Influence of Rock Mineralogy on Reactive Fracture Evolution in

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Energy and the Environment

The Influence of Rock Mineralogy on Reactive Fracture Evolution in Carbonate-rich Caprocks Kasparas Spokas, Catherine A. Peters, and Laura Pyrak-Nolte Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.8b01021 • Publication Date (Web): 09 Aug 2018 Downloaded from http://pubs.acs.org on August 10, 2018

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Environmental Science & Technology

The Influence of Rock Mineralogy on Reactive Fracture Evolution in Carbonate-rich Caprocks Kasparas Spokas1, Catherine A. Peters1*, Laura Pyrak-Nolte2,3,4 1

Department of Civil & Environmental Engineering, Princeton University, Princeton, New Jersey, 08544 2 Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana, 47907 3 Lyle School of Civil Engineering, Purdue University, West Lafayette, Indiana, 47907 4 Department of Earth, Atmospheric and Planetary, Purdue University, West Lafayette, Indiana, 47907 *Corresponding author: Dr. Catherine A. Peters ([email protected]), E417A Engineering Quad, Department of Civil & Environmental Engineering, Princeton University, Princeton, New Jersey, 08544.

ACS Paragon Plus Environment

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1 2 3

Abstract:

4

storage of greenhouse gases, because of the possibility of unwanted upward fluid migration. The

5

risks of fluid leakage may be exacerbated if fractures are subjected to physical and chemical

6

perturbations that alter their geometry. This study investigated this by constructing a 2D fracture

7

model to numerically simulate fluid flow, acid-driven reactions, and mechanical deformation.

8

Three rock mineralogies were simulated: a limestone with 100% calcite, a limestone with 68%

9

calcite, and a banded shale with 34% calcite. One might expect transmissivity to increase fastest

10

for rocks with more calcite due to its high solubility and fast reaction rate. Yet, results show that

11

initially transmissivity increases fastest for rocks with less calcite because of their ability to

12

deliver unbuffered-acid downstream faster. Moreover, less reactive minerals become persistent

13

asperities that sustain mechanical support within the fracture. However, later in the simulations,

14

the spatial pattern of less reactive mineral, not abundance, controls transmissivity evolution.

15

Results show a banded mineral pattern creates persistent bottlenecks, prevents channelization,

16

and stabilizes transmissivity. For sites for geologic storage of CO2 that have carbonate caprocks,

17

banded mineral variation may limit reactive evolution of fracture transmissivity and increase

18

storage reliability.

Fractures present environmental risks for subsurface engineering activities, such as geologic

19 20 21

1. Introduction The leakage of fluids from engineered subsurface reservoirs poses environmental

22

pollution risk (1-2), jeopardizes security of greenhouse gas containment (3), and may

23

compromise regulatory compliance (4). In subsurface environments, fractures, faults and

24

abandoned or leaky wells can act as upward leakage pathways because of their high permeability


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25

relative to surrounding media (5-7). As a result, such leakage pathways present a large risk for

26

many subsurface engineering activities, such as geologic carbon storage, natural gas storage, oil

27

and gas extraction, enhanced-oil recovery, geothermal energy production, and deep-well

28

injection of hazardous wastes.

29 30

In the context of geologic carbon storage, the injection of supercritical CO2 creates

31

geochemical and geomechanical perturbations that could exacerbate the likelihood of vertical

32

leakage of CO2. Dissolution of CO2 into resident brine creates an acidified fluid that has

33

favorable conditions for dissolving carbonate minerals (8-11). The flow of acidic fluids through

34

fractures could result in mineral dissolution that enlarges the fracture aperture and its

35

permeability (12). Moreover, injection of fluids could change effective stresses on fractures (13),

36

which could alter geochemical-geomechanical coupled processes. To avert the risks associated

37

with unwanted fracture leakage, the factors that influence the geochemical and geomechanical

38

alteration of fractures must be better understood.

39 40

Reactive flow laboratory experiments and modeling studies have found that the fracture

41

surface dissolution pattern, i.e. the spatial distribution of apertures and how it evolves, is a very

42

important determinant of how the fluid flow increases. For example, channelization, which

43

results from a positive-feedback between the delivery of acid and aperture enlargement (14), can

44

lead to very fast increase in fluid flow. Other factors that have been identified include flow rate

45

(15-24), fracture length-scale (25), fluid reactivity (14, 25-29), aperture geometry (probabilistic

46

distribution and spatial correlation) (17, 24, 30-31) and particle decohesion and mineral

47

precipitation (33-34).


