; Soldal, M.; Johnsen, Ø.; Aagaard, P. Effect of sub-core scale

348

heterogeneities on acoustic and electrical properties of a reservoir rock: a CO2 flooding

349

experiment of brine saturated sandstone in a computed tomography scanner. Geophys. Prospect.

350

2013, 61 (1), 235-250; DOI 10.1111/j.1365-2478.2012.01061.x.

351

9. Berg, S.; Ott, H.; Klapp, S.A.; Schwing, A.; Neiteler, R.; Brussee, N.; Makurat, A.; Leu, L.;

352

Enzmann, F.; Schwarz, J.; Kersten, M.; Irvine, S.; Stampanoni, M. Real-time 3D imaging of

ACS Paragon Plus Environment

21

Environmental Science & Technology

Page 22 of 25

353

Haines jumps in porous media flow. Proc. Natl. Acad. Sci. USA. 2013,110 (10), 3755-3759; DOI

354

10.1073/pnas.1221373110.

355

10. Ferer, M; Ji, C.; Bromhal, G.S.; Cook, J.; Ahmadi, G.; Smith, D.H. Crossover from capillary

356

fingering to viscous fingering for immiscible unstable flow: Experiment and modeling. Phys.

357

Rev. E 2004, 70, 016303; DOI 10.1103/PhysRevE.70.016303.

358

11. Cottin, C.; Bodiguel, H.; Colin, A. Drainage in two-dimensional porous media: From

359

capillary

360

10.1103/PhysRevE.82.046315.

361

12. Zhang, C.; Oostrom, M.; Wietsma, T.W.; Grate, J.W.; Warner, M.G. Influence of viscous

362

and capillary forces on immiscible fluid displacement: Pore-scale experimental study in a water-

363

wet micromodel demonstrating viscous and capillary fingering. Energy Fuels 2011, 25 (8), 3493-

364

3505; DOI 10.1021/ef101732k.

365

13. Wang, Y.; Zhang, C.; Wei, N.; Oostrom, M.; Wietsma, T.W.; Li, X.; Bonneville, A.

366

Experimental Study of Crossover from Capillary to Viscous Fingering for Supercritical CO2-

367

Water Displacement in a Homogeneous Pore Network. Environ. Sci. Technol. 2013, 47 (1), 212-

368

218; DOI 10.1021/es3014503.

369

14. Al-Housseiny, T.T.; Tsai, P.A.; Stone, H.A. Control of interfacial instabilities using flow

370

geometry. Nature Phys. 2012, 8, 747-750; DOI 10.1038/nphys2396.

371

15. Lenormand, R.; Zarcone, C.; Sarr, A. Mechanisms of the displacement of one fluid by

372

another in a network of capillary ducts. J. Fluid Mech. 1983, 135, 337-353; DOI

373

10.1017/S0022112083003110.

374

16. Homsy, G.M. Viscous fingering in porous media. Ann. Rev. Fluid Mech. 1987, 19, 271-311;

375

DOI 10.1146/annurev.fl.19.010187.001415.

376

17. Weitz, D.A.; Stokes, J.P.; Ball, R.C.; Kushnick, A.P. Dynamic capillary pressure in porous

377

media: Origin of the viscous-fingering length scale. Phys. Rev. Lett. 1987, 59 (26), 2967-2970;

378

DOI 10.1103/PhysRevLett.59.2967.

fingering

to

viscous

flow.

Phys.

Rev.

E

2010,

82,

046315;

DOI

ACS Paragon Plus Environment

22

Page 23 of 25

Environmental Science & Technology

379

18. Lenormand, R.; Zarcone, C. Capillary fingering: Percolation and fractal dimension. Transp.

380

Porous Media 1989, 4 (6), 599-612; DOI 10.1007/BF00223630.

381

19. Yiotis, A.G.; Psihogios, J.; Kainourgiakis, M.E.; Papaioannou, A.; Stubos, A.K. A lattice

382

Boltzmann study of viscous coupling effects in immiscible two-phase flow in porous media.

383

Colloids Surf. A 2007, 300 (1), 35-49; DOI 10.1016/j.colsurfa.2006.12.045.

384

20. Zhu, P.; Papadopoulos, D. Visualization and quantification of two-phase flow in transparent

385

miniature packed beds. Phys. Rev. E 2012, 86, 046313; DOI 10.1103/PhysRevE.86.046313.

386

21. Lenormand, R.; Touboul, E.; Zarcone, C. Numerical models and experiments on immiscible

387

displacements

388

10.1017/S0022112088000953.

389

22. Haines, W.B. Studies in the physical properties of soils. V. The hysteresis effect in capillary

390

properties, and the modes of water distribution associated therewith. J. Agric. Sci. 1930. 20 (1),

391

97–116; DOI 10.1017/S002185960008864X.

392

23. Måløy, K.J.; Furuberg, L.; Feder, J.; Jøssang, T. Dynamics of Slow Drainage in Porous

393

Media. Phys. Rev. Lett. 1992, 68, 2161-2164; DOI 10.1103/PhysRevLett.68.2161.

394

24. Ferer, M.; Bromhal, G.S.; Smith, D.H. Two-phase flow in porous media: Crossover from

395

capillary fingering to compact invasion for drainage. Phys. Rev. E 2005, 71, 026303; DOI

396

10.1103/PhysRevE.71.026303.

