Received: December 15, 2015 Revised: March 1, 2016

Transcription

1 rjm00 ACSJCA JCA /W Unicode research.3f (R3.6.i11: alpha 39) 2015/07/15 14:30:00 PROD-JCAVA rq_ /20/ :43:35 12 JCA-DEFAULT pubs.acs.org/ef 1 Where Lower Calcite Abundance Creates More Alteration: Enhanced 2 Rock Matrix Diffusivity Induced by Preferential Dissolution 3 Hang Wen, Li Li,*,,, Dustin Crandall, and Alexandra Hakala 4 John and Willie Leone Family Department of Energy and Mineral Engineering, The Pennsylvania State University, University Park, 5 Pennsylvania 16802, United States 6 Earth and Environmental Systems Institute (EESI), The Pennsylvania State University, University Park, Pennsylvania 16802, United 7 States 8 EMS Energy Institute, The Pennsylvania State University, University Park, Pennsylvania 16802, United States 9 Geological and Environmental Systems Directorate, Research and Innovation Center, National Energy Technology Laboratory, 10 Pittsburgh, Pennsylvania 15236, United States 11 ABSTRACT: Fractured rocks are essential for flow, solute transport and energy production in geosystems. Existing studies on 12 mineral reactions in fractured rocks mostly consider single mineral systems where reactions occur at the fracture wall without 13 changing rock matrix properties. This work presents multicomponent reactive transport numerical experiments in a fractured 14 rock from the Brady s field, a geothermal reservoir at a depth of 1,396 m in the Hot Springs Mountains, Nevada. Initial porosity, 15 permeability, mineral composition (quartz, clay, and calcite), and fracture geometry are based on microscopy characterization and 16 X-ray tomography. The model was calibrated using a CO 2 -saturated water flooding experiment. Three numerical experiments 17 were carried out with the same initial physical properties however different calcite content. Although total dissolved masses are 18 similar among the three cases, abundant calcite (50% (v/v), calcite50) leads to a localized, thick zone of large porosity increase 19 while low calcite content (10% (v/v), calcite10) creates an extended and narrow zone of small porosity increase resulting in 20 surprisingly larger change in effective transport property. After 300 days of dissolution, effective matrix diffusion coefficients 21 increase by 9.9 and 19.6 times in calcite50 and calcite10, respectively, inducing corresponding 2.1 and 3.2 times rise in the slopes 22 of power law tailing, a measure of transport properties. This counterintuitive results suggest that lower abundance of reactive 23 minerals leads to greater alteration in the fractured media. Detailed analysis show that the effective rates of the fast-dissolving 24 calcite are limited by diffusive transport in the altered matrix and the shape of the altered zone. In contrast, the while effective 25 dissolution of slow-dissolving quartz depends on effective diffusion within the entire rock matrix. Calcite dissolution only occurs 26 at the thin altered unaltered matrix interface of tens of micrometers thickness occupying less than 1% of the total calcite content. 27 In contrast, all quartz are effectively dissolving. This work highlights the importance of mineralogical complexity in determining 28 mineral dissolution and rock matrix property evolution. 1. INTRODUCTION 29 Fractured rocks play a critically important role in geosystems, 30 including geothermal reservoirs, 1,2 nuclear waste repositories, 3,4 31 hydrocarbon reservoirs, 5 and deep saline aquifers for carbon 32 geosequestration. 6,7 These applications perturb the subsurface, 33 leading to geochemical disequilibrium and rock fluid inter- 34 actions including mineral reactions, sorption, and ion exchange. 35 These reactions change fluid composition, rock structure, and 36 conductive properties, ultimately affecting long-term function- 37 ing of geosystems. 8,9 Fractures present predominant conductive 38 pathways for energy, mass, and flow in these systems, while the 39 adjacent rock matrix significantly retards solute transport 40 through diffusive mass exchange with fractures The 41 interactions among fractures and rock matrix can play a pivotal 42 role in the property evolution of fractured rocks. 43 Extensive experimental and numerical studies have explored 44 fracture characteristics and property alteration induced by 45 reactive flow, including initial aperture size and fracture 46 roughness, 14,15 fracture orientation, 16 and fracture length. 17,18 47 Injection rates, temperature, chemical composition, 16,19,20 and 48 mechanical stress 21,22 have also been examined and shown to 49 be important for describing the evolution of fracture properties. Recent studies have explored the application of dimensionless 50 numbers, including Damkoḧler and Pećlet numbers, in unifying 51 dissolution behavior under different flow regimes. 23,24 52 Most of these studies include single minerals without 53 explicitly considering multicomponent reactive transport with 54 thermodynamically and kinetically distinct geochemical reac- 55 tions. Mineral dissolution/precipitation has been assumed to 56 occur only at the fracture surface and therefore does not alter 57 the properties of the rock matrix. 15,25 Natural rocks, however, 58 are typically composed of multiple minerals. For example, 59 limestones are mostly carbonates coexisting with quartz, 60 feldspars, and clays. 26 Sandstones are dominated by quartz 61 and often co-occur with clays and carbonate cements. 27 Mineral 62 reactivity varies by orders of magnitude. Under far-from- 63 equilibrium conditions, carbonate dissolves at rates orders of 64 magnitude higher than those of quartz dissolution. 28,29 In 65 fractured rocks composed of multiple minerals, fast-reacting 66 minerals preferentially dissolve along fracture matrix interfaces 67 Received: December 15, 2015 Revised: March 1, 2016 XXXX American Chemical Society A