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The effect of mineral heterogeneity, which we define as the presence of more than one

49

mineral phase, is less understood (12, 33-34, 35, 38-42). Mineral heterogeneity can result in

50

barriers to flow and result in the dislocation of less reactive mineral grains that clog the fracture

51

opening (12, 33). Moreover, less reactive minerals in the rock matrix can lead to the formation of

52

reaction-induced porous layers (12, 36, 38) that have been shown to suppress reaction rates by

53

serving as a diffusion barrier for mass transfer (37). In contrast, Deng et al., (39) demonstrated

54

that mineral heterogeneity can enhance fracture channelization if the reactive mineral area is

55

contiguous in the direction of flow. Similar observations have been made for porous media about

56

the effects of variable porosity, mineral heterogeneity, and “worm-holing” (43-46).

57 58

It remains unclear how mineral heterogeneity will affect the coupling of geochemical and

59

geomechanical processes. For homogenous rocks, one hypothesis is that the dissolution of rock

60

material holding the fracture walls apart could lead to wall closure and a reduction of

61

permeability (16, 25, 47-53). Subsurface rocks, however, are often not mineralogically

62

homogenous. For heterogeneous rock mineralogies, a hypothesis is that less reactive rock

63

material remains stable, props the fracture open, and inhibits fracture closure and permeability

64

decrease. This would suggest less reactive minerals could prevent dissolution-induced fracture

65

closure.

66 67

The objective of this study was to investigate the effects of mineral heterogeneity on

68

geochemical-geomechanical coupling and overall fracture evolution. This study models reactive

69

transport through fractures in mineralogically heterogeneous carbonate rocks subject to

70

mechanical stress normal to the fracture plane. To evaluate this objective, we coupled a two-


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71

dimensional (2D) fracture reactive transport model (39) and a mechanical deformation model

72

(54-55) to simulate flow, reaction and deformation at multiple confining stresses. A 2D fracture

73

reactive transport model has the potential for over-prediction of reaction in a 2D framework due

74

to over-prediction of flow and concentration gradients that could limit reaction rates (20, 39).

75

Despite this, 2D reactive transport modeling is a valuable analytical tool that allows for

76

computationally practical simulation of fracture evolution (20, 23, 30, 39), enabling exploration

77

of a large parameter space and hypothetical scenarios that are beyond experimental feasibility.

78 79

The effect of pressure dissolution (56, 57), which is a form of plastic deformation, was

80

also investigated. However, the effects of pressure dissolution were found to be small at the

81

geologic carbon storage depth (1000 meters) and temperature (323 K) modeled in this study.

82

This is because the stress at the contacting asperities were either below or not much higher than

83

the critical stress (56). Therefore, we do not include pressure dissolution results in the body of

84

the article and include it in the Supporting Information.

85 86

Simulations were performed under different constant effective normal stresses of 10 and

87

50 MPa to represent a range of possible overburden, tectonic, and fluid forces present in geologic

88

carbon storage environments. This study utilized only a single flow regime, one that results in

89

channelization in a homogenous rock fracture. This decision was purposeful, to highlight the

90

capability of mineral heterogeneity to override flow rate effects to shape the evolution of fracture

91

geometry.

92 93

The cases of mineral heterogeneity were based on rocks relevant in subsurface engineering activities, including an evaporite limestone and a carbonate-rich shale. The fracture


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94

was positioned to be orthogonal to the sedimentary bedding layers to represent vertical flow.

95

The model includes calcite as the only reactive mineral and separates heterogenous mineralogies

96

into binary mineral maps of calcite and effectively unreactive mineral. In many studies, the

97

dissolution of calcite is the primary driver of fracture enlargement and permeability increase (12,

98

14, 36-37, 39). In comparison to other minerals, calcite’s high solubility, fast dissolution kinetics,

99

and natural abundance makes calcite the mineral most likely to dissolve in quantities that cause

100

significant permeability increase (10). Other acid-sensitive minerals, such as dolomite, have

101

kinetic dissolution rate constants that are at least an order of magnitude lower than calcite (58),

102

and soluble silicates such as anorthite are rarely sufficiently abundant in sedimentary rock for

103

their dissolution to create large changes in void space. The importance of calcite is further

104

reinforced by experimental core flooding (45-46, 59) and field observation in limestone caves

105

(60). Minerals prone to oxidation reactions, such as pyrite, are also not considered because the

106

typical oxygen fugacity of deep saline formations is on the order of 10-63 bar (61), too low to

107

drive significant reaction.

