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Alteration of minerals and temporal evolution of solution in reactive flow through granitic rock fractures
International Journal of Rock Mechanics and Mining Sciences 123 (2019) 104105
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Alteration of minerals and temporal evolution of solution in reactive flow through granitic rock fractures
T
Qiao Lipinga, Anda Huangb, Wang Zhechaoa,∗, Wenyuan Gaoc, Jie Liua a
Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang, Liaoning, 110819, P. R. China School of Civil Engineering, Shandong University, Jinan, Shandong, 250061, P. R. China c Department of Geology Sciences, School of Resources and Civil Engineering, Northeastern University, Shenyang, Liaoning, 110819, P. R. China b
ARTICLE INFO
ABSTRACT
Keywords: Reactive flow Alteration Granitic rock fracture Temporal evolution ion concentration Reaction rate
The alteration of minerals and temporal evolution of solution in reactive flow through granitic rock fractures were investigated. Two experiments at different flow rates of solutions (i.e., Reynolds numbers for the flow) were performed on granitic rock fractures with comparable hydraulic apertures. The fracture surface morphologies and masses of the fracture walls were measured before and after the experiments. The alteration of the minerals on fracture surfaces exhibited nonuniform features induced by heterogeneity in the soluble minerals and their nonuniform distribution on the rock fracture surfaces. The ion concentrations and pH values of the solutions were measured during the experiments. The variations of the ion concentrations in the solutions were complementary to the dissolution or precipitation of minerals on the fracture surfaces. The water-rock reaction was identified as the primary process dominating the reactive flow in the experiments. According to the principles of mass and charge conservation, thirteen chemical reactions were identified between the minerals on the fracture surfaces and solutions in the experiments and 3 out of the thirteen contributed more than 90% of the reactants in amount of substance. The dissolution rate of sphene for the experiment at Reynolds number 676 was higher than that at 3750 because of the higher reaction rate between the solutions and the rock minerals. A correction coefficient was introduced and calculated to describe the effect of flow rate on the reaction rate.
1. Introduction Flow and transport processes in fractured rock masses have received considerable attention in recent years.1 The processes alter the physical and chemical properties of groundwater and rock masses.2 The transport of solutes through fractured geological media is of critical importance for evaluating the impacts of nuclear waste disposal3–7, general hazardous waste disposal8, CO2 geological sequestration9, oil and gas development10, aquifer protection11,12, tunnel construction13, landslides14, dam foundations15 and underground oil/gas storage16–18 on the geological environment. Rock fractures dominate the flow and transport processes in fractured rock mass.19 Reactive flow in fractures has been extensively investigated using numerical and analytical methods. Deterministic and stochastic numerical simulations of reactive flow processes have been performed for rock fractures in numerous studies.20–24 Analytical methods have been used to describe the processes with simple boundary conditions in fractures.25–28 In the above numerical and
∗
analytical studies, various aspects of reactive flow have been investigated qualitatively. However, experimental data are required to validate the findings from these numerical and analytical studies. Predicting changes in the flow and transport properties of fractures is still a challenge due to the complexity of water-rock interactions and the uncertain role of fracture heterogeneity.29,30 Experiments conducted at the laboratory scale are needed for this kind of characterization. In the literature, experiments have been conducted to address the effects of the Damköhler number31, Peclet number32, flow rate and dissolution pattern30,33, and solution contents34 on the hydraulic conductivity of rock fractures. For reactive flow in rock fractures, the minerals on the fracture surfaces dissolve and the components and concentrations of solutes evolve in the process.35,36 A simultaneous observation of the alteration of fracture surface minerals and temporal evolution of solutions would provide a comprehensive understanding of reactive flow in rock fractures. In addition, fractures in rocks consisting of single minerals such as limestone, marble or rock salt were used in most of the existing studies. The experimental studies are few on
Corresponding author. School of Resources and Civil Engineering, Northeastern University, 11#, 3rd Ave, Wenhua Rd, Shenyang, 110819, P. R. China. E-mail address: [email protected] (Z. Wang).
https://doi.org/10.1016/j.ijrmms.2019.104105 Received 14 January 2019; Received in revised form 6 July 2019; Accepted 4 September 2019 1365-1609/ © 2019 Elsevier Ltd. All rights reserved.