2 f1 Energy & Fuels 68 and leave behind slow-reacting minerals, therefore forming 69 altered zones with higher porosity and diffusivity in the rock 70 matrix at the vicinity of the fracture. Such property alteration 71 can change fracture matrix mass exchange and have profound 72 implications for fractured rock evolution. 73 Recent experimental studies have documented formation of 74 altered zones in the presence of multiple reactive minerals. 75 Gouze et al. 30 observed dissolution overhangs in fractured 76 marine carbonates (85% calcite) and called for a revisit of the 77 conventional effective aperture definition. Noiriel et al suggested that altered zones in fractured argillaceous limestones 79 act as diffusion barriers for fluid accessibility to rock matrix. 80 Ellis et al. 32 and Noiriel et al. 8 observed that calcite preferential 81 dissolution in fractured limestones leads to nonuniform 82 aperture increase and altered zones mostly composed of 83 dolomite and clay, which changes both fracture roughness and 84 hydraulic conductivity. 33 In a fractured argillaceous sample, 85 however, calcite dissolution increases matrix porosity by 50% 86 while hydraulic conductivity remains unchanged. 6 In these 87 experiments, the complexity of chemical analysis and sample 88 geometry characterizations prevent detailed mechanistic under- 89 standing and quantification of fracture matrix property 90 evolution. 91 The objective of this study is to understand and quantify the 92 role of mineral composition, in particular preferential calcite 93 dissolution, in determining property evolution of the fractured 94 rock, including both the fracture and rock matrix. Numerical 95 experiments of multicomponent reactive transport were carried 96 out in a fractured rock built upon image data from CT 97 scanning. The fractured rock contains mostly quartz and illite/ 98 muscovite with a minor amount of calcite. The initial calcite 99 abundance was varied to understand its role in determining 100 property evolution relevant to flow and transport. 2. CHARACTERIZATION OF THE FRACTURED ROCK 101 Sample Characterization. A core sample with a diameter of cm was from a depth of 1,396 m at Brady s field in the Hot Springs 103 Mountains, Nevada, an extensively studied field for enhanced 104 geothermal application. 34 The subsurface contains over 2 km of 105 faulted and fractured mesozoic granite and metamorphic rocks that 106 rest upon ash flow tufts and/or metamorphic basement rocks. The 107 sample was fractured artificially using a hydraulic core splitter. The 108 rock matrix porosity, measured by helium porosimeter HP (TEMCO, Inc.), varies between 0.87 and 1.54%. The rock 110 permeability, determined by servohydraulic, triaxial test system 111 Autolab-1500 (New England Research, Inc.), ranges between and m 2. X-ray diffraction analysis indicated rock 113 composition of primarily quartz (25 50% (v/v)), illite/muscovite 114 (25 50% (v/v)), and calcite (5 25% (v/v)). The formation water is 115 mostly sodium chloride at an estimated concentration of mol/l 116 and is considered at equilibrium with calcite Fracture Geometry Acquisition. High-resolution CT scanning 118 was performed to obtain 3D fracture geometry at a resolution of μm using an M-5000 industrial computed tomography system (North 120 Star Imaging Inc.). Details of the CT parameters are documented in 121 Crandall et al. 36 The radiographs were reconstructed into a 3D 122 geometry and exported using efx software (North Star Imaging). An 123 OTSU threshold technique and careful examination of CT registration 124 was used to isolate the fracture. 36 Details of the technique capability, 125 limitations, and challenges for the fracture matrix identification can be 126 found in Wildenschild et al. 37 and Schlueter et al. 38 To reduce the 127 computational cost, a longitudinal 2D slice of 49.3 mm mm mm was extracted and was discretized into 174,720 grid blocks 129 ( voxels, Figure 1). Zero aperture locations within this 130 two-dimensional cross-section were assigned a nominal aperture value 131 to enable continuity of flow in this subdomain. 3. MULTICOMPONENT REACTIVE TRANSPORT NUMERICAL EXPERIMENTS Flow Field Calculation. Although fluid flow within a fracture can be fully described by the Navier Stokes (N S) equations, its combination with detailed, multicomponent geochemical reactive transport representation and evolving flow fields with changing matrix properties is computationally expensive. 39 Various approaches exist to simplify flow field calculation in fractured media, including the cubic law, 40 the classical local cubic law (LCL), 41,42 along with other extensions and modifications. 43,44 Among these, we chose to use a recent development, the modified local cubic law (MLCL). 45 MLCL takes into account weak inertia, tortuosity, and roughness, while at the same time it is relatively straightforward to implement. Briefly, the MLCL solves the following equation for the pressure field: T cos( θ) P = 0 C where T is the local transmissivity (m 2 /s) in the main flow direction x; C is the correction factor incorporating local roughness and inertia; θ is the local flow-orientation angle estimated based on tortuosity in the x direction; and P is fluid pressure (Pa). The local transimissivity T ix in the grid block ix 3 2 af( xix) af( xix+ 1) T 3 1 ix 3 af( xix) + af( xix+ ) 12μ is calculated following =, with a 1 3 f (x ix ) and 153 a f (x ix+1 ) being the flow-oriented aperture calculated based on 154 apparent aperture at the grid blocks ix and ix+1, respectively; μ 155 is fluid viscosity ( Pa s at 150 C 46 ). Values of C 156 depend on local fracture and flow characteristics and are 157 provided in a lookup table in the Supporting Information of 158 Wang et al The pressure solution to eq 1 gives a one-dimensional flow 160 field in the main flow x direction, which is further distributed 161 into flow velocities in the z direction transverse to the main 162 flow based on the parabolic law: = z u x() z 1.5Ux a ( x) f Figure 1. (A1 and A2) Three-dimensional fracture sample map with images from high-resolution X-ray computed tomography. (B) A twodimensional cross-section indicated by the red box A B in panel A2 is used for the 2D simulations in this work. (1) (2) B

