Enhanced Rock Matrix Diffusivity Induced by Preferential Dissolution

Apr 7, 2016 - John and Willie Leone Family Department of Energy and Mineral Engineering, The Pennsylvania State University, University Park,...
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Where Lower Calcite Abundance Creates More Alteration: Enhanced Rock Matrix Diffusivity Induced by Preferential Carbonate Dissolution Hang Wen, Li Li, Dustin Crandall, and J. Alexandra Hakala Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.5b02932 • Publication Date (Web): 07 Apr 2016 Downloaded from http://pubs.acs.org on April 10, 2016

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Where Lower Calcite Abundance Creates More Alteration: Enhanced Rock Matrix

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Diffusivity Induced by Preferential Carbonate Dissolution

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Hang Wen1, Li Li1,2,3*, Dustin Crandall4, Alexandra Hakala4 1

John and Willie Leone Family Department of Energy and Mineral Engineering, The Pennsylvania

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State University, University Park, PA 16802 2

Earth and Environmental Systems Institute (EESI), The Pennsylvania State University, University

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Park, PA 16802 3

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EMS Energy Institute, The Pennsylvania State University, University Park, PA 16802

Geological and Environmental Systems Directorate, Research and Innovation Center, National Energy Technology Laboratory, Pittsburgh, PA 15236

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*Corresponding author ([email protected])

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Manuscript Resubmission to Energy & Fuels on March 1, 2016

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Abstract: Fractured rocks are critical for flow, solute transport and energy production in

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geosystems. Existing studies on mineral reactions in fractured rocks mostly consider single

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mineral systems where reactions occur at the fracture wall without changing rock matrix

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properties. This work presents multi-component reactive transport numerical experiments in a

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real fractured rock from the Brady’s field, a geothermal reservoir at a depth of 1,396 m in the Hot

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Springs Mountains, Nevada. Initial porosity, permeability, mineral composition (quartz, clay, and

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calcite), and fracture geometry are based on microscopy characterization and X-ray tomography.

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The model was calibrated using a CO2-saturated water flooding experiment. Three numerical

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experiments were carried out with the same initial physical properties however different calcite

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content. Although total dissolved masses are similar in all cases, abundant calcite (50% v/v,

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Calcite50) leads to localized, thick zone of large porosity increase while low calcite content

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(10% v/v, Calcite10) creates an extended and narrow zone of smaller alteration resulting in

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surprisingly larger change in effective transport property. After 300 days of dissolution, effective

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matrix diffusion coefficients increase by 9.9 and 19.6 times in Calcite50 and Calcite10,

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respectively, inducing corresponding 2.1 and 3.2 times rise in the slopes of power law tailing, a

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measure of transport properties. This suggests counter-intuitive results that lower abundance of

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reactive minerals leads to greater alteration in the fractured media. Alteration in matrix diffusion

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significantly affects mineral dissolution. The effective rates of fast dissolving calcite are limited

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by diffusive transport in the altered matrix and the shape of the altered zone, while effective

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dissolution of quartz with much lower rates depends on effective diffusion of the entire rock

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matrix. Simulation results indicate that calcite dissolution is transport-limited and only occurs at

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the thin altered-unaltered matrix interface of tens of micron thickness occupying less than 1% of

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the total surface area. In contrast, all quartz surface areas are effectively dissolving. This work

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highlights the importance of mineralogical complexity in determining mineral dissolution and

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poorly understood rock matrix property evolution.

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1. Introduction

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Fractured rocks play a critically important role in geosystems, including geothermal

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reservoirs1,2, nuclear waste repositories3,4, hydrocarbon reservoirs5, and deep saline aquifers for

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carbon geosequestration6,7. These applications perturb the subsurface, leading to geochemical

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disequilibrium and rock-fluid interactions including mineral reactions, sorption, and ion

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exchange. These reactions change fluid composition, rock structure and conductive properties,

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ultimately affecting long-term functioning of geosystems8,9. Fractures present predominant

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conductive pathways for energy, mass, and flow in these systems, while the adjacent rock matrix

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significantly retards solute transport through diffusive mass exchange with fractures10-13. The

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interactions among fracture and rock matrix can play a pivotal role in the property evolution of

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fractured rocks.