International Journal of Rock Mechanics and Mining Sciences 123 (2019) 104105
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Fig. 1. (a) Skecth of the experiment apparatus (b) Longitudinal profile of the rock fracture (part 7) (c) Cross-sectional profile of the rock fracture (part 7).
reactive flow in rock fractures consisting of several minerals, where the alterations of the minerals on fracture surfaces would exhibit heterogeneous behavior. In this study, the fundamentals of reactive flow in single rock fracture were reviewed and a correction coefficient was introduced to describe the effect of flow rate on the reaction rate. A set of experiment apparatus was designed and manufactured for the investigations on reactive flow in rock fractures. Two experiments at different flow rates of solutions (i.e., Reynolds numbers (Re) for the flow) were performed on granitic rock fractures with comparable hydraulic apertures. The fracture surface morphologies and masses of the fracture walls were measured before and after the experiments. The ion concentrations and pH values of the solution were measured during the experiments. Based on the experiment results, the alteration of the minerals on fracture surfaces and the temporal evolution of the solute in reactive flow through granitic rock fractures were simultaneously investigated.
2. Fundamentals of reactive flow in single rock fractures 2.1. Governing equations For reactive flow in single fractures, the solute concentration and fracture aperture are to be solved under the specified initial and boundary conditions. The governing equations for solute concentration and fracture aperture are respectively expressed as37:
C = t
(Dm C )
b = rMs / t
s
(uC ) + R c
(1) (2)
where C is the solute concentration, [mol·L−1]; t is the time, [s]; Dm is the coefficient of diffusion, [m2·s−1]; u is the flow rate, [m·s−1]; Rc is the rate of solute concentration change induced by the chemical 2
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Fig. 2. (a) Rectangular plate samples with a size of 50 × 50 × 10 mm (b) Rock fracture consisting of 6 small rectangular plate samples and silicone pad formed as illustrated in Fig. 1
soluble minerals, [g·mol−1]; and ρs is the mass density of soluble minerals, [kg·m−3].
1.0
H y d ra u lic a p ertu re (m m )
Re=2500 Re=3750 Re=676 0.8
2.2. Characteristic dimensionless parameters
Re=500 Re=676 Re=3750
In reactive flow, advection, molecular diffusion and chemical reaction processes are coupled. To compare the influences of the mechanisms of the three processes, two dimensionless parameters are widely used, namely, the Pelect number and Damköhler number. The Pelect number describes the effect of advection relative to that of molecular diffusion on solute transport and is expressed as26:
0.6 0.4 0.2
Pe =
0.0 0
5
10
15
20 Time (d)
25
30
35
40
ub 2Dm
(3)
The Damköhler number describes the effect of chemical reaction relative to that of molecular diffusion on solute transport and is expressed as26:
Fig. 3. Variations of hydraulic apertures with time for the fractures in the two experiments.
Da =
reaction between the solution and fracture surface mineral, [mol·L−1·s−1]; b is the fracture aperture, [m]; r = bRc is the reaction rate of surface soluble minerals, [mol·m−2·s−1]; Ms is the molar mass of
kk b2 4Dm
where kk is the [mol·m−2·s−1]. 3
(4) first-order
kinetic
reaction
rate
coefficient,
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Fig. 5. Variations of ion concentrations with time in the solution for the experiment at Re = 3750.
Fig. 4. Variations of ion concentrations with time in the solution for the experiment at Re = 676.
To incorporate the effect of variable aperture during the processes, Dijk and Berkowitz26 introduced the effective fracture aperture, effective flow rate, effective Pelect number and effective Damköhler number. The initial effective fracture aperture (beff ,0 ) is expressed as:
1
beff ,0 =
1 x=l 1 dx l x = 0 b03
1/3
(5)
where b0 is the initial fracture aperture, [m]; l is the fracture length, [m]; and x is the coordinate along flow direction. The initial effective maximum flow rate (ueff ,0 ) is expressed as: 2 1 pbeff ,0 8 lµ
(6)
Fig. 6. Variations of pH values with time in the solutions for the two experiments.
where Δp is the pressure difference along the fracture, [Pa], and μ is the dynamic viscosity of fluids, [Pa·s]. Then, the dimensionless initial effective Pelect and Damköhler numbers are expressed, respectively, as:
on the reactive flow of sodium sulfate solution through granitic rock fractures.