108 109

2. Methods

110

2.1 System & Boundary Conditions

111

The simulated fracture geometry in this study derives from a previous experimental

112

fracture (14), which was generated in the laboratory by inducing a fracture in an Indiana

113

limestone rock core using the modified-Brazilian method. This experimental fracture geometry

114

was generated by imaging the fracture using 3D X-ray computed tomography (xCT) (62) (Figure

115

1a). To generate the 2D model of the fracture, the 3D geometry was projected onto a plane and a

116

digitized variable aperture map with a resolution of 30 µm was generated. Then, a new fracture


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117

geometry was generated in which apertures were randomly sampled from a statistically

118

representative log-normal distribution of the fracture apertures. It was assumed that there was no

119

spatial correlation length. The aperture map was then coarsened by spatial averaging to a

120 121

resolution of 560 µm (∆x and ∆y) to achieve computational efficiency. The resulting fracture size is 22.5 mm in width by 50 mm in the direction of flow (Figure 1b). The fracture plane is

122

discretized in the x and y dimensions and each grid cell has a unique aperture, b, i.e. the local

123

distance between the two fracture walls. The average aperture is 311 µm with a standard

124

deviation of 1.67 µm (Figure 1c). This is the initial fracture geometry for all the simulations. This

125

enables control of this condition in a way that cannot be controlled in experiments, where

126

separate fractures are subject to variations caused by the fracturing method.

127 128

The simulated reactive fluid was based on a 1 M NaCl brine equilibrated with CO2 at 7.7

129

MPa, resulting in a pH of 3.3 (14). Boundary conditions include no-flow boundaries along the

130

sides of the fracture and a constant pressure gradient of 6.6 Pa along the length of the fracture. A

131

constant pressure gradient was chosen to represent the conditions that may exist in the subsurface

132

for an upward fracture through a caprock that lies above a pressurized injection formation. It is

133

assumed that increasing flow through the fracture does not change large-scale formation fluid

134

pressures. Flow was simulated for ~72 hours, a timeframe that is regular for reactive flow

135

experiments at this scale, which allows for significant alteration of the fracture geometry, and is

136

not computationally cumbersome.

137

In the deformation model, the fracture is treated as two fracture walls that are held open

138

by elastic asperities. The asperities are represented as cylinders (Figure 1d) to allow for

139

analytical solutions to the elastic deformation equations. This is in contrast with the reactive


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transport model in which the asperities are modeled as rectangular prisms (Figure 1e). In the

deformation model, the diameter of the columns equals ∆x, the width of the cells in the reactive

142

transport model. Contact occurs when asperities span the distance between the two fracture walls

143

and provide mechanical support. Free-boundary conditions were assumed around the perimeter

144

of the sample. More resolved columns did not substantially change the mechanical equilibrium

145

of the fracture. While sensitivity of grid resolution was not tested for the coupled geochemical-

146

geomechanical model, previous reactive transport modeling studies have reported little to no

147

sensitivity (39, 63). a)

b) c)

[um]

y 50

x

Flo w

22.5 mm

22.5 mm

d)

m m

σn e) i Surface A i-j

j ∆y ∆y

∆x

148 149 150 151 152 153 154

22.5 mm

∆x

Figure 1. a) Schematic of an xCT image of a fractured rock core (cropped to show detail), b) 2D representation of the discretized fracture in the reactive transport model with normal stress applied orthogonal to the fracture plane, c) initial aperture map, d) the cylindrical column representation in the deformation model, and e) reactive surface area for cell i is quantified by the sum of all exposed areas (red).


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155 156 157


2.2 Reactive Transport Model To simulate reactive transport, a modified version of the 2D, variable aperture, multispecies reactive transport model developed by Deng et al., (39) was used.

158 159 160 161

For species s, the governing equation in a discrete grid cell is

= −∇ ∙ + ∇ ∙ ∙ ∇ +

(1)

where b is aperture, Cs is the molar concentration of species s, is the net volumetric flow rate,

162

Dm is the molecular diffusion coefficient, and R is the rate of reaction of species s due to calcite

163

reaction. Mechanical dispersion and tortuosity implicitly are not explicitly modeled as they arise

164

from in-plane velocity variations caused by directional aperture variation between discrete cells.

165

In addition, the model does not consider electrostatic effects and uses the same value for Dm for

166

all species, as in previous reactive transport modeling studies (38-39, 64).