397

25. Ferer, M.; Bromhal, G.S.; Smith, D.H. Crossover from fractal capillary fingering to compact

398

flow: The effect of stable viscosity ratios. Phys. Rev. E 2007, 76, 046304; DOI

399

10.1103/PhysRevE.76.046304.

400

26. McNamara, G.R.; Zanetti, G. Use of the Boltzmann equation to simulate lattice-gas

401

automata. Phys. Rev. Lett. 1988, 61 (20), 2332-2335; DOI 10.1103/PhysRevLett.61.2332.

402

27. Chen, S.; Doolen, G.D. Lattice Boltzmann method for fluid flows. Ann. Rev. Fluid. Mech.

403

1998, 30, 329-364; DOI 10.1146/annurev.fluid.30.1.329.

in

porous

media. J. Fluid.

Mech. 1988,

189

(9),

165-187;

DOI

ACS Paragon Plus Environment

23

Environmental Science & Technology

Page 24 of 25

404

28. Aidun, C.K.; Clausen, J.R. Lattice-Boltzmann method for complex flows. Ann. Rev. Fluid.

405

Mech. 2010, 42, 439-472; DOI 10.1146/annurev-fluid-121108-145519.

406

29. Succi, S. Lattice Boltzmann Equation; Oxford University Press, Oxford, U.K., 2001.

407

30. Rothman D.H.; Zaleski S. Lattice-Gas Cellular Automata: Simple Models of Complex

408

hydrodynamics; Cambridge University Press, Cambridge, U.K., 1997.

409

31. Wolf-Gladrow D. Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An

410

Introduction; Springer, New York, 2000.

411

32. Gunstensen, A.K.; Rothman, D.H.; Zaleski, S.; Zanetti, G. Lattice Boltzmann model of

412

immiscible fluids. Phys. Rev. A 1991, 43 (8), 4320-4327; DOI 10.1103/PhysRevA.43.4320.

413

33. Shan, X.; Chen, H. Lattice Boltzmann model for simulating flows with multiple phases and

414

components. Phys. Rev. E 1993, 47 (3), 1815-1820; DOI 10.1103/PhysRevE.47.1815.

415

34. Swift, M.R.; Orlandini, E.; Osborn, W.R.; Yeomans, J.M. Lattice Boltzmann simulations of

416

liquid-gas and binary fluid systems. Phys. Rev. E 1996, 54 (5), 5041-5052; DOI

417

10.1103/PhysRevE.54.5041.

418

35. He, X.; Chen, S.; Doolen, G.D. A novel thermal model for the lattice Boltzmann method in

419

incompressible limit. J. Comput. Phys. 1998, 146 (1), 282-300; DOI 10.1006/jcph.1998.6057.

420

36. Huang, H.; Wang, L.; Lu, X. Evaluation of three lattice Boltzmann models for multiphase

421

flows

422

10.1016/j.camwa.2010.06.034.

423

37. Latva-Kokko, M.; Rothman; D.H. Diffusion properties of gradient-based lattice Boltzmann

424

models of immiscible fluids. Phys. Rev. E 2005, 71, 056702; DOI 10.1103/PhysRevE.71.056702.

425

38. Mavko, G.; Mukerji, T.; Dvorkin, J. The Rock Physics Handboolk; Cambridge University

426

Press, Cambridge, U.K., 1998.

427

39. Tucker, M.E. Sedimentary petrology: an introduction to the origin of sedimentary rocks,

428

third edition; Blackwell Publishing, Oxford, U.K., 2001.

in

porous

media.

Comput.

Math.

Appl.

2011,

61

(12),

3606-3617;

DOI

ACS Paragon Plus Environment

24

Page 25 of 25

Environmental Science & Technology

429

40. Folk, R.L.; Ward, W.C. Brazos river bar: a study in the significance of grain size parameters.

430

J. Sediment. Res. 1957, 27 (1), 3-26.

431

41. Jerram, D.A. Visual comparators for degree of grain-size sorting in two and three-

432

dimensions. Comput. Geosci. 2001, 27 (4), 485-492; DOI 10.1016/S0098-3004(00)00077-7.

433

42. Chiquet, P.; Daridon, J.; Broseta, D.; Thibeau, S. CO2/water interfacial tensions under

434

pressure and temperature conditions of CO2 geological storage. Energy Convers. Manage. 2007,

435

48 (3), 736-744; DOI 10.1016/j.enconman.2006.09.011.

436

43. Ouyang, L. New correlations for predicting the density and viscosity of supercritical carbon

437

dioxide under conditions expected in carbon capture and sequestration operations. Open Pet.

438

Eng. J. 2011, 4, 13-21.

439

44. Mito, S.; Xue, Z.; Ohsumi, T. Case study of geochemical reactions at the Nagaoka CO2

440

injection site, Japan. Int. J. Greenhouse Gas Control 2008, 2 (3), 309-318; DOI

441

10.1016/j.ijggc.2008.04.007.

442

45. Lake, L. Enhanced Oil Recovery; Prentice-Hall, Englewood Cliffs, NJ, 1989.

443

ACS Paragon Plus Environment

25