ueff ,0 =
Peeff ,0 =
ueff ,0 beff ,0 2Dm
2.3. Reaction rates
(7)
and
Daeff ,0 =
In general, the reaction rates between minerals and solutions depend on the solute concentrations in the solution. For a dilute solution, the reaction rate of a mineral can be expressed as36:
2 kk beff ,0
4Dm
(8)
r = ks (1
These dimensionless initial effective Pelect and Damköhler numbers are used in Section 5 to compare the influences of the three mechanisms
C /Csat )
(9)
where Csat is the concentration of a solute in the equilibrium state, 4
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caverns18,39, the concentration of Na+ is 0.9–3.9 mmol/L, and that of SO42− is 0–1.7 mmol/L in the real underground water. The concentrations of Na+ and SO42− in the experimental solution were in the range of the field underground water. 3.2. Experiment apparatus A set of experiment apparatus was designed and manufactured for the investigations on the reactive flow through rock fractures. The experiment apparatus mainly consists of rock fracture, pump, flow meter, pressure transducer and data recording system. The flow rate was measured by flow meter and ranged from 0.04–0.4 m3/h with an accuracy of 1%. The pressure was measured by pressure transducer and ranged from 0–0.5 MPa with an accuracy of 0.5%. The sketch of the experiment apparatus is shown in Fig. 1(a), and the rock fracture as the critical part of the apparatus is illustrated in Fig. 1(b) and (c) . As shown in Fig. 1, the characteristics of the system are as follows: (1) the flow rate of solutions can be specified and the transport characteristics of solutions in different flow regimes can be obtained; (2) a single rock fracture surface was formed to investigate the alteration of minerals and temporal evolution of solution in reactive flow through granitic rock fractures. 6 pieces of rectangular plate samples were arrayed in the socket made of steel plate as the rock fracture surface, while the rock fracture aperture was determined by the thickness of the positioned silicone pad, as shown in Fig. 1(b) and (c).
Fig. 7. Mass changes of rock blocks before and after the experiments.
[mol·L−1] and ks is the first-order static reaction rate coefficient, [mol·m−2·s−1]. Considering the effect of temperature on the reaction rate, ks can be expressed as:
ks = ks25 exp
Ea 1 R T
1 298.15
(10) −2 −1
where ks25 is the static reaction rate coefficient at 25 °C, [mol·m ·s ]; Ea is the reaction activation energy, [kJ·mol−1]; R is the universal gas constant, [kJ·mol−1·K]; and T is the absolute temperature, [K]. For a specified solute, ks25, Ea and R are constant and ks considering the temperature effect can be determined. In Eq. (9), the reaction rate is determined for the solution in a static state. The flow of the solution will alter the reaction rate as a consequence of the flow of reactants in solution. In this study, a correction coefficient (fRe) is introduced to describe the effect of flow on the reactive rate, and the reaction rate for a mineral considering reactive flow can be revised as:
r = kk (1
C / Csat ) = ks fRe (1
C /Csat )
3.3. Experiment procedure The experiment procedure includes experiment preparation and observation of minerals alteration and solution temporal evolution. To investigate the effect of flow regime on the minerals alteration and solution temporal evolution, two experiments were conducted with specified Reynolds number of 676 and 3750. The flow rates were controlled by regulating the pump pressure. At the preparation stage, 6 rectangular plate samples with the size of 50 × 50 × 10 mm were manufactured for each experiment, and the samples were polished using sander, as shown in Fig. 2(a). The fracture length was the sum of 6 samples and the gaps between each sample, and the total value was 0.36 m. The rock fracture apertures were determined by the positioned silicone pad for two experiment types as shown in Fig. 2(b). A digimatic micrometer with an accuracy of 0.001 mm was used to measure the thickness of the silicone pad. Considering that the silicone pad can be compressed after fixed by the screw, the heights of the apparatus without silicone pad and with silicone pad after fixed were both measured, and the difference between the two values was determined as the fracture aperture. The fracture apertures were 1.857 mm and 1.664 mm for the two experiments, respectively. During the experiment process, observations of minerals alteration and solution temporal evolution were performed. To investigate the mineral alteration on the rock fracture surface, the masses, the topographies, and the mineral compositions of the rock samples were obtained before and after the experiments. The masses of the samples were weighed using an electronic balance with an accuracy of 0.01 g. The initial topography of the fracture surface was measured using 3D digital microscope Keyence VHX-2000E. The SEM analyses were performed on the samples with the size of 1 × 1 cm using Zeiss Ultra plus Scanning Electron Microscope. The Electron Probe X-ray Microanalyser (EPMA) was used to investigate the mineral alteration of the rock fracture surface, and it can quantify the mineral contents of rocks. To obtain the solution temporal evolution, 100 ml aqueous chemical solution was sampled every 5 days and the initial solution with the same volume was added into the experiment apparatus. The ion composition and concentrations of the sampled solution were analyzed via wholespectrum direct-reading ICP-AES. The pH value of the sampled solution was measured using a PHS-25 digital pH meter.