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Extensive experimental and numerical studies have explored fracture characteristics and

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property alteration induced by reactive flow, including initial aperture size and fracture

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roughness14,15, fracture orientation16, and fracture length17,18. Injection rates, temperature, and

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chemical composition16,19,20, and mechanical stress21,22 have also been examined and shown to be

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important for describing evolution of fracture properties. Recent studies have explored the

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application of dimensionless numbers, including Damköhler and Péclet numbers in unifying

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dissolution behavior under different flow regimes23,24.

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Most of these studies include single minerals without explicitly considering multi-

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component reactive transport with thermodynamically and kinetically distinct geochemical

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reactions. Mineral dissolution / precipitation has been assumed to occur only at the fracture 3 ACS Paragon Plus Environment

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surface and therefore does not alter the properties of rock matrix15,25. Natural rocks, however, are

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typically composed of multiple minerals. For example, limestones are mostly carbonates

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coexisting with quartz, feldspars, and clays26. Sandstones are dominated by quartz and often co-

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occur with clays and carbonate cements27. Mineral reactivity varies by orders of magnitude.

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Under far-from-equilibrium conditions, carbonate dissolves at rates orders of magnitude higher

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than those of quartz dissolution28,29. In fractured rocks composed of multiple minerals, fast-

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reacting minerals preferentially dissolve along fracture-matrix interfaces and leave behind slow-

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reacting minerals, therefore forming altered zones with higher porosity and diffusivity in the rock

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matrix at the vicinity of the fracture. Such property alteration can change fracture-matrix mass

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exchange and have profound implications for fractured rock evolution.

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Recent experimental studies have documented formation of altered zones in the presence

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of multiple reactive minerals. Gouze et al.30 observed dissolution overhangs in fractured marine

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carbonates (85% calcite) and called for a revisit of conventional effective aperture definition.

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Noiriel et al.31 suggested that altered zones in fractured argillaceous limestones act as diffusion

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barriers for fluid accessibility to rock matrix. Ellis et al.32 and Noiriel et al.8 observed that calcite

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preferential dissolution in fractured limestones leads to non-uniform aperture increase and

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altered zones mostly composed of dolomite and clay, which changes both fracture roughness and

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hydraulic conductivity33. In a fractured argillaceous sample, however, calcite dissolution

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increases matrix porosity by 50% while hydraulic conductivity remains unchanged6. In these

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experiments, the complexity of chemical analysis and sample geometry characterizations prevent

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detailed mechanistic understanding and quantification of fracture-matrix property evolution.

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The objective of this study is to understand and quantify the role of mineral composition,

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in particular preferential calcite dissolution, in determining property evolution of the fractured

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rock, including both the fracture and rock matrix. Numerical experiments of multi-component

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reactive transport were carried out in a fractured rock built upon image data from CT scanning.

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The fractured rock contains mostly quartz and illite/muscovite with minor amount of calcite. The

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initial calcite abundance was varied to understand its role in determining property evolution

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relevant to flow and transport.

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2. Characterization of the Fractured Rock

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Sample characterization. A core sample with a diameter of 2.54 cm was from a depth of 1,396

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m at Brady’s field in the Hot Springs Mountains, Nevada, an extensively studied field for

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enhanced geothermal application34. The subsurface contains over 2 km of faulted and fractured

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mesozoic granite and metamorphic rocks that rest upon ash flow tufts and/or metamorphic

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basement rocks. The sample was fractured artificially using a hydraulic core splitter. The rock

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matrix porosity, measured by helium porosimeter HP-401 (TEMCO, Inc.), varies between 0.87%

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- 1.54%. The rock permeability, determined by servo-hydraulic, tri-axial test system Autolab-

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1500 (New England Research, Inc.), ranges between 6.0×10-20 and 2.0×10-19 m2. X-ray

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diffraction analysis indicated rock composition of primarily quartz (25% - 50% v/v),

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illite/muscovite (25% - 50% v/v) and calcite (5% - 25% v/v). The formation water is mostly

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sodium chloride at an estimated concentration of 0.032 mol/L and is considered at equilibrium

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with calcite35.