167 168

To numerically solve eq 1, a five-point central difference approximation was used. The

169

procedure performs four sequential calculations during each time step: solute transport due to the

170

fluid pressure field, chemical equilibration with respect to instantaneous aqueous phase reactions,

171

kinetically-limited reaction of calcite based on local chemistry, and the final aqueous phase

172

equilibration after reaction. See Supporting Information for all modeling parameter values used.

173

The time step is determined such that the Courant number, a parameter used to ensure

174

convergence of finite difference approximations, is well-below unity. The flow field for the

175

entire 2D system is updated to reflect reaction-induced changes in fracture geometry. To

176

calculate the flow field, the 2D parallel-plate cubic law model is assumed to be valid locally

177

within each cell and a 2D steady-state mass balance is solved (65-66). Transmissivities at the cell


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178

boundaries are calculated using the harmonic mean of the cell’s and the adjacent cell’s

179

transmissivity, an update to the model of Deng et al., (39).

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180 181 182

Changes to fracture hydraulic properties are reported using transmissivity T measured along the entire length of the fracture using Darcy’s Law, =

183

QμL ∆

(2)

184

where Q is the volumetric flow rate through the fracture, µ is the viscosity of water, L is the

185

length of the fracture, and ∆P is the pressure difference along the fracture (66). The use of

186

transmissivity, rather than permeability, is purposeful as transmissivity is the parameter that

187

controls leakage in the subsurface. The importance of distinguishing the two quantities when

188

characterizing the evolution of fracture geometry both in simulation and experiments is provided

189

in the Supporting Information.

190 191

Chemical equilibrium of the aqueous phase is modeled by the carbonate system. The set

192

of primary components for which independent balance equations are written is Ca2+, CO32-, and

193

H+. Secondary aqueous species concentrations are calculated using mass action laws and a

194

charge balance equation.

195 196

The reaction rate is based on Transition State Theory, which accounts for the kinetic rate

197

and a thermodynamic driving force. The reaction rate requires the reactive surface area, and in

198

this application an important modification was made to allow for contacting asperities to dissolve.

199

In Deng et al., (39), the area modeled as exposed to reactive fluid in a cell is the planar area

200

2∆x∆y. In that model, contacting asperities cannot dissolve because they do not have an aperture


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201

(b=0), so there is no flow through the cell to dissolve the planar area rock surface. In this study,

202

the model considers the surface area exposed to flow to be both the surfaces parallel to and

203

perpendicular to flow (Figure 1e). This is represented by the eq 3 for reaction in cell i. Because

204

each perpendicular face is exposed to the solution chemistry of its adjacent cell, the calculation

205

of dissolution on each face in a cell is treated individually,

206

R =

2∆"∆# k%a'(), + , 1 −

>DE + ∑>DF ;A=> ∗ k%a'(),> + @ 1 −

207 208 209 210

%./012 + 3.

7)8

/415 1

6

9

%./012 + 3. A

7)8

/415 1

6

A

BC

(3)

where Ksp is the calcite solubility product constant, j refers to an adjacent cell, GH=I refers to the surface of cell i facing cell j (Figure 1d) that is calculated by A=> = J

∆x %b> − b + if b> − b > 0 0 if I − H < 0

(4)

(∆x = ∆y. The volume of the fluid, S, and local aperture are used to convert the reaction rate

211

into units of moles per area per time. The sum of the dissolution to all five faces is converted to

212

an aperture change in cell i to avoid variably changing cell dimensions. This assumption does not

213

account for potential thinning of asperities that could be more susceptible to deformation or

214

effects of reaction on rock mechanical properties. In experiments, these processes could lead to

215

asperity fragments breaking off, leading to fracture closure or clogging from mobile rock

216

particles that become lodged in fracture bottlenecks.

217 218 219

The dissolution kinetics of calcite is modeled assuming three parallel reactions driven by H+(aq), H2CO3(aq) and H2O (l):

\Z Z = TUV + WXY ⟷ TXY + WUV XY


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\Z = TUV + W\ UVXY ⟷ TXY + 2WUVXY

\Z = = TUV + W\ U] ⟷ TXY + WUV XY + UWXY

220

As such, the kinetic coefficient of calcite dissolution is the difference between the sum of the

221

forward rates of reaction and the backwards rate:

222 223 224

kT( = kF a^Z + k \ a^\_`V + k V a^\` − k a_`15 a_.12 1

(5)

where k1, k2, k3, kb are rate coefficients determined for high carbonic acid conditions by Deng et al., (24),aS is the activity of the species denoted by subscript s and T( is the vector of species

225

activities used in the equation. In this work, activities were determined using activity coefficients

226

calculated using the Davies equation. Because the ionic strength is dominated by the invariant

227

species, sodium and chloride, the activity coefficients are largely invariant and are modeled as

228

constants throughout the simulations.