(11)
In the following calculation, the reaction rate of surface soluble minerals r is determined from the experiment result. The first-order static reaction rate coefficient ks is determined according to Eq. (10) considering the effect of temperature. The solute concentration C is obtained from the experiment result, and the concentration of a solute in the equilibrium state Csat is a constant for a specified solute. Thereby, the proposed correction coefficient fRe can be calculated, as well as the parameter of kk. 3. Experiment method 3.1. Materials The rock specimens used in the experiments were granitic rocks from the Cretaceous and Proterozoicus ages and collected from Huangdao underground oil storage caverns which is the first large-scale underground water-sealed crude oil storage cavern project constructed in China. A sodium sulfate solution was chosen to be the experimental solution. Sodium hydroxide and sulphuric acid were used to prepare the sodium sulfate solution, and 6 L distilled water was used. The planed ion concentrations of Na+ was 1.5 mmol/L for the two experiments (Re = 676 and Re = 3750), respectively. However, the measured original ion concentration of Na+ for the two experiments (Re = 676 and Re = 3750) were 1.527 mmol/L and 1.274 mmol/L, respectively, while the measured concentration of SO42− for the two experiments (Re = 676 and Re = 3750) were 1.031 mml/L and 1.010 mmol/L, and the pH value for the two experiments (Re = 676 and Re = 3750) were 4. The error in the concentration of Na+ was considered as the test error. According to the field study of Huangdao underground oil storage 5
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Fig. 8. Surface topography of the 6 rectangular plate samples before and after the experiments measured using 3D digital microscope Keyence VHX-2000E with an amplification time of 200 (samples #1~#6 from top to bottom).
4. Experiment result
The variations of hydraulic apertures with time for the two experiments are shown in Fig. 3. The hydraulic apertures remained basically unchanged during the experiments. The average hydraulic aperture was 0.53 mm for the experiment with Re = 676, while the average hydraulic aperture was 0.57 mm for the experiment with Re = 3750. Therefore, the hydraulic apertures are comparable in the two experiments.
4.1. Hydraulic apertures In this study, the hydraulic aperture can be obtained using cubic law40:
Q=
we3 P 12µl
(12)
4.2. Temporal evolution of solutions
where Q is the volumetric flow rate, [m3/s], and e, l and w are the hydraulic aperture, length and width of fracture, respectively, [m].
The variations of ion concentrations in the solutions with time for 6
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Fig. 9. (a) Surface topography of the rock sample #6 (b) Slightly alterated zones (saz) (c) Intensively alterated zones (iaz) on the surface after the experiment at Re = 3750.
the cases of Re = 676 and Re = 3750 are shown in Figs. 4 and 5, respectively. The variations of pH values in the solutions with time are shown in Fig. 6. From the results, the concentrations of Ca2+, K+ and Mg2+ in the solutions increased with time. The concentration of Ca2+ increased at the beginning of the experiment and then tended to be stable. The concentration of Na+ first increased to some extent and then decreased slightly and tended to be stable. The concentrations of Al3+, Fe2+, and SiO32− were close to 0 mmol/L and had no obvious variation. The large fluctuations were observed for SO42−, and this may be caused by the addition of 100 ml original solution and some unknown reason. The pH values of the solutions increased to approximately pH = 8 at the first 5 days and then tended to be stable at pH = 8, and the reason was explained in the following discussion. The variations of pH values were similar in the two experiments.
