Subscriber access provided by ORTA DOGU TEKNIK UNIVERSITESI KUTUPHANESI
Article
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
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Energy & Fuels is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 43
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
1 2 3
4
5
Where Lower Calcite Abundance Creates More Alteration: Enhanced Rock Matrix
6
Diffusivity Induced by Preferential Carbonate Dissolution
7 8 9 10 11
Hang Wen1, Li Li1,2,3*, Dustin Crandall4, Alexandra Hakala4 1
John and Willie Leone Family Department of Energy and Mineral Engineering, The Pennsylvania
12 13
State University, University Park, PA 16802 2
Earth and Environmental Systems Institute (EESI), The Pennsylvania State University, University
14
Park, PA 16802 3
15 16 17
4
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
18 19
*Corresponding author (
[email protected])
20 21
Manuscript Resubmission to Energy & Fuels on March 1, 2016
22
1 ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 43
23
Abstract: Fractured rocks are critical for flow, solute transport and energy production in
24
geosystems. Existing studies on mineral reactions in fractured rocks mostly consider single
25
mineral systems where reactions occur at the fracture wall without changing rock matrix
26
properties. This work presents multi-component reactive transport numerical experiments in a
27
real fractured rock from the Brady’s field, a geothermal reservoir at a depth of 1,396 m in the Hot
28
Springs Mountains, Nevada. Initial porosity, permeability, mineral composition (quartz, clay, and
29
calcite), and fracture geometry are based on microscopy characterization and X-ray tomography.
30
The model was calibrated using a CO2-saturated water flooding experiment. Three numerical
31
experiments were carried out with the same initial physical properties however different calcite
32
content. Although total dissolved masses are similar in all cases, abundant calcite (50% v/v,
33
Calcite50) leads to localized, thick zone of large porosity increase while low calcite content
34
(10% v/v, Calcite10) creates an extended and narrow zone of smaller alteration resulting in
35
surprisingly larger change in effective transport property. After 300 days of dissolution, effective
36
matrix diffusion coefficients increase by 9.9 and 19.6 times in Calcite50 and Calcite10,
37
respectively, inducing corresponding 2.1 and 3.2 times rise in the slopes of power law tailing, a
38
measure of transport properties. This suggests counter-intuitive results that lower abundance of
39
reactive minerals leads to greater alteration in the fractured media. Alteration in matrix diffusion
40
significantly affects mineral dissolution. The effective rates of fast dissolving calcite are limited
41
by diffusive transport in the altered matrix and the shape of the altered zone, while effective
42
dissolution of quartz with much lower rates depends on effective diffusion of the entire rock
43
matrix. Simulation results indicate that calcite dissolution is transport-limited and only occurs at
44
the thin altered-unaltered matrix interface of tens of micron thickness occupying less than 1% of
45
the total surface area. In contrast, all quartz surface areas are effectively dissolving. This work
2 ACS Paragon Plus Environment
Page 3 of 43
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
46
highlights the importance of mineralogical complexity in determining mineral dissolution and
47
poorly understood rock matrix property evolution.
48
1. Introduction
49
Fractured rocks play a critically important role in geosystems, including geothermal
50
reservoirs1,2, nuclear waste repositories3,4, hydrocarbon reservoirs5, and deep saline aquifers for
51
carbon geosequestration6,7. These applications perturb the subsurface, leading to geochemical
52
disequilibrium and rock-fluid interactions including mineral reactions, sorption, and ion
53
exchange. These reactions change fluid composition, rock structure and conductive properties,
54
ultimately affecting long-term functioning of geosystems8,9. Fractures present predominant
55
conductive pathways for energy, mass, and flow in these systems, while the adjacent rock matrix
56
significantly retards solute transport through diffusive mass exchange with fractures10-13. The
57
interactions among fracture and rock matrix can play a pivotal role in the property evolution of
58
fractured rocks.
59
Extensive experimental and numerical studies have explored fracture characteristics and
60
property alteration induced by reactive flow, including initial aperture size and fracture
61
roughness14,15, fracture orientation16, and fracture length17,18. Injection rates, temperature, and
62
chemical composition16,19,20, and mechanical stress21,22 have also been examined and shown to be
63
important for describing evolution of fracture properties. Recent studies have explored the
64
application of dimensionless numbers, including Damköhler and Péclet numbers in unifying
65
dissolution behavior under different flow regimes23,24.
66
Most of these studies include single minerals without explicitly considering multi-
67
component reactive transport with thermodynamically and kinetically distinct geochemical
68
reactions. Mineral dissolution / precipitation has been assumed to occur only at the fracture 3 ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 43
69
surface and therefore does not alter the properties of rock matrix15,25. Natural rocks, however, are
70
typically composed of multiple minerals. For example, limestones are mostly carbonates
71
coexisting with quartz, feldspars, and clays26. Sandstones are dominated by quartz and often co-
72
occur with clays and carbonate cements27. Mineral reactivity varies by orders of magnitude.