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Fracture geometry acquisition. High-resolution CT scanning was performed to obtain 3D

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fracture geometry at a resolution of 31.8 µm using an M-5000 Industrial Computed Tomography

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System (North Star Imaging Inc.). Details of the CT parameters are documented in Crandall et

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al.36 The radiographs were reconstructed into a 3D geometry and exported using eFX software

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(North-Star Imaging). An OTSU threshold technique and careful examination of CT registration 5 ACS Paragon Plus Environment

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was used to isolate the fracture36. Details of the technique capability, limitations, and challenges

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for the fracture-matrix identification can be found in Wildenschild et al.37 and Schlueter et al.38

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To reduce the computational cost, a longitudinal 2D slice of 49.3 mm × 0.032 mm × 3.5 mm was

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extracted and was discretized into 174,720 grid blocks (1560 × 1 × 112 voxels, Figure 1). Zero

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aperture locations within this two dimensional cross-section were assigned a nominal aperture

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value to enable continuity of flow in this sub-domain.

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Figure 1. (A1 and A2) Three-dimensional fracture sample map with images from high-resolution

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X-ray computed tomography. (B) A two-dimensional cross section indicated by the red box A-B

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in A2 is used for the 2D simulations in this work.

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3. Multi-component reactive transport numerical experiments

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Flow field calculation. Although fluid flow within a fracture can be fully described by the

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Navier-Stokes (N-S) equations, its combination with detailed, multi-component geochemical

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reactive transport representation and evolving flow fields with changing matrix properties is

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computationally expensive39. Various approaches exist to simplify flow field calculation in

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fractured media, including the cubic law40, the classical Local Cubic Law (LCL)41,42, along with 6 ACS Paragon Plus Environment

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other extensions and modifications43,44. Among these, we chose to use a recent development, the

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modified local cubic law (MLCL)45. MLCL takes into account weak inertia, tortuosity, and

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roughness, while at the same time it is relatively straightforward to implement. Briefly, the

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MLCL solves the following equation for the pressure field:

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T  ∇ ⋅  cos (θ ) ∇P  = 0 C 

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where T is the local transmissivity (m2/s) in the main flow direction x; C is the correction factor

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incorporating local roughness and inertia; θ is the local flow-orientation angle estimated based

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on tortuosity in x direction; and P is fluid pressure (Pa). The local transimissivity Tix in the grid 2a f ( xix ) a f ( xix +1 ) 3

(1)

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block ix is calculated following Tix =

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being the flow-oriented aperture calculated based on apparent aperture at the grid blocks ix and

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ix+1, respectively; µ is fluid viscosity (1.91×10-4 Pa·s at 150 °C46). Values of C depend on local

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fracture and flow characteristics and are provided in a lookup table in the Supporting Information

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of Wang et al.45

a f ( xix ) + a f ( xix +1 ) 3

3



1 , with a f ( xix ) and a f ( xix +1 ) 12 µ

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The pressure solution to Equation (1) gives a one-dimensional flow field in the main flow

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x direction, which is further distributed into flow velocities in the z direction transverse to the

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main flow based on the parabolic law47:

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2     z u x ( z ) = 1.5U x 1 −      0.5a f ( x )    

(2)

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where z is the transverse distance to the center of the aperture (m), u x ( z ) is the local fluid

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velocity (m/s) in the longitudinal direction, U x is the average velocity (m/s) at the x location

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calculated from the MLCL. By doing so we obtain a 2D flow field with flow velocities in the x 7 ACS Paragon Plus Environment

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direction following MLCL and in the z direction following the parabolic law, ensuring that flow

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is zero at the fracture wall and is fastest in the center of the fracture.

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In this study, the fractured rock has an average flow velocity of 1.15×10-5 m/s that is

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within the typical range (10-3 - 10-6 m/s) for geothermal energy operations48 and a Re number of

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0.23 that is within the applicable range of the MLCL method (Re≤1). Here Re is defined as

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ρ Q / µ , where Q is the volumetric flow rate per unit fracture width (m2/s). Values of C in

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Equation (1) vary from 1.00 to 1.15; values of θ vary from 0° to 36.8° , potentially leading to

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about 3% deviation from N-S solutions45.