two representative zones are analyzed as shown in Fig. 9. Fig. 9(b) and (c) show the images of the two zones on the rock sample #6 after the experiment at Re = 3750 magnified by 2000 times. As shown in Fig. 9(b), only slight corrosion occurred in the light-flesh zone considered as slightly alterated zone (the zone labeled saz in the figure), while obvious corrosion holes and cavities were observed in the darkgray zone considered as intensively alterated zone (the zone labeled iaz in the figure). The two representative zones of #6 rock sample after the experiment at Re = 3750 were magnified for different times as shown in Fig. 10. Fig. 10(b) and (c) show the microstructures in the slightly alterated zone magnified by 1000 and 3000 times, respectively. A slight alteration of minerals, e.g., corrosion and erosion holes in the zone can be observed due to the reactive flow of the solution. Fig. 10(d)-(f) show the microstructures in the intensively alterated zone magnified by 300, 3000 and 10000 times, respectively. Intensive mineral dissolution, e.g., inter-granular and intra-granular holes, was observed on fracture surface. There were some precipitate minerals observed on the fracture surface although the solution flowed at the specified rate. The heterogeneity in minerals on the fracture surface induced the difference in alteration degree in different zones. EPMA analysis was conducted to quantify the alteration of the rock minerals. Fig. 11 shows the microscopic electron micrographs and atomic spectrograms of #6 rock sample after the experiment at Re = 3750. The point analysis of spectral element content and mineral composition at different locations of #6 rock sample after the experiment at Re = 3750 can be obtained by the EPMA analysis as listed in Table 1. The major elements of the minerals in locations of #7, 9, 10 and 11 were Si, O, Al, K and Na, which was consistent with the composition of potassium feldspar, albite, quartz and mica. The elements Fe appeared in location of #13, and it indicated that there was a large quantity of magnetite. The element contents of Ca, Ti, Si and O were existed in locations of #18 and 19, and this was consistent with the composition of sphene. The element contents of Ca in locations of #18 and 19 were higher than those in the other locations.
4.3. Alteration of minerals of rock fractures 4.3.1. Mass of fracture walls The mass of rock walls changed in the rock fracture alteration process. Fig. 7 shows the mass changes of the 6 pieces rock samples before and after the experiments. In the case of Re = 676, the mass variations in the 6 pieces rock samples from #1 to #6 were −20, −20, 10, 20, 0 and −30 mg, respectively, with a total mass decrease of 40 mg. In the case of Re = 3750, the mass variations in the 6 pieces of the rock samples from #1 to #6 were −40, 30, 10, 50, 20 and −30 mg, respectively, with a total mass increase of 40 mg. 4.3.2. Fracture surface topography The topography of the 6 rectangular plate samples before and after the experiments were measured using 3D digital microscope Keyence VHX-2000E with an amplification factor of 200 as shown in Fig. 8. The visible changes, including the color and the border, can be seen on the rock samples before and after the experiments. In general, there are two main zones on the rock samples, i.e., the dark-gray zones on the fracture surfaces (as marked in the pictures after the experiments) and the lightflesh zones. In the case of Re = 676, the areas of dark-gray zones (marked zones) of the 6 rock samples from #1 to #6 were measured to be 3.38, 1.37, 1.23, 1.94, 5.98, and 1.93 cm2, respectively, with a total area of 15.83 cm2. In the case of Re = 3750, the areas of dark-gray zones (marked zones) of the 6 rock samples from #1 to #6 were 2.53, 2.39, 1.55, 2.45, 2.37 and 3.18 cm2, respectively, with a total area of 14.47 cm2. The alteration depths in the intensively alterated zones were estimated from 0.5 to 0.8 mm.
5. Discussion 5.1. Dominating mechanism The initial effective Pelect number and initial effective Damköhler number Peeff,0 and Daeff,0 were determined for the cases of Re = 676 and Re = 3750 using Eqs. (5)–(8), respectively. The parameters used in the determination were presented in Table 2. In the case of Re = 676, the values of Peeff,0 and Daeff,0 were 1.87 × 105 and 6.25 × 10−5, respectively. In the case of Re = 3750, the values of Peeff,0 and Daeff,0 were 9.25 × 105 and 3.70 × 10−5, respectively. The effect of advection was an order of 105 that of molecular diffusion on solute transport, while the effect of reaction was an order of 10−5 that of molecular
4.3.3. Alteration of minerals on fracture surfaces SEM analyses with different magnification factors were conducted on the two representative zones to investigate the mineral alteration. Taking #6 rock sample of the experiment at Re = 3750 for an example, 7
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Fig. 10. SEM images of fracture surface on the #6 rock sample after the experiment at Re = 3750 showing mineral alteration.