229 230

2.3 Elastic Deformation Model

231

This study utilizes the deformation model summarized in Pyrak-Nolte & Morris, (54) which

232

simulates elastic deformation of fracture surfaces and the asperities that provide regions of

233

contact between the two surfaces. To determine the solution for a specific normal stress on the

234

fracture, σn, the separation between the fracture walls, D, is incrementally reduced until the sum

235

of all the forces on all contacting asperities equals the force on the fracture surfaces:

236

∑ f = σb A

(6)

237

where fi is the force acting on the column in grid cell i, and A is the total area of the fracture

238

domain. For a contacting asperity in cell i, the elastic deformation is solved geometrically:

239

(7)

D + W = Le − ∆L


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240 241


where Wi is the deformation of the fracture wall, feH is the original height of the column, and ∆fH is defined as

∆L = f ∗

242

gh

ij.1

(8)

243

where E is the elastic modulus of the column and a is the radius of the column. For a specific D,

244

eq 7 is written for every contacting asperity and a set of linear equations is solved for all fi.

245 246 247

Because Wi and ∆fH depend on fi, this requires an iterative process to calculate the solution at

each cell to ensure elastic deformation kH does not result in a loss of contact between the two

fracture surfaces. This study does not model incremental adjustments of the orientation of the

248

fracture walls, as this is most relevant for uniform dissolution patterns in a homogenous reactive

249

rock (52), which are not considered in this study.

250

To couple the mechanical deformation model with the reactive transport model, a

251

numerical scheme was devised in which, at every time step, the calculation of fracture

252

geomechanical equilibrium precedes the calculation of the flow field. Therefore, the dissolution

253

of rock material, which shortens column heights, results in a new initial fracture geometry in the

254

mechanical deformation model and results in a new mechanical equilibrium that affects the flow

255

field. This numerical scheme is repeated until the end of the simulation.

256 257

2.4 Heterogenous Mineralogies

258

Two heterogeneous mineral patterns were analyzed in this study: the Amherstburg

259

limestone and the Eagle Ford shale. For comparison, an all-calcite case similar to Deng et al.

260

(14) and Deng et al. (39) was used to represent a granular homogeneous limestone made up

261

entirely of calcite, such as the Indiana limestone. The Amherstburg limestone is a dolomitic-

262

limestone evaporite, and it serves as the primary caprock for the U.S. Department of Energy pilot

263

CO2 injection project that was conducted in Ostego County, Michigan. The dominant minerals in


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264

the Amhestburg limestone are calcite, dolomite, quartz, fluorite and clay minerals (41). The

265

mineralogical makeup of the fracture shows nodular pattern of calcite and substantially slower

266

reacting dolomite (12, 33, 39). The Eagle Ford shale is an organic-rich laminated shale

267

containing 34% calcite from an oil-producing region in west Texas (67). The dominant minerals

268

in the Eagle Ford shale are calcite, quartz, and clay minerals (67). The distinguishing feature of

269

this rock mineralogy is the layered structure of the minerals, reflecting the bedding planes of the

270

sedimentary rock.

271

Binary mineral maps depicting calcite and effectively unreactive minerals were

272

constructed for the homogeneous and the two heterogeneous fractures with the same resolution

273

as the fracture aperture discretization (Figure 2). For the Amherstburg limestone, x-ray

274

attenuation contrast differences in xCT images presented in Ellis & Peters, (41) were used to

275

map the location of calcite. This study uses a coarsened version of mineral map “A” from Ellis &

276

Peters, (41) which was also used in Deng et al. (39). Results from this study are not a repetition

277

however, as we apply a new aperture geometry and simulate geochemical-geomechanical

278

coupling. For the Eagle Ford shale, the basis for the mineral map was a micro-XRF elemental

279

map of a rock fracture surface generated by Fitts et al., (68). To generate the binary mineral map,

280

the elemental map (shown in the Supporting Information) was segmented based on high calcium

281

content (and low iron content). The threshold for segmentation was chosen such that the final

282

fracture contains 34% calcite. It is acknowledged that the spatial dimensions of the XRF map is

283

on the mm-scale while the simulated fracture is on the cm-scale. Still, the XRF map provides a

284

useful mineral pattern that is indicative of many sedimentary rocks at multiple length scales.