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Based on measurements, the initial fracture and matrix porosity values assigned 100%

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and 1%, respectively. The fracture aperture values based on image data vary between 95.4 and

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858.6 µm, about 3 to 27 times of CT voxel resolution. Based on the local intrinsic fracture

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permeability κ 0 =

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fracture permeability values from 7.5×10-10 m2 to 6.1×10-8 m2. These values are orders of

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magnitude larger than the measured rock matrix permeability (6.0×10-20 - 2.0×10-19 m2), ensuring

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the no-slip boundary condition at the fracture boundary. This results in an effective fracture

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permeability of 2.4×10-9 m2. With mineral dissolution during fluid flow, the altered rock matrix

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can reach porosity increase as high as 50% with permeability values approaching 10-14 m2 50.

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With the updated fracture-matrix permeability contrast of larger than four orders of magnitude,

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the no-slip fracture boundary produces errors less than 1.0% in the flow calculations for the

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fractured rock51-54.

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Reactive transport equation. The reactive transport code CrunchFlow39 solves mass

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conservation equations integrating flow, transport, and geochemical reactions:

T cos θ from Equation (1)45,49, these values correspond to intrinsic local 12a f C

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∂ ˆ i = ri ,tot ( i = 1, 2,..., Ntot ) (φ Ci ) + ∇ ⋅ −φ Dˆ ∇ ( Ci ) + uC ∂t

{

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}

(3)

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where φ is porosity, Ci is the concentration of primary aqueous species i (mol/m3), Dˆ is the

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hydrodynamic dispersion tensor (m2/s), uˆ is the flow velocity (m/s), ri ,tot is the summation of

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rates of multiple reactions that the species i is involved (mol/ m3/s) , and Ntot is the total number

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of primary species. The longitudinal component of the dispersion coefficients (m2/s), for

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example, is expressed as DL = D* + aLu x . Here D* is the effective diffusion coefficient (m2/s) in

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an individual grid block and is calculated using Archie’s law D* = φ 1.5 Do , where Do is molecular

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diffusion coefficient (m2/s) in water, and α L is longitudinal dispersivity (m). A molecular

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diffusion coefficient of 6.0×10-9 m2/s (calculated from the Stokes-Einstein equation) is used for

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all species at 150°C 55,56. The longitudinal and transverse dispersivity are 0.02 cm and 0.001 cm,

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respectively57,58. The extended Debye-Hückel equation is used to take into account the salinity

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effects59.

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Based on the flow field calculated from Equations (1) and (2), CrunchFlow solves

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Equation (3) for the concentrations of the Ntot species by discretizing over time and space. The

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computational domain was assigned with fracture and rock matrix zones explicitly following the

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images of the fractured rock. The rock matrix was assigned according to measured mineralogy in

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Table 1. The porosity in the fracture is 100% so the effective diffusion coefficient equals to the

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molecular diffusion coefficient in water55. With negligible flow in the matrix, it is expected that

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D* dominates the dispersion coefficient. Mineral dissolution can open up pore space and enhance

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diffusion in the matrix.

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Reaction network, thermodynamics, and kinetics. The geochemical analysis of the rock sample

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suggests coexisting quartz, clay, and calcite. Table 1 lists 15 reactions and their thermodynamics 9 ACS Paragon Plus Environment

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and kinetic parameters. The dissolution rates of quartz, muscovite and calcite depend on aqueous

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chemistry and are kinetically controlled. The reaction network includes aqueous complexation

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reactions that are considered fast and thermodynamically controlled60. A total of 19 species were

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used with the primary species being SiO2(aq), H+, CO2(aq), K+, Al3+, Ca2+, Na+, and Cl- while all

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other species are secondary, the concentrations of which are expressed in terms of primary

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species using laws of mass action of aqueous complexation reactions61. The reaction rates ri ,tot

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follow the Transition State Theory (TST) rate law62:   IAPj nk ri ,tot = −∑ j =1 Aij km , j 1 −    K eq , j

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    

(4)