73
Under far-from-equilibrium conditions, carbonate dissolves at rates orders of magnitude higher
74
than those of quartz dissolution28,29. In fractured rocks composed of multiple minerals, fast-
75
reacting minerals preferentially dissolve along fracture-matrix interfaces and leave behind slow-
76
reacting minerals, therefore forming altered zones with higher porosity and diffusivity in the rock
77
matrix at the vicinity of the fracture. Such property alteration can change fracture-matrix mass
78
exchange and have profound implications for fractured rock evolution.
79
Recent experimental studies have documented formation of altered zones in the presence
80
of multiple reactive minerals. Gouze et al.30 observed dissolution overhangs in fractured marine
81
carbonates (85% calcite) and called for a revisit of conventional effective aperture definition.
82
Noiriel et al.31 suggested that altered zones in fractured argillaceous limestones act as diffusion
83
barriers for fluid accessibility to rock matrix. Ellis et al.32 and Noiriel et al.8 observed that calcite
84
preferential dissolution in fractured limestones leads to non-uniform aperture increase and
85
altered zones mostly composed of dolomite and clay, which changes both fracture roughness and
86
hydraulic conductivity33. In a fractured argillaceous sample, however, calcite dissolution
87
increases matrix porosity by 50% while hydraulic conductivity remains unchanged6. In these
88
experiments, the complexity of chemical analysis and sample geometry characterizations prevent
89
detailed mechanistic understanding and quantification of fracture-matrix property evolution.
90
The objective of this study is to understand and quantify the role of mineral composition,
91
in particular preferential calcite dissolution, in determining property evolution of the fractured
4 ACS Paragon Plus Environment
Page 5 of 43
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
92
rock, including both the fracture and rock matrix. Numerical experiments of multi-component
93
reactive transport were carried out in a fractured rock built upon image data from CT scanning.
94
The fractured rock contains mostly quartz and illite/muscovite with minor amount of calcite. The
95
initial calcite abundance was varied to understand its role in determining property evolution
96
relevant to flow and transport.
97
2. Characterization of the Fractured Rock
98
Sample characterization. A core sample with a diameter of 2.54 cm was from a depth of 1,396
99
m at Brady’s field in the Hot Springs Mountains, Nevada, an extensively studied field for
100
enhanced geothermal application34. The subsurface contains over 2 km of faulted and fractured
101
mesozoic granite and metamorphic rocks that rest upon ash flow tufts and/or metamorphic
102
basement rocks. The sample was fractured artificially using a hydraulic core splitter. The rock
103
matrix porosity, measured by helium porosimeter HP-401 (TEMCO, Inc.), varies between 0.87%
104
- 1.54%. The rock permeability, determined by servo-hydraulic, tri-axial test system Autolab-
105
1500 (New England Research, Inc.), ranges between 6.0×10-20 and 2.0×10-19 m2. X-ray
106
diffraction analysis indicated rock composition of primarily quartz (25% - 50% v/v),
107
illite/muscovite (25% - 50% v/v) and calcite (5% - 25% v/v). The formation water is mostly
108
sodium chloride at an estimated concentration of 0.032 mol/L and is considered at equilibrium
109
with calcite35.
110
Fracture geometry acquisition. High-resolution CT scanning was performed to obtain 3D
111
fracture geometry at a resolution of 31.8 µm using an M-5000 Industrial Computed Tomography
112
System (North Star Imaging Inc.). Details of the CT parameters are documented in Crandall et
113
al.36 The radiographs were reconstructed into a 3D geometry and exported using eFX software
114
(North-Star Imaging). An OTSU threshold technique and careful examination of CT registration 5 ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 6 of 43
115
was used to isolate the fracture36. Details of the technique capability, limitations, and challenges
116
for the fracture-matrix identification can be found in Wildenschild et al.37 and Schlueter et al.38
117
To reduce the computational cost, a longitudinal 2D slice of 49.3 mm × 0.032 mm × 3.5 mm was
118
extracted and was discretized into 174,720 grid blocks (1560 × 1 × 112 voxels, Figure 1). Zero
119
aperture locations within this two dimensional cross-section were assigned a nominal aperture
120
value to enable continuity of flow in this sub-domain.
121 122
Figure 1. (A1 and A2) Three-dimensional fracture sample map with images from high-resolution
123
X-ray computed tomography. (B) A two-dimensional cross section indicated by the red box A-B
124
in A2 is used for the 2D simulations in this work.