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285 286 287 288

Figure 2. Binary fracture mineralogy maps of the a) all-calcite, b) Amherstburg limestone, and c) Eagle Ford shale with respect to calcite. White denotes calcite and black denotes other minerals.

289

In the reactive transport simulations, for cells labeled as not reactive, the R in eq 1 is

290

equal to zero. Thus, the only possibility for aperture change in unreactive areas is compression

291

due to geomechanical stress.

292 293

3. Results

294

3.1 Effect of Normal Stress

295

Simulations of reactive flow and elastic deformation with the three mineralogies for σn

296

values of 10 and 50 MPa are presented in this section. The results are presented as maps of

297

change in aperture, the difference in aperture between the current and initial state, ∆b, over time

298

(Figure 3). Alteration of fracture apertures reflects contributions from both reaction-driven

299

mineral dissolution and mechanical deformation.

300 301

For higher σn, the reaction front’s propagation along the flow direction is slower than at

302

lower stress (Figure 3). There are two explanations for this. First, the initial compression of the

303

fracture to 10 and 50 MPa results in initial fracture transmissivities of 5.6 x 10-12 and 3.1 x 10-12

304

m4, respectively. Low transmissivity results in the delivery of a smaller amount of reactive fluid


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305

and slower advancement of the reaction front than for higher values of transmissivity. Second,

306

dissolution of contacting asperities removes the support that holds the fracture surfaces apart.

307

Figure 4a presents a snapshot of contact asperities of the 50 MPa all-calcite simulation at 36

308

hours. During reactive flow, asperities are preferentially dissolved due to their large surfaces

309

perpendicular to flow. The removal of asperities loads remaining asperities with more

310

compression force that results in further elastic compression and a decrease in aperture. This

311

fracture closure creates new asperities that were initially too short prior to reactive flow. This

312

competition between asperity destruction and creation remains roughly in balance throughout the

313

simulations, and fracture contact area remains mostly constant (see Supporting Information). The

314

greater the normal stress on the fracture, the larger the forces that need to be redistributed and the

315

greater the column compression. High normal stress increases the load to be redistributed and

316

results in stronger geochemical-geomechanical coupling. Under 50 MPa, dissolution-induced

317

compression results in negative changes in aperture downstream, i.e. apertures become smaller

318

than the initial aperture prior to flow (Figure 4a). In comparison, the aperture change for the 10

319

MPa simulation shows no negative values because the fast reaction front increases apertures

320

downstream and the redistribution of the load onto the remaining asperities results in only a

321

small amount of additional compression.

322 323

Comparison between the 10 MPa and 50 MPa simulations of the Amherstburg limestone

324

and the Eagle Ford shale also shows a relative decrease in aperture (Figure 4b and 4c) and

325

transmissivity rise (Figure 3). However for heterogeneous fractures, nonreactive areas are not

326

chemically eroded (Figure 4c) and provide sustained mechanical support. This weakens the

327

geochemical-geomechanical coupling and inhibits fracture closure. As a result, the difference


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328 329


between the 10 and 50 MPa horizontally-averaged ∆b profiles is the smallest for the Eagle Ford Shale (Figure 4c).

330 331

3.2 Effect of Mineral Heterogeneity

332

Comparison of the three fracture evolutions showcases how mineral heterogeneity, and

333

specifically the spatial distribution of less reactive minerals, can result in an increase or decrease

334

in the rate of transmissivity increase compared to the all-calcite fracture. For the all-calcite

335

mineralogy (Figure 3a), high solution reactivity near the fracture inlet causes the greatest

336

increase in aperture, but the increase in alkalinity from mineral dissolution neutralizes the acid

337

and reduces the reactivity downstream and limits transmissivity increase due to unreacted

338

downstream apertures. However after 20-30 hours, once instabilities in the reaction front are

339

established, flow channels are established because of the positive feedback between enlarging

340

aperture and reactive flow delivery. Soon after the channel spans the length of the fracture,

341

transmissivity rapidly increases. This is confirmed when comparing snapshots of aperture change

342

maps with simulation time (Supporting Information).