3 Energy & Fuels Table 1. Reaction Network, Reaction Thermodynamics, and Kinetics at 150 C chemical reactions a log K eq log[k/((mol/m 2 )/s)] b SSA (m 2 /g) c Mineral Dissolution and Precipitation (Kinetically Controlled) SiO 2(s) SiO 2(aq) CaCO 3(s) Ca + CO KAl 2(AlSi3O 10)(OH) 2(s) + 3H2O + H + K + 3Al(OH) 3(aq) + 3SiO 2(aq) Aqueous Speciation (at Equilibrium) + HO 2 H + OH HCO 2 3 H + HCO HCO3 H + CO CaHCO3 Ca + HCO CaCO (aq) Ca + CO Ca + OH CaOH SiO (aq) + 2H O 2H + H SiO SiO 2(aq) + 2H2O H + H3SiO Al(OH) (aq) Al + 3OH 3 2+ Al(OH) (aq) AlOH + 2OH Al(OH) 3(aq) Al(OH) 2 + OH Al(OH) 3(aq) AlO(OH) 2 + H 5.50 a Equilibrium constants K eq were interpolated using data from the EQ3/6 database. 63 b Kinetic rate constants were adjusted to produce data in Andreani et al. 6 They fall well into the reported range in the literature. k quartz is the same as that from the direct experimental measurement at 150 C. 29 Ea 1 1 The k calcite and k muscovite at 150 C were calculated using the formula, k = k25 exp ( R ). For calcite and muscovite, the k 25 values are and (mol/m 2 )/s while the E a values are 23.5 and 22.0 kj/mol, respectively c Specific surface areas (SSA) are from refs 29, 65, and where z is the transverse distance to the center of the aperture 166 (m), u x (z) is the local fluid velocity (m/s) in the longitudinal 167 direction, and U x is the average velocity (m/s) at the x location 168 calculated from the MLCL. By doing so we obtain a 2D flow 169 field with flow velocities in the x direction following MLCL and 170 in the z direction following the parabolic law, ensuring that flow 171 is zero at the fracture wall and is fastest in the center of the 172 fracture. 173 In this study, the fractured rock has an average flow velocity 174 of m/s that is within the typical range ( m/s) for geothermal energy operations 48 and a Re number of that is within the applicable range of the MLCL method 177 (Re 1). Here Re is defined as ρq/μ, where Q is the 178 volumetric flow rate per unit fracture width (m 2 /s). Values of C 179 in eq 1 vary from 1.00 to 1.15; values of θ vary from 0 to 36.8, 180 potentially leading to about 3% deviation from N S 181 solutions Based on measurements, the initial fracture and matrix 183 porosity values assigned 100% and 1%, respectively. The 184 fracture aperture values based on image data vary between and μm, about 3 to 27 times of CT voxel resolution. Based on the local intrinsic fracture permeability κ = T cos θ af C 187 from eq 1, 45,49 these values correspond to intrinsic local fracture 188 permeability values from to m 2. These 189 values are orders of magnitude larger than the measured rock 190 matrix permeability ( to m 2 ), ensuring 191 the no-slip boundary condition at the fracture boundary. This 192 results in an effective fracture permeability of m 2. With mineral dissolution during fluid flow, the altered rock 193 matrix can reach porosity increase as high as 50% with 194 permeability values approaching m With the updated 195 fracture matrix permeability contrast of larger than 4 orders of 196 magnitude, the no-slip fracture boundary produces errors less 197 than 1.0% in the flow calculations for the fractured rock Reactive Transport Equation. The reactive transport code 199 CrunchFlow 39 solves mass conservation equations integrating 200 flow, transport, and geochemical reactions: 201 ( ϕci) + { ϕd ( Ci) + uc i} = ri,tot ( i = 1,2,..., Ntot) t (3) where ϕ is porosity, C i is the concentration of primary aqueous species i (mol/m 3 ), D is the hydrodynamic dispersion tensor (m 2 /s), u is the flow velocity (m/s), r i,tot is the summation of rates of multiple reactions in which the species i is involved ((mol/m 3 )/s), and N tot is the total number of primary species. The longitudinal component of the dispersion coefficients (m 2 / s), for example, is expressed as D L = D* + a L u x. Here D* is the effective diffusion coefficient (m 2 /s) in an individual grid block and is calculated using Archie s law D* = ϕ 1.5 D o, where D o is molecular diffusion coefficient (m 2 /s) in water, and α L is longitudinal dispersivity (m). A molecular diffusion coefficient of m 2 /s (calculated from the Stokes Einstein equation) is used for all species at 150 C. 55,56 The longitudinal and transverse dispersivity are 0.02 and cm, respectively. 57,58 The extended Debye Hu ckel equation is used to take into account the salinity effects C

4 t1 t1 t1 Energy & Fuels 219 Based on the flow field calculated from eqs 1 and 2, 220 CrunchFlow solves eq 3 for the concentrations of the N tot 221 species by discretizing over time and space. The computational 222 domain was assigned with fracture and rock matrix zones 223 explicitly following the images of the fractured rock. The rock 224 matrix was assigned according to measured mineralogy in Table The porosity in the fracture is 100% so the effective diffusion 226 coefficient equals the molecular diffusion coefficient in water With negligible flow in the matrix, it is expected that D* 228 dominates the dispersion coefficient. Mineral dissolution can 229 open up pore space and enhance diffusion in the matrix. 230 Reaction Network, Thermodynamics, and Kinetics. 231 The geochemical analysis of the rock sample suggests coexisting 232 quartz, clay, and calcite. Table 1 lists 15 reactions and their 233 thermodynamics and kinetic parameters. The dissolution rates 234 of quartz, muscovite, and calcite depend on aqueous chemistry 235 and are kinetically controlled. The reaction network includes 236 aqueous complexation reactions that are considered fast and 237 thermodynamically controlled. 60 A total of 19 species were used 238 with the primary species being SiO 2 (aq), H +,CO 2 (aq), K +, 239 Al 3+,Ca 2+,Na +, and Cl while all other species are secondary, 240 the concentrations of which are expressed in terms of primary 241 species using laws of mass action of aqueous complexation 242 reactions. 