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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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Energy & Fuels
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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.
(
)( )
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Ra, j = Qtot Cij ,out − Cij ,in
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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
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(5) says that the apparent rates at the core scale are essentially the difference between input rates
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and output rates of dissolved species. As has been discussed in literature8,68, this is equivalent to
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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
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area where the mineral is at disequilibrium and is quantified with IAP/Keq