Ca2+ was much higher than those of other cations. In addition, the EPMA result can tell that the mineral with Ca2+ was sphene. Therefore, it was considered that sphene was the dominating mineral in water-rock reactions for the granitic rock fractures and solutions. From Figs. 4 and 5, the concentration of Ca2+ increased quickly within the first 10 days and the rate was slow in the following 20 days. Eventually, the concentration of Ca2+ tended to become stable in the last 10 days. This result indicated that the water-rock reaction rate was time-dependent. According to the alteration of minerals on rock fracture surfaces and the temporal evolution in the solutions, the chemical reaction equations
diffusion on solute transport. Under the experiment conditions, convection had the greatest influence on the flow of reactive solutes, and chemical reaction had the lowest influence. Therefore, chemical reaction was the dominating mechanism for the alteration of minerals and temporal evolution of solution in reactive flow through the granitic rock fractures under the experiment conditions. 5.2. Chemical reaction equations As shown in Figs. 4 and 5, the increment in the concentration of 8
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#12: H4SiO4→H2O + H2SiO3→H2O + H++HSiO3−
can be identified using the conservations of mass and charges. For this study, the chemical reaction equations were determined as: +
#1: CaTiSiO5+4H →TiO #2: TiO
2+
2+
#13: KFe3AlSi3O10(OH)2+10H+→Al3++K++2H4SiO4+3Fe2+
2+
+H4SiO4+Ca
Table 3 presents Molar fractions of chemical reactions and masses of dissolution and precipitation minerals during different periods of time. According to the data in Table 3, the major 3 chemical reactions in the experiments are as follows:
+2H2O→H2TiO3↓+2H+
#3: H2O + CO2↔HCO3− + H+ #4: Ca2++SO42−→CaSO4↓
#1: CaTiSiO5+4H+→TiO2++H4SiO4+Ca2+
+
#5: 2NaAlSi3O8+2H +2H2O→Al2(Si2O5)(OH)4↓+4SiO2+ 2Na+Al2(Si2O5)(OH)4↓+4SiO2+2Na+
#2: TiO2++2H2O→H2TiO3↓+2H+ #3: H2O + CO2↔HCO3− + H+
#6: Fe3++3H2O↔Fe(OH)3↓+3H+
The reactants in the major 3 chemical reactions accounted for 90% of the total reactants in all the chemical reactions by the amount of substance. At the beginning, the sodium sulphate was acidic with pH value of 4, and sphene can dissolute under the acidic condition. The dissolution of sphene tended to be stable while the solution tended to be neutral. This is also in accordance with the variation of pH value. As the above mentioned, the pH values of the solutions in the two experiments increased to approximately pH = 8 at the first 5 days and then tended
#7: Fe3O4+8H+→2Fe3++Fe2++4H2O #8: Fe2++2H2O↔Fe(OH)2↓+2H+ #9: Al3++3H2O↔Al(OH)3↓+3H+ #10: 2KAlSi3O8+2H++2H2O→Al2(Si2O5)(OH)4↓+4SiO2+2K+ #11: KAlMg3Si3O10(OH)2+10H+→Al3++K++2H4SiO4+3Mg2+
Fig. 11. Microscopic electron micrographs and atomic spectrograms of #6 rock sample after the experiment at Re = 3750. 9
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Fig. 11. (continued)
chemical reaction #1. This was in accordance with the increase of the concentration of Ca2+.
Table 1 Point analysis of spectral element content and mineral composition at different locations of #6 rock sample after the experiment at Re = 3750.