61 The reaction rates r i,tot follow the transition state 243 theory (TST) rate law: 62 r nk IAP j = Ak ij m, j 1 Keq, j i,tot 244 j= 1 (4) 245 where nk is the total number of mineral reactions that species i 246 is involved in, A ij is reactive surface area per unit volume (m 2 / 247 m 3 ) of mineral j that involves species i, and k m,j is rate constant 248 ((mol/m 2 )/s) indicating reactivity. The term IAP j /K eq,j 249 quantifies disequilibrium, where IAP j is the ionic activity 250 product and K eq,j is the corresponding equilibrium constant. 251 When IAP j /K eq,j is close to 1.0, the system is close to 252 equilibrium and the reaction rates are essentially zero, meaning 253 the system is not reacting. The kinetic rate parameters were 254 obtained by calibrating CO 2 -saturated water flooding experi- 255 ment in Andreani et al., 6 as will be discussed in the model 256 calibration section later. 257 Computational Domain and Conditions. The temper- 258 ature was set at 150 C that is within the range of C 259 in the Brady s field. 35 Quantitative X-ray diffraction analysis 260 suggests a matrix rock composed of 10% calcite (CaCO 3, v/v), % quartz (SiO 2, v/v), and 40% muscovite (KAl 2 (AlSi 3 O 10 )- 262 (OH) 2, v/v) in the calcite10 case. We also consider two 263 additional cases: calcite30 with 30% calcite, 40% quartz, and % muscovite; and calcite50 with 50% calcite, 30% quartz, and % muscovite. Minerals are assumed to be homogeneously 266 distributed because detailed spatial distribution is unavailable. A 267 pressure gradient is applied at the left and right boundaries; 268 however no-flux boundaries are imposed for the top and 269 bottom boundaries. The injection water contains 0.15 mol/l 270 NaCl at a ph of 6.5, similar to the brine composition at the site. 271 All other species have concentrations less than mol/l. The initial water in the matrix contains mol/l 273 NaCl with a ph of 7.6 and is equilibrated with calcite at 150 C. 274 Dissolution Rates at the Core Scale. The core-scale 275 apparent dissolution rate R a,j for the mineral j (mol/s) is 276 calculated through mass conservation: 68 R = Q [ C C ] 277 a, j tot ij,out ij,in (5) Here Q tot is the total volumetric flow rate (L/s); C ij,out and C ij,in 278 are the effluent and influent concentrations of primary species i 279 that are only involved in mineral reaction j (mol/l). Equation says that the apparent rates at the core scale are essentially the 281 difference between input rates and output rates of dissolved 282 species. As has been discussed in literature, 8,68 this is equivalent 283 to calculating the mass change in the solid phase over time. In 284 systems where mineral dissolution leads to concentration 285 gradients and therefore spatial variations in IAP/K eq, not all 286 mineral surface areas are bathed in water that are far-from- 287 equilibrium and are effectively dissolving. Following our 288 previous work, an effective surface area A e is defined as the 289 amount of surface area where the mineral is at disequilibrium 290 and is quantified with IAP/K eq < When R a,j is 291 normalized by A e, we obtain effective area-normalized rates 292 R e,j ((mol/m 2 )/s) that truly reflect the intrinsic reactivity of the 293 system: 294 R ej, = R A aj, e Fractured Rock Property Evolution. The porosity and permeability evolve when minerals dissolve. The grid block scale porosity of the rock matrix is updated according to change in mineral mass and volume. Rock matrix permeability at the grid block scale is updated using the porosity permeability relationship κ = κ 3 ϕ 0( ϕ ) 0 (6), where κ 0 is the initial matrix permeability (m 2 ) and ϕ 0 and ϕ are the porosity before and 302 after mineral dissolution, respectively. 50,69, Three average fracture apertures are calculated at the core 304 scale, including the mechanical aperture a m, chemical aperture 305 a c, and hydraulic aperture a h. The mechanical aperture a m is the 306 arithmetic mean of local apertures: L am = ax ()dx L (7) where L is the domain length. The chemical aperture a c is calculated based on mineral volume change: ac = ( Δ Vj) + a A s c0 where A s = L w is the surface area of the fracture wall (m 2 ), w is the domain width (m) in the transverse direction perpendicular to the flow, ΔV j is the volume change of mineral j (m 3 ), and a c0 is the initial chemical aperture (μm), which equals the initial mechanical aperture size. The hydraulic aperture a h is calculated from the cubic law using total flow rates representing hydraulic conductivity of the fractured rock: 71 12μQ tot ah = w( ΔP/ L) 1/3 Here ΔP is the differential pressure (Pa). The effective f racture h permeability is calculated through κ e = Effective Diffusion Coefficients. Diffusion coefficients 322 evolve due to mineral dissolution. The effective altered dif f usion 323 coefficient D m,az * quantifies diffusion in the altered zone and is 324 calculated using the analytical solution from Dai et al assuming that the local diffusion coefficient D m,l * in the altered 326 zone follows a unimodal distribution: 327 a (8) (9) D

5 f2 Energy & Fuels σ m,az 2 D* D* 1 + m,az m, G,az (10) 329 Here D m,g,az * is the geometric mean of D m,l * in the altered zone 330 and σ 2 m,az is the variance of ln(d m,l * ) in the altered zone. 331 The effective matrix diffusion coefficient D m,l * quantifies 332 diffusion coefficient in the entire rock matrix including both 333 altered and unaltered zones. The D m,l * is calculated following 334 the analytical solution from Dai et al. 72 assuming that (1) D m,l * 335 follows a bimodal distribution due to the formation of altered 336 zone and (2) the altered zone is homogeneous: 2 σ ml, * = * 2 D + + * * ml, DmGL,, 1 ( Daz Duz) 4 L 2 L/ λ f f λm 1 + e m az uz λm 337 (11) 338 where D m,g,l * (m 2 /s) is the geometric mean of D m,l * ; σ 2 m,l is the 339 variance of ln(d m,l * ) in the matrix; D az * and D uz * (m 2 /s) are the 340 arithmetic mean of ln(d m,l * ) for the altered zone and unaltered 341 rock matrix, respectively; f az and f uz are the volume fractions of 342 the altered zone and unaltered rock matrix in the