125
3. Multi-component reactive transport numerical experiments
126
Flow field calculation. Although fluid flow within a fracture can be fully described by the
127
Navier-Stokes (N-S) equations, its combination with detailed, multi-component geochemical
128
reactive transport representation and evolving flow fields with changing matrix properties is
129
computationally expensive39. Various approaches exist to simplify flow field calculation in
130
fractured media, including the cubic law40, the classical Local Cubic Law (LCL)41,42, along with 6 ACS Paragon Plus Environment
Page 7 of 43
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
131
other extensions and modifications43,44. Among these, we chose to use a recent development, the
132
modified local cubic law (MLCL)45. MLCL takes into account weak inertia, tortuosity, and
133
roughness, while at the same time it is relatively straightforward to implement. Briefly, the
134
MLCL solves the following equation for the pressure field:
135
T ∇ ⋅ cos (θ ) ∇P = 0 C
136
where T is the local transmissivity (m2/s) in the main flow direction x; C is the correction factor
137
incorporating local roughness and inertia; θ is the local flow-orientation angle estimated based
138
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)
3
block ix is calculated following Tix =
140
being the flow-oriented aperture calculated based on apparent aperture at the grid blocks ix and
141
ix+1, respectively; µ is fluid viscosity (1.91×10-4 Pa·s at 150 °C46). Values of C depend on local
142
fracture and flow characteristics and are provided in a lookup table in the Supporting Information
143
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
139
144
The pressure solution to Equation (1) gives a one-dimensional flow field in the main flow
145
x direction, which is further distributed into flow velocities in the z direction transverse to the
146
main flow based on the parabolic law47:
147
2 z u x ( z ) = 1.5U x 1 − 0.5a f ( x )
(2)
148
where z is the transverse distance to the center of the aperture (m), u x ( z ) is the local fluid
149
velocity (m/s) in the longitudinal direction, U x is the average velocity (m/s) at the x location
150
calculated from the MLCL. By doing so we obtain a 2D flow field with flow velocities in the x 7 ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 8 of 43
151
direction following MLCL and in the z direction following the parabolic law, ensuring that flow
152
is zero at the fracture wall and is fastest in the center of the fracture.
153
In this study, the fractured rock has an average flow velocity of 1.15×10-5 m/s that is
154
within the typical range (10-3 - 10-6 m/s) for geothermal energy operations48 and a Re number of
155
0.23 that is within the applicable range of the MLCL method (Re≤1). Here Re is defined as
156
ρ Q / µ , where Q is the volumetric flow rate per unit fracture width (m2/s). Values of C in
157
Equation (1) vary from 1.00 to 1.15; values of θ vary from 0° to 36.8° , potentially leading to
158
about 3% deviation from N-S solutions45.
159
Based on measurements, the initial fracture and matrix porosity values assigned 100%
160
and 1%, respectively. The fracture aperture values based on image data vary between 95.4 and
161
858.6 µm, about 3 to 27 times of CT voxel resolution. Based on the local intrinsic fracture
162
permeability κ 0 =
163
fracture permeability values from 7.5×10-10 m2 to 6.1×10-8 m2. These values are orders of
164
magnitude larger than the measured rock matrix permeability (6.0×10-20 - 2.0×10-19 m2), ensuring
165
the no-slip boundary condition at the fracture boundary. This results in an effective fracture
166
permeability of 2.4×10-9 m2. With mineral dissolution during fluid flow, the altered rock matrix
167
can reach porosity increase as high as 50% with permeability values approaching 10-14 m2 50.
168
With the updated fracture-matrix permeability contrast of larger than four orders of magnitude,
169
the no-slip fracture boundary produces errors less than 1.0% in the flow calculations for the
170
fractured rock51-54.
171
Reactive transport equation. The reactive transport code CrunchFlow39 solves mass
172
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
8 ACS Paragon Plus Environment
Page 9 of 43
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
∂ ˆ i = ri ,tot ( i = 1, 2,..., Ntot ) (φ Ci ) + ∇ ⋅ −φ Dˆ ∇ ( Ci ) + uC ∂t
{
173
}
(3)
174
where φ is porosity, Ci is the concentration of primary aqueous species i (mol/m3), Dˆ is the
175
hydrodynamic dispersion tensor (m2/s), uˆ is the flow velocity (m/s), ri ,tot is the summation of
176
rates of multiple reactions that the species i is involved (mol/ m3/s) , and Ntot is the total number
177
of primary species. The longitudinal component of the dispersion coefficients (m2/s), for
178
example, is expressed as DL = D* + aLu x . Here D* is the effective diffusion coefficient (m2/s) in
179
an individual grid block and is calculated using Archie’s law D* = φ 1.5 Do , where Do is molecular
180
diffusion coefficient (m2/s) in water, and α L is longitudinal dispersivity (m). A molecular
181
diffusion coefficient of 6.0×10-9 m2/s (calculated from the Stokes-Einstein equation) is used for
182
all species at 150°C 55,56. The longitudinal and transverse dispersivity are 0.02 cm and 0.001 cm,
183
respectively57,58. The extended Debye-Hückel equation is used to take into account the salinity
184
effects59.