343 344

For the Amherstburg limestone (Figure 3b), a channel develops on the left side, much

345

like for the all-calcite fracture, around the nodular areas of unreactive minerals. This channel

346

development arises from a connected path of reactive minerals in the direction of flow and the

347

same channelization process observed for the all-calcite fracture (Figure 3b). In comparison with

348

the all-calcite simulation, the transmissivity of the Amherstburg limestone rises faster due to

349

faster reaction-front propagation, as can be slightly seen in Figure 3b. At 52 hours for the 50

350

MPa simulations, the transmissivity of the all-calcite simulation has risen by a factor of 2.8. In


17


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351

contrast, the Amherstburg limestone simulation transmissivity has risen by a factor of 13.0. The

352

reaction-front propagates faster for the Amherstburg limestone because there is less calcite rock

353

material to dissolve and neutralize the reactive fluid, which allows flow to remain reactive and

354

dissolve rock material farther downstream.

355 a)

All-Calcite

Transmissivit y Evolution

∆b [µm] 500+

1515

100% Calcite

400

200

5

50 MPa

T/Torigina l

10 MPa

T/ Toriginal

10 10

300

55

100

0

Amherstburg Limestone

b)

8 8

16 16

24 24

∆b [µm] 500+

32 32

Time [Hrs]

40 40

48 48

56 56

64 64

56 56

64 64

Time [Hrs] 15

15

400

200

50 MP a

10 MP a

T/To rigin al

T/ Toriginal

68% Calcite

10 10

300

55 100

0 0

Eagle Ford Shale

c)

88

16 16

24 24

∆b [µm]

32 32

Time [Hrs]

40 40

48 48

Time [Hrs] 15

500+

300

200

T/ Toriginal

34% Calcite

400

10

10 MPa

Flow

5

356 357 358 359 360 361 362 363

50 MPa

100

y

x

8

10 MPa

16

24

50 MPa

32

40

48

56

64

Time [Hrs]

Figure 3. Left: Aperture change maps (∆b) for reactive transport simulations after 36 hours with 10 MPa and 50 MPa stress: a) all-calcite, b) Amherstburg limestone and c) Eagle Ford shale. Right: Transmissivity evolution of the three mineralogies at 10 MPa and 50 MPa.

The dissolution patterns and transmissivity trajectories of the Eagle Ford shale simulations, however, are starkly different. For this rock, the reactive and nonreactive minerals


18

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364

are in a layered pattern corresponding to the sedimentary bedding layers of the shale. This

365

banded mineralogy is orthogonal to flow and inhibits channelization, which results in flow

366

“bottle-necks” along the layers of unreactive minerals (Figure 3c). Dissolution patterns of the

367

Eagle Ford shale simulations agree with images from previous reactive transport studies

368

examining layered rocks (12).

369 370

Comparing the transmissivity trajectories for the three mineralogies (Figure 3), the Eagle

371

Ford, which is the mineralogy with the least calcite content, has transmissivity trajectories that

372

are very different from the all-calcite and Amherstburg limestone simulations. Initially, the Eagle

373

Ford shale has the fastest transmissivity increase, reflecting the rapid front-propagation, due to

374

reduced acid neutralization, and sustained support caused by the large distributed amount of

375

unreactive area. This alone would suggest that transmissivity increase is inversely related to

376

reactive mineral content initially. Later in the simulations, however, the pattern of reactive

377

mineral controls the increase in transmissivity. The transmissivity of Eagle Ford stabilizes as the

378

unreactive layers remain and limit the transmissivity along the fracture plane.

379 380 381 382


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383 384 385 386 387 388

Figure 4. Left: Location of contact points for reactive transport under 50 MPa after 36 hrs. Right: Horizontally-averaged aperture change under 50 MPa (Red) and 10 MPa (Blue) of the a) allcalcite, b) Amherstburg Limestone, and c) Eagle Ford Shale. The initial asperity map at 50 MPa is provided in the Supporting Information.

389

4. Environmental Significance

390

This work is a novel contribution to subsurface engineering because it shows that certain

391

spatial patterns of less reactive minerals provide sustained flow bottlenecks and impede

392

channelization, even under flow regimes that promote channel formation in mineralogically

393

homogenous fractures. This study supports the idea that the spatial distribution of minerals, not


20

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394

just abundance, has a significant effect on the overall evolution of the fracture and its

395

transmissivity. The fastest transmissivity increase overall occurs in heterogeneous fractures that

396

have a contiguous pathway of reactive mineral in the direction of flow that allows for

397

channelization and reduced acid neutralization. This is consistent with findings by Deng et al.,

398

(39). Conversely, mineral heterogeneity can also result in barriers to transmissivity increase, as

399

was seen with bands of unreactive minerals perpendicular to flow, which act as sustained

400

bottlenecks to flow. This results in an entirely different transmissivity trajectory, one that

401

stabilizes rather than accelerating continuously.