matrix, 343 respectively; λ m is the correlation length (m) of D m,l * in the 344 matrix calculated by the geostatistical software Surfer MODEL CALIBRATION 345 The model is calibrated using the experimental data in 346 Andreani et al. 6 The planar fractured rock in Andreani et al had mineral composition similar to the fractured rock in this 348 work with 25% calcite, 25% quartz, 45% clay (24% kaolinite, % muscovite, 10% interstratified illite/smecitite, and 1% 350 chlorite) and some other minor minerals. The rock matrix had 351 a low porosity and permeability of about 7.1% and m 2, respectively. CO 2 -saturated brine was injected into the 353 fractured rock at an average velocity of m/s during 354 the first 120 h of the flow-through experiment at 25 C and MPa. We model the fracture as two parallel plates of an 356 aperture of 48.5 μm as indicated in Andreani et al. 6 The 357 physical setup of fracture is very similar to those in our previous 358 work. 74 The mineral composition and abundance, permeability, 359 porosity, and water composition were all set the same as those 360 measured in the experiment. The mineral surface areas are from 361 literature (Table 1). Figure 2 compares the model output of the 362 flux-weighted averaged concentration and the measured Ca(II) Figure 2. Comparison of measured and modeled effluent concentrations (mol/l) of (A) effluent Ca(II) and (B) SiO 2 (aq). Data are from Andreani et al. 6 Although not shown here, the simulated hydraulic aperture a h is constant during the experiment, which is consistent with the experimental observation. and SiO 2(aq). Although not shown here, the hydraulic aperture a h calculated from the simulation remained constant during the numerical experiment, which is consistent with the experimental observation. The rate constants were adjusted to reproduce the data. Values of these rate constants and specific surface area fall into reported values in literature, as noted in Table 1. This indicates that at the small scale of tens of micrometers, reaction kinetics measured in well-mixed reactors can be used directly without upscaling efforts, as suggested in Li et al RESULTS AND DISCUSSION f3 375 f Spatiotemporal Evolution. Brine injection results in evolving geochemical conditions in the fractured rock (Figure 3). On day 1, the initial equilibrium condition dominated and calcite dissolution was slow in all three cases except at the inlet. On day 50, in calcite10, the brine penetrated deeper along the fracture direction, leading to a reactive thin line with low IAP/ K eq,calcite and calcite dissolution rates orders of magnitude higher than those in the matrix (Figures 3A1 B1). The saturation index IAP/K eq,calcite indicated that the solution was at equilibrium with calcite across the domain (red color in Figure 3A1) except at the thin rock matrix interface that represented the reaction front in the flow transverse direction. The preferential calcite dissolution opened a large calcite-depletion area (Figure 3E1), leading to the formation of a light blue altered zone of high porosity at the vicinity of the fracture (Figure 3F1). Over time the thin reactive interface grew rapidly along the main flow direction, however much slower in the transverse direction because of the increasingly large diffusion barrier as calcite dissolution continued along the transverse direction. The overall calcite dissolution was therefore limited by diffusion in the transverse direction that cannot transport dissolution products out of the matrix sufficiently fast. For the slower reacting quartz, there was a much wider zone with low- IAP/K eq,quartz values and relatively high quartz dissolution rates close to the fracture wall (Figure 3C1,D1), indicating a lower extent of diffusion limitation. Over time the brine etched away calcite leading to an expanding zone of calcite depletion (Figure 3E1,F1) and therefore enhanced effective local diffusion coefficient. Due to the large permeability contrasts between the fracture and matrix, however, the flow distribution remained largely unchanged with negligible flow through the rock matrix (Figure 3G). The spatial distributions of IAP/K eq and dissolution rates in general followed evolving patterns of 405 calcite content (Figure 3E1). 406 In calcite30 and calcite50, abundant calcite resulted in faster 407 dissolution and quicker approach to equilibrium than in 408 calcite10 (Figure 3A,B). In addition, the calcite depleted zone 409 also had larger local diffusion coefficient due to the larger 410 porosity increase, which facilitated continued calcite dissolution 411 deeper into the matrix. As such, calcite dissolved only at the 412 vicinity of the inlet, leading to the formation of wider and 413 shorter altered zones (Figure 3F2,F3). The profiles of IAP/K eq 414 and mineral reaction rates followed similar patterns. On day , although the altered zone expanded along the fracture, the 416 major alteration was still mostly at the inlet. The length of the 417 altered zone along the longitudinal direction was negatively 418 proportional while its width was positively proportional to 419 calcite abundance. This was because the equilibrium length, the 420 length at which calcite reaches equilibrium decreases with 421 increasing calcite abundance. 422 E

6 Energy & Fuels Figure 3. Temporal and spatial evolution of (A) IAP/Keq,calcite, (B) calcite dissolution rates ((mol/m2)/s), (C) IAP/Keq,quartz, (D) quartz dissolution rates ((mol/m2)/s), (E) calcite volume (%), (F) porosity (%), and (G) flow velocity (m/s). The flow field remained relatively constant during the numerical experiments due to the large initial fracture matrix permeability contrast and the remaining minerals in altered matrix therefore only the initial flow velocity distribution is shown here Dissolution Rates at the Core Scale. Despite the differing calcite abundance, the dissolved calcite mass and apparent dissolution rates were the same at early stages in all cases (Figure 4A), indicating transport limitation in facilitating calcite F f4