185
Based on the flow field calculated from Equations (1) and (2), CrunchFlow solves
186
Equation (3) for the concentrations of the Ntot species by discretizing over time and space. The
187
computational domain was assigned with fracture and rock matrix zones explicitly following the
188
images of the fractured rock. The rock matrix was assigned according to measured mineralogy in
189
Table 1. The porosity in the fracture is 100% so the effective diffusion coefficient equals to the
190
molecular diffusion coefficient in water55. With negligible flow in the matrix, it is expected that
191
D* dominates the dispersion coefficient. Mineral dissolution can open up pore space and enhance
192
diffusion in the matrix.
193
Reaction network, thermodynamics, and kinetics. The geochemical analysis of the rock sample
194
suggests coexisting quartz, clay, and calcite. Table 1 lists 15 reactions and their thermodynamics 9 ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 10 of 43
195
and kinetic parameters. The dissolution rates of quartz, muscovite and calcite depend on aqueous
196
chemistry and are kinetically controlled. The reaction network includes aqueous complexation
197
reactions that are considered fast and thermodynamically controlled60. A total of 19 species were
198
used with the primary species being SiO2(aq), H+, CO2(aq), K+, Al3+, Ca2+, Na+, and Cl- while all
199
other species are secondary, the concentrations of which are expressed in terms of primary
200
species using laws of mass action of aqueous complexation reactions61. The reaction rates ri ,tot
201
follow the Transition State Theory (TST) rate law62: IAPj nk ri ,tot = −∑ j =1 Aij km , j 1 − K eq , j
202
(4)
203
where nk is the total number of mineral reactions that species i is involved in, Aij is reactive
204
surface area per unit volume (m2/m3) of mineral j that involves species i, and km,j is rate constant
205
(mol/m2/s) indicating reactivity. The term IAPj/Keq,j quantifies disequilibrium, where IAPj is the
206
ionic activity product and Keq,j is the corresponding equilibrium constant. When IAPj/Keq,j is
207
close to 1.0, the system is close to equilibrium and the reaction rates are essentially zero,
208
meaning the system is not reacting. The kinetic rate parameters were obtained by calibrating
209
CO2-saturated water flooding experiment in Andreani et al.6, as will be discussed in the model
210
calibration section later.
211 212 213 214
Table 1. Reaction Network, Reaction Thermodynamics and Kinetics at 150 °C
10 ACS Paragon Plus Environment
Page 11 of 43
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
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
-
-
215
a
Equilibrium constants Keq were interpolated using data from the EQ3/6 database63.
216
b
Kinetic rate constants were adjusted to produce data in Andreani et al.6 They fall well into
217
reported range in literature. kquartz is the same as that from the direct experimental measurement
218
at 150 °C29. The kcalcite and kmuscovite at 150 °C were calculated using the formula,
11 ACS Paragon Plus Environment
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 12 of 43
219
-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
220
2.82×10-14 mol/m2/s while the Ea values are 23.5 and 22.0 kJ/mol, respectively64-67.
221
c
222
Computational domain and conditions. The temperature was set at 150 °C that is within the
223
range of 137 °C - 205 °C in the Brady’s field35. Quantitative X-ray diffraction analysis suggests a
224
matrix rock composed of 10% calcite ( CaCO3 , v/v), 50% quartz ( SiO2 , v/v), and 40% muscovite
225
( KAl2 AlSi3O10 OH 2 , v/v) in the Calcite10 case. We also consider two additional cases:
226
Calcite30 with 30% calcite, 40% quartz, and 30% muscovite; and Calcite50 with 50% calcite,
227
30% quartz, and 20% muscovite. Minerals are assumed to be homogeneously distributed because
228
detailed spatial distribution is unavailable. A pressure gradient is applied at the left and right
229
boundaries however no-flux boundaries are imposed for the top and bottom boundaries. The
230
injection water contains 0.15 mol/L NaCl at a pH of 6.5, similar to the brine composition at the
231
site. All other species have concentrations less than 1.00×10-5 mol/L. The initial water in the
232
matrix contains 0.039 mol/L NaCl with a pH of 7.6 and is equilibrated with calcite at 150°C.
233
Dissolution rates at the core scale. The core-scale apparent dissolution rate Ra, j for the mineral j
234
(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
237
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)
12 ACS Paragon Plus Environment
Page 13 of 43
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
241
leads to concentration gradients and therefore spatial variations in IAP/Keq, not all mineral
242
surface areas are bathed in water that are far from equilibrium and are effectively dissolving.
243
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
