Influence of Rock Mineralogy on Reactive Fracture Evolution in


Aug 9, 2018 - Fractures present environmental risks for subsurface engineering activities, such as geologic storage of greenhouse gases, because of th...
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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.

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1 2 3

Abstract:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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storage reliability.

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

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

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

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

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

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

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

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

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injection of hazardous wastes.

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

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geochemical and geomechanical perturbations that could exacerbate the likelihood of vertical

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

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

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

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

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

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

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alteration of fractures must be better understood.

39 40

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

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

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

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

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

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

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

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precipitation (33-34).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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closure.

66 67

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

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

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transport through fractures in mineralogically heterogeneous carbonate rocks subject to

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

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

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

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

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

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

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

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

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

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

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

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

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

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the article and include it in the Supporting Information.

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

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

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

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

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

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geometry.

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

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

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

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

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

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

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

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

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

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

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

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

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

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drive significant reaction.

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2. Methods

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2.1 System & Boundary Conditions

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

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

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

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

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

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

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

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

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

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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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not computationally cumbersome.

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

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

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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

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

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

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

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

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

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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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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.

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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,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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QμL ∆

(2)

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

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

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

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

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

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in the Supporting Information.

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

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

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

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charge balance equation.

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

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

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

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

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

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

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

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

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

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

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R =





2∆"∆# k%a'(), + , 1 −

>DE + ∑>DF ;A=> ∗ k%a'(),> + @ 1 − 



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%./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

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

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

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

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

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

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particles that become lodged in fracture bottlenecks.

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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

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

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forward rates of reaction and the backwards rate:

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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

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

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

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

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constants throughout the simulations.

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2.3 Elastic Deformation Model

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

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

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

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

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

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∑ f = σb A

(6)

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

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

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(7)

D + W = Le − ∆L

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

∆L = f ∗

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gh

ij.1



(8)

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

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

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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

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

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

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

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

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

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

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

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

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2.4 Heterogenous Mineralogies

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

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

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

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

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

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

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

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

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

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

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

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

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sedimentary rock.

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Binary mineral maps depicting calcite and effectively unreactive minerals were

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

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

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

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

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

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

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

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

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

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

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

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

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

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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.

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

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

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due to geomechanical stress.

292 293

3. Results

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3.1 Effect of Normal Stress

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

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

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

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

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mineral dissolution and mechanical deformation.

300 301

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

321

small amount of additional compression.

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

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

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

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

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

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

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3.2 Effect of Mineral Heterogeneity

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

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

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

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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

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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,

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

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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

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

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

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

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

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

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dissolve rock material farther downstream.

355 a)

All-Calcite

Transmissivit y Evolution

∆b [µm] 500+

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y

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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

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

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

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

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

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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

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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

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

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

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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

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

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

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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-

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

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

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geochemical-geomechanical processes.

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

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

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

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

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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

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transmissivity increase, our simulations show that mineralogically heterogeneous fractures with

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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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