7 Energy & Fuels f5 Figure 4. Temporal evolution of (A) dissolved calcite and quartz mass (mol) and (B) core-scale apparent dissolution rates (R a, mol/s). Calcite apparent dissolution rates in the calcite10 case decreases due to the expanding altered zone at the rock matrix interface that becomes an increasingly significant diffusion barrier. 427 dissolution. The curves diverged later with apparent rates 428 decreasing from the initial to mol/s 429 on day 300 in calcite10 while remaining almost constant in 430 calcite30 and calcite50 (Figure 4B). This was because in 431 calcite10 the effects of the altered zone as a diffusive barrier for 432 mass transport gradually increased (Figure 3F1), therefore 433 slowing down calcite dissolution. This has been observed in 434 experiments with preferential carbonate dissolution, 31, although some attributed the rate decrease to clay coating. In 436 calcite30 and calcite50, although brine also depleted calcite 437 close to the inlet over time, the more abundant calcite led to 438 larger porosity increase in the altered zone and therefore faster 439 effective diffusion than in calcite 10, which facilitated continued 440 calcite accessibility. 441 The apparent dissolution rates of quartz in calcite10 were and 1.78 times that of R a,quartz in calcite30 and calcite after 300 days, respectively. Quartz dissolution rates increased 444 slowly over time in all cases. Although not shown here, the 445 effective surface area of calcite, defined as the surface area at 446 disequilibrium with IAP/K eq,calcite < 0.99, 68 were 2 3 orders of 447 magnitude lower than the total surface area calculated based on 448 total calcite mass, indicating that almost all calcite surfaces were 449 at equilibrium and not dissolving. The thickness of this reactive 450 interface at the rock matrix boundary is about μm. 451 In contrast, all IAP/K eq,quartz values was lower than 0.6, implying 452 that almost all quartz surfaces were dissolving at rates within an 453 order of magnitude from those under far-from-equilibrium 454 conditions. 455 Evolution of Average Aperture Size. The preferential 456 calcite dissolution generated a porous altered zone between the 457 fracture and unaltered matrix; however it did not increase the 458 fracture aperture itself due to the remaining minerals in the 459 matrix and the high fracture matrix permeability contrast. That 460 is, in calcite50, although the matrix permeability in the altered 461 zones increased from to m 2 after days, a fracture matrix permeability contrast was still about orders of magnitude. The brine still mostly flew through the 464 fracture instead of the matrix. 52,53 As a result, a m remained a 465 constant μm in all cases (Figure 5). Although not shown 466 here, values of a h remained a constant initial μm for the 467 same reasons. The chemical aperture a c, however, increased in 468 all cases. Values of a c increased from to μm 469 after 300 days, where calcite10 had the smallest a c value with 470 the least dissolved mass. The evolution of the equivalent overall 471 matrix porosity followed very similar trends to a c, increasing 472 from the initial 1.0% to %. This explained experimental Figure 5. Temporal evolution of mechanical aperture (a m ) and chemical aperture (a c ). observations in some dissolution experiments that the effective 473 permeability remained unchanged even with a large matrix 474 porosity increase Evolution of Effective Diffusion Coefficients. The 476 effective diffusion coefficients of the altered zone, D m,az *, 477 increased in all cases due to the continuous porosity increase 478 (Figure 6). Calcite50 had the largest altered zone porosity Figure 6. (A) Temporal evolution of effective matrix diffusion coefficient D m,l * (m 2 /s) for the entire matrix and effective altered diffusion coefficient D m,az * (m 2 /s) in the altered matrix; (B) effective matrix diffusion coefficient D m,l * (m 2 /s) as a function of overall matrix porosity (%). (51%), resulting in the largest D m,az * after 300 days ( m 2 /s). This value is 7.9 and 2.0 times of D m,az * in calcite10 and 481 calcite30, respectively. With the D m,az * increase and the 482 enlargement of the altered zone during mineral dissolutions, 483 the core-scale effective matrix diffusion coefficient D m,l * also 484 increased in all cases. Although calcite10 has the lowest altered 485 zone diffusivity and the least dissolved mass, its D m,l * was the 486 highest among all cases and increased from the original to m 2 /s after 300 days, an increase of times. The calcite30 and calcite50 cases saw smaller increases of and 9.9 times for D m,l *, respectively. This is somewhat 490 counterintuitive because calcite10 had the least dissolved calcite 491 and therefore was expected to have the lowest reactivity and 492 least alterations of flow and transport properties. 493 Figure 6B shows that D m,l * increased as a function of overall 494 matrix porosity increase, indicating a much significant extent of 495 D m,l * increase in calcite10 compared to the other two cases. This 496 emphasizes the importance of the spatial organization or the 497 shape of altered zones in determining the actual tortuous length 498 of solute transport in the rock matrix and ultimately the D m,l * in 499 the core scale. That is, the D m,l * has a greater dependence on the 500 connectedness of matrix porosity than on the matrix porosity 501 itself f6 G