402

This study also makes a significant contribution to understanding the interrelation

403

between mineral dissolution and geomechanical forces. Fracture transmissivity evolution in

404

homogeneous carbonate rocks is delayed by normal stress because when asperities dissolve,

405

fracture walls compress, and stress is redistributed to new contact points. For fractures in rocks

406

with heterogeneous mineralogy, fracture transmissivity is less affected by geomechanical forces

407

because the persistence of asperities composed of nonreactive minerals resists fracture

408

compression. An implication for future experimental and modeling studies is that ignoring

409

confining stress or artificially propping fractures open with epoxy would reduce or eliminate

410

geomechanical processes. Such conditions may lead to an overestimation of the enlargement in

411

aperture and transmissivity expected in subsurface fractures caused by the flow of reactive fluids.

412

Although not modeled in this study, another implication for future studies is that reaction-

413

induced decohesion of unreactive minerals (33) or fracture formation orthogonal to flow under

414

stress could further affect fracture closure and needs to be investigated in the context of coupled

415

geochemical-geomechanical processes.

416


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417

Beyond the laboratory scale, the retardation or acceleration of reactive fronts by

418

mineralogy or stress may have significant consequences for the timing of transmissivity increase

419

in larger scale fractures in subsurface engineered environments. As shown in the study,

420

channelization could lead to significant increases in transmissivity at short timescales. At the

421

field scale, the onset of transmissivity increase associated with the breakthrough of a channel

422

along the length of the fracture could take a long time. Furthermore, delay of channel

423

breakthrough caused by different normal stress conditions or rock compositions will be much

424

longer than the delays observed in this laboratory-scale study. Conversely, if injection of fluids

425

in the subsurface increases pore pressure and reduces the effective normal stress (13), this could

426

speed up channel breakthrough and result in earlier transmissivity increase. Questions remain as

427

to whether the nodular spatial pattern of unreactive minerals in the Amhersburg becomes

428

homogenously distributed at larger scales. As noted in Deng et al. (39), extending the lateral

429

width of the simulated fracture could result in the emergence of a continuous reactive mineral

430

pathway. However, upward fractures of larger length scales often penetrate multiple stratified

431

bands of lithologies, some of which may be relatively unreactive compared to carbonate-rich

432

layers (69). Identifying such bands of unreactive minerals and their lateral extent at specific sites

433

will be important to assess the risk of altering leakage pathways. This has significant

434

implications for the choice of caprock formations and should be included in carbon storage risk

435

assessments (70-71).

436 437

In summary, our work suggests that the spatial pattern of minerals is an equally important

438

evaluation criterion of caprock integrity in addition to the abundance of reactive minerals.

439

Although pure calcite limestone formations are assumed to be the most susceptible to


22

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440

transmissivity increase, our simulations show that mineralogically heterogeneous fractures with

441

contiguous calcite mineral pathways could result in faster transmissivity increases than for all-

442

calcite limestone fractures. Conversely, calcite-rich layered mineralogies with unreactive layers

443

act as flow barriers that stabilize transmissivity increase. Therefore, even calcite-rich caprocks

444

with bands of relatively less reactive minerals that are perpendicular to potential flow paths can

445

withstand chemical perturbations and may be reliable caprocks for geologic CO2 sequestration

446

sites.

447 448

Acknowledgement:

449 450 451 452

Department of Energy under Grant DE-FE0023354 to Princeton University (via Penn State University). LJPN contributions were supported by the Center for Nanoscale Controls on Geologic CO₂ (NCGC), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award # DE-AC02-05CH1123.

453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476

Supporting Information: X-ray fluorescence map of the Eagle Ford shale used for mineralogical map. Methodology and results of including pressure dissolution in model. Table of modeling parameters. Discussion of the importance of distinguishing permeability and transmissivity using results. Figure tracking the evolution of contact area for the all-calcite fracture simulation at the three normal stresses.

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For Table of Contents only: Fracture Aperture Evolution

Transmissivit y Evolution

Nodula r

T/ Toriginal

Minera lo

gy

15

10

g Mineralo Banded

665 666 667

Flow

5

8

Banded mineralogy creates

16

24 32 40 Time [Hrs]

48

y

56


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Influence of Rock Mineralogy on Reactive Fracture Evolution in

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