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where nk is the total number of mineral reactions that species i is involved in, Aij is reactive

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surface area per unit volume (m2/m3) of mineral j that involves species i, and km,j is rate constant

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(mol/m2/s) indicating reactivity. The term IAPj/Keq,j quantifies disequilibrium, where IAPj is the

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ionic activity product and Keq,j is the corresponding equilibrium constant. When IAPj/Keq,j is

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close to 1.0, the system is close to equilibrium and the reaction rates are essentially zero,

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meaning the system is not reacting. The kinetic rate parameters were obtained by calibrating

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CO2-saturated water flooding experiment in Andreani et al.6, as will be discussed in the model

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calibration section later.

211 212 213 214

Table 1. Reaction Network, Reaction Thermodynamics and Kinetics at 150 °C

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log Keqa

Chemical reactions

Log k (mol/m2/s)b

SSA (m2/g)c

-2.66

-8.48

0.032

-10.16

-4.60

0.0037

42.33

-12.35

5.8400

-11.63

-

-

-6.73

-

-

-10.20

-

-

-1.71

-

-

-5.00

-

-

2.43

-

-

-21.90

-

-

-8.85

-

-

-25.94

-

-

-16.51

-

-

-7.73

-

-

Mineral dissolution and precipitation (kinetic controlled)

Aqueous speciation (at equilibrium)

-5.50

-

-

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a

Equilibrium constants Keq were interpolated using data from the EQ3/6 database63.

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b

Kinetic rate constants were adjusted to produce data in Andreani et al.6 They fall well into

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reported range in literature. kquartz is the same as that from the direct experimental measurement

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at 150 °C29. The kcalcite and kmuscovite at 150 °C were calculated using the formula,

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 -E  1 1  -6 k=k25 exp  a    . For calcite and muscovite, the k25 values are 1.55×10 and R 273.15+150 298.15   

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2.82×10-14 mol/m2/s while the Ea values are 23.5 and 22.0 kJ/mol, respectively64-67.

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c

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Computational domain and conditions. The temperature was set at 150 °C that is within the

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range of 137 °C - 205 °C in the Brady’s field35. Quantitative X-ray diffraction analysis suggests a

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matrix rock composed of 10% calcite ( CaCO3 , v/v), 50% quartz ( SiO2 , v/v), and 40% muscovite

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( KAl2 AlSi3O10 OH 2 , v/v) in the Calcite10 case. We also consider two additional cases:

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Calcite30 with 30% calcite, 40% quartz, and 30% muscovite; and Calcite50 with 50% calcite,

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30% quartz, and 20% muscovite. Minerals are assumed to be homogeneously distributed because

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detailed spatial distribution is unavailable. A pressure gradient is applied at the left and right

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boundaries however no-flux boundaries are imposed for the top and bottom boundaries. The

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injection water contains 0.15 mol/L NaCl at a pH of 6.5, similar to the brine composition at the

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site. All other species have concentrations less than 1.00×10-5 mol/L. The initial water in the

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matrix contains 0.039 mol/L NaCl with a pH of 7.6 and is equilibrated with calcite at 150°C.

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Dissolution rates at the core scale. The core-scale apparent dissolution rate Ra, j for the mineral j

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(mol/s) is calculated through mass conservation68:

Specific surface areas (SSA) are from29,65,67.

(

)( )

235

Ra, j = Qtot Cij ,out − Cij ,in 

236

Here Qtot is total volumetric flow rate (L/s), Cij ,out and Cij ,in are the effluent and influent

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concentrations of primary species i that are only involved in mineral reaction j (mol/L). Equation

238

(5) says that the apparent rates at the core scale are essentially the difference between input rates

239

and output rates of dissolved species. As has been discussed in literature8,68, this is equivalent to

240

calculating the mass change in the solid phase over time. In systems where mineral dissolution

(5)

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leads to concentration gradients and therefore spatial variations in IAP/Keq, not all mineral

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surface areas are bathed in water that are far from equilibrium and are effectively dissolving.

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Following our previous work, an effective surface area Ae is defined as the amount of surface

244

area where the mineral is at disequilibrium and is quantified with IAP/Keq