8 f7 Energy & Fuels 503 Dependence of Effective Mineral Dissolution Rate on 504 Matrix Diffusion. The core-scale effective dissolution rates 505 R e,clacite and R e,quartz were calculated by dividing the apparent 506 rates R a,clacite and R a,quartz (mol/s) with their corresponding 507 effective surface area at disequilibrium with IAP/K eq < (Figure 3A,C). At early stages, R e,clacite were essentially the same 509 among all three cases (Figure 7A) because calcite dissolved at Figure 7. Temporal evolution of (A) effective calcite dissolution rate R e,calcite ((mol/m 2 )/s) (normalized by effective surface area) and (B) effective quartz dissolution rate R e,quartz ((mol/m 2 )/s); (C) R e,calcite as a function of D m,az * /w a (m/s), where w a is the average thickness of the altered zone from the altered unaltered interface to the fracture matrix boundary; (D) R e,quartz as a function of D m,l *. In panels C and D, R e,calcite and R e,quartz in the first 20 days were excluded, because dissolution still mainly occurred at the fracture boundary and was controlled by the flow and transport in the fracture at these early times. 510 the fracture boundary and was controlled by the flow and 511 transport in the fracture. With the formation of altered zones 512 (about 20 days), the R e,clacite was limited by matrix diffusion and 513 decreased with time. The R e,clacite was lowest in calcite10 after days, about 10 times smaller than calcite intrinsic kinetic 515 rate constant ( (mol/m 2 )/s). In contrast, R e,quartz 516 increased with time and calcite10 had the highest effective 517 quartz dissolution rates. This diverging behavior between effective calcite and quartz dissolution reflects different controls 518 on the dissolution of the two minerals with orders of magnitude 519 difference in their intrinsic dissolution rates. 520 Figure 7C shows that the effective dissolution rates R e,clacite 521 consistently depend on D m,az * /w a instead of D m,az *. Here w a is 522 the average thickness of the altered zone representing the shape 523 of the altered zone. This indicates that calcite effective 524 dissolution is limited by the diffusion through the altered 525 zone and therefore the geometric characteristics of the altered 526 zone. In contrast, D m,az * could not capture the transport 527 distance from the altered unaltered matrix interface to flowing 528 brine in the fracture. The R e,quartz values increase with D m,l * in all 529 cases (Figure 7D), approaching the quartz intrinsic kinetic rate 530 constant ( mol/m 2 /s). This indicates the control by 531 effective diffusion in the whole matrix rather than the altered 532 zone only. 533 Solute Transport and Heterogeneity Quantification. 534 The slope of the BTCs power law tailings was used to quantify 535 evolving structure heterogeneity of fractured rock and property 536 relevant to solute transport. 76,77 A commonly observed 537 phenomenon in heterogeneous geologic media in general, the 538 BTCs tailings in fractured media are often caused by the much 539 slower solute transport in rock matrix and/or eddies arising 540 from tortuosity and roughness. 78,79 The BTC tailings scale in 541 the power law form of (1 C/C 0 ) t m, where m is the slope 542 of power law tailing. In general, homogeneous media have 543 symmetric BTCs, shorter tails, and larger m values, while highly 544 heterogeneous media have longer tails and smaller m values, 545 exhibiting largely different time scales of mass transport in 546 different parts of geologic media. 80, To quantify the change in the fractured rock property 548 relevant to solute transport, here we carried out numerical 549 experiments of nonreactive tracer (bromide) transport through 550 the fractured rock before and after the dissolution experiments. 551 The slopes of power law tailings were 1.22 in all cases on day and became larger on day 300 (Figure 8), indicating faster fracture matrix mass transfer/exchange due to the increase of 554 effective matrix diffusion after calcite dissolution. The slopes of 555 power law tailings in calcite30 and calcite50 increased to and 2.53, respectively, while that of calcite10 increased to a 557 much larger value of 3.95, indicating that the extended altered 558 zone reduced the matrix-fracture differences and therefore 559 generated a less heterogeneous medium. In calcite30 and 560 calcite50, however, the localized degraded zones led to less 561 homogenization. 562 Discussion. Although this study uses a 2D slice of fractured 563 rock, the general conclusion should also apply for 3D fractured f8 Figure 8. Tracer breakthrough (1 C/C 0, with C 0 being the inlet concentration) as a function of the number of residence time (t) on day 1 and day 300 for (A) calcite10, (B) calcite30, and (C) calcite50. Symbols are the model prediction at different times. Lines are power law equations that fit the model predicted BTCs tailings (R 2 > 0.97). The residence time on day 1 was 6.44 min in all cases. On day 300, the residence times were 10.59, 12.13, and min for calcite10, calcite30, and calcite50, respectively, because of the increase in pore volume from the rock matrix. H

9 Energy & Fuels 565 rocks. That is, we will in general see more dissolution close to 566 the inlet with higher calcite abundance. As such, the 567 heterogeneity in the rock matrix induced by calcite dissolution 568 and the dependence of dissolution rates on the effective 569 diffusion coefficient under different calcite abundance should 570 follow similar trends in 3D fractured rocks. 571 This work reveals conditions where less abundant reactive 572 rock surprisingly creates more alteration in the rock matrix. 573 Although counterintuitive, this has been observed in karst 574 morphology and it is widely believed that a slowing down in the 575 kinetics of calcite dissolution is the key factor facilitating 576 karstification over reasonable time and length scales, 82,83 which 577 is often referred to as the kinetic trigger. 578 This work is based on the assumption that reactive minerals 579 are homogeneously distributed within the matrix. This may not 580 be the case in natural geosystems. For example, clay minerals 581 are often coated on reactive mineral surfaces. 31 Under such 582 conditions, the dissolution will likely be dictated by mineral 583 spatial distribution. The heterogeneous distribution may 584 facilitate the development of irregular void space, the re- 585 distribution of clay particles, and the formation of microporous 586 clay coating at the fluid rock interface, leading to the 587 alternations of fracture surface roughness and effective fracture 588 permeability. The initial porosity in the rock matrix is also 589 considered as homogeneously distributed. As mineral dis- 590 solution proceeds, however, porosity increases to different 591 extent due to the spatial variation in dissolution rates. The 592 calculation of effective matrix diffusion coefficients takes into 593 the porosity in the altered and unaltered zones in the rock 594 matrix, therefore reflecting heterogeneous distribution of 595 evolving porosity. 596 Our model does not consider geomechanical processes that 597 can potentially change fracture aperture. Fluid injection may 598 induce overpressure (hydroshearing) that can cause fracture 599 slips and reactivation, 7,84 especially in brittle crystalline rocks 600 and under fast and large quantity injection conditions. 85, Porosity increase in the rock matrix can change mechanical 602 stress, decohesion of clay particles, particle re-distribution, and 603 potentially clogging. 31 These processes, however, are more 604 likely to occur under conditions with carbonate abundance over %. 6,31,32 6. CONCLUSIONS 606 Fractured rocks typically contain minerals of drastically 607 differing reactivity. Most previous work on fracture alterations 608 focuses on rocks with single minerals and therefore retreating 609 fracture wall during mineral dissolution. Although experimental 610 studies have been carried out for fractured media with complex 611 mineralogy, 8,32,33 their long-term property evolution has 612 remained poorly understood. Pore-scale imaging technique 613 has inspired a lot of interest in direct simulation of flow and 614 reactive transport processes in recent years. 87,88 To the best of 615 our knowledge, this work presents one of the early multi- 616 component reactive transport numerical experiments using a 617 real fractured rock composed of multiple minerals. 89 The 618 combination of detailed fracture structure representation at the 619 resolution of tens of micrometers and physics-based reactive 620 transport modeling incorporating matrix diffusion process 621 allows for mechanistic understanding of fracture and rock 622 matrix evolution during fluid injection. 623 This work reveals that preferential carbonate dissolution 624 leaves behind the less reactive minerals, including clay and 625 quartz, in the rock matrix, leading to the enlargement of an altered zone and enhanced effective diffusion in the rock matrix. Although with relatively similar dissolved calcite mass and matrix porosity increase in the three cases, calcite abundance controls the spatial organization of the altered zone. With abundant calcite, dissolution quickly reached equilibrium within a short distance from the inlet, leading to a short and wide altered zone with porosity increase of 30 50%. In contrast, low calcite content results in a long and narrow altered zone with porosity increase of 10%. This difference in the shape of the altered zone imposes strong impacts on the rock matrix diffusivity. The effective matrix diffusion coefficient D m,l * depends strongly on the structure of the altered zone with an increase of 19.6 times in calcite10 and 9.9 times in calcite50 after 300 days of dissolution. The extended altered zone in calcite10 enhances the interconnectedness of matrix porosity and reduces the sharp difference between the fracture and matrix, therefore leading to faster solute transport in the fractured rock. Matrix diffusion significantly affects the effective dissolution of multiple minerals in the long run. The effective rates of fastdissolving calcite are controlled by diffusive transport in the altered matrix and therefore depend on the shape of the altered zone. With the altered zone etching deep into the rock matrix, effective calcite dissolution rates decrease with time in the low calcite abundance case. Effective quartz dissolution, however, depends on effective diffusion of the entire rock matrix. Calcite dissolution is in general fast and therefore is transport-limited in all three cases. In fact, the calculation shows that calcite dissolves only at the thin altered unaltered interface that occupies less than 1% of the total surface area. The thickness of the dissolving interface is tens of micrometers. This is similar to observations in other studies that quantify carbonate dissolution in heterogeneous media. 68,90 That is, for fast dissolving carbonate, dissolution quickly becomes transport-limited so that only a very small fraction of the minerals that sit at the high-flow low-flow interfaces effectively dissolve. In contrast, quartz dissolves at much lower rates and all surface areas are effectively dissolving. This work sheds light on the unique characteristics of reactive transport in fractured, mineralogically complex rocks that are different from those with single minerals. 15,25 Although the hydraulic conductivity of the fractured rock remains relatively constant, the significant increase in the matrix diffusivity leads to much faster solute transport after the preferential calcite dissolution. This work indicated that the alteration in rock matrix can be significant in rocks composed of minerals of differing reactivity and can have strong impacts of mineral dissolution and transport properties of the fractured rock. This finding has interesting implications for water and energy applications that involve water rock interactions, including geological carbon sequestration, 91 geothermal and fossil fuel energy production, 92 and contaminant remediation and nuclear waste disposal in fractured rock. 93,94 For example, as rock matrix provides additional sorption and buffering capacity for contaminants, enhanced matrix diffusion induced by mineral dissolution may be critical in predicting the mobility of contaminants. The results indicate that it is critical to consider the detailed rock matrix mineralogy even with relatively low percentage fast-reacting mineral because the long-term property evolution of the fractured rock (e.g., solute transport) can inversely depend on the abundance of the fastreacting mineral I