5.3. Temporal evolution of reactions
oxide contents (wt%)
Locations #7
#9
#10
#11
#13
#18
#19
Na2O Al2O3 SiO2 K2O CaO MgO FeO TiO2 Total Mineral
0.76 18.82 65.22 15.21 0.00 0.00 0.00 0.00 100.00 potassium feldspar
9.54 21.02 67.42 0.36 1.67 0.00 0.00 0.00 100.00 albite
0.00 0.00 100.00 0.00 0.00 0.00 0.00 0.00 100.00 quartz
0.52 35.82 47.32 12.25 0.00 0.56 3.53 0.00 100.00 mica
0.00 0.61 0.00 0.00 0.00 0.00 99.39 0.00 100.00 magnetite
0.00 1.39 30.67 0.00 28.69 0.00 1.54 37.71 100.00 sphene
0.00 3.18 30.88 0.00 28.33 0.00 1.35 35.15 98.89 sphene
Fig. 12 shows the variations of the percentages of the total amount of substance of the chemical reactions with time in the two experiments at Re = 676 and Re = 3750. In the first 5 days, the percentages were 37.04% and 37.40% for the cases of Re = 676 and Re = 3750, respectively. The percentages dropped to 16.88% and 14.5% for the two cases in the 5–10 days, 9.36% and 6.70% in 10–15 days. Eventually, the percentages were less than 1% in the last 5 days. Table 3 presents the changes in masses of dissolution and precipitation minerals. For the case Re = 676, the mass of the dissolution minerals was 3481.38 mg, and the mass of the precipitated minerals was 3756.51 mg with a gain in mass of 275.13 mg for rock sample. For the case Re = 3750, the mass of the dissolution minerals was 2855.13 mg, and the mass of the precipitation minerals was 3096.52 mg with a gain in mass of 241.39 mg for rock sample. The mass changes of the rock samples from the above analysis were higher than those measured from the experiments due to the settlement of the products on the tubing and in the tank, which was not collected and measured. The mass changes after the experiments at Re = 676 and 3750 are small, i.e., 275.13 mg and 241.39 mg. Then assuming a density of 3.5 g/ cm3 for reactive minerals, the geometrical aperture changes during the tests can be estimated 0.0052 mm and 0.0046 mm, respectively. Therefore, the permeability changes little for the two experiments.
Table 2 Parameters for the determination of initial effective Pelect number and initial effective Damköhler number. Re
b(mm)
u(m/s)
l(m)
Dm(m2•s−1)
μ(Pa•s)
ks(mol/ (m2•s))
kk(mol/ (m2•s))
676 3750
1.857 1.664
0.27 1.49
0.36 0.36
1.34E-09 1.34E-09
0.74E-03 0.66E-03
8.91E-12 8.91E-12
9.71E-8 7.17E-8
to be stable at pH = 8. This is because the chemical reaction of the mineral sphene was the main reaction following the chemical reaction #1. The ions H+ decreased in the whole process. Although some ions H+ generated, considering that the other 2 dominant chemical reactions #2 and #3, the generated H+ was quickly consumed in the
5.4. Chemical reaction rate As observed in the experiments, the chemical reaction between 10
Mineral mass
Mole fractions
Category
2+
2+
CaTiSiO5+4H →TiO +H4SiO4+Ca TiO2++2H2O→H2TiO3↓+2H+ H2O + CO2↔HCO3− + H+ Ca2++SO42−→CaSO4↓ 2NaAlSi3O8+2H++2H2O→Al2(Si2O5)(OH)4↓+4SiO2+2Na+Al2(Si2O5)(OH)4↓+4SiO2+2Na+ Fe3++3H2O↔Fe(OH)3↓+3H+ Fe3O4+8H+→2Fe3++Fe2++4H2O Fe2++2H2O↔Fe(OH)2↓+2H+ Al3++3H2O↔Al(OH)3↓+3H+ 2KAlSi3O8+2H++2H2O→Al2(Si2O5)(OH)4↓+4SiO2+2K+ KAlMg3Si3O10(OH)2+10H+→Al3++K++2H4SiO4+3Mg2+ H4SiO4→H2O + H2SiO3→H2O + H++HSiO3− KFe3AlSi3O10(OH)2+10H+→Al3++K++2H4SiO4+3Fe2+ Dissoluted minerals (mg) Precipitated minerals (mg) Mass changes (mg)
+
23.11% 23.11% 46.33% 3.93% 1.54% 1.18% 0.47% 0.12% 0.08% 0.00% 0.07% 0.05% 0.01% −2487.59 2717.38 229.79
0–10 d
Re = 676
Table 3 Molar fractions of chemical reactions and masses of dissolution and precipitation minerals during different periods of time.
22.30% 22.30% 46.97% 2.35% 0.53% 3.32% 1.66% 0.19% 0.08% 0.19% 0.05% 0.03% 0.03% −955.63 999.94 44.31
10–30 d 23.27% 23.27% 40.47% 2.53% 3.04% 2.02% 1.01% 1.01% 0.67% 2.02% 0.67% 0.01% 0.01% −38.16 39.19 1.03
30–40 d
10–30 d 24.08% 24.08% 44.93% 3.37% 0.18% 0.90% 0.45% 0.90% 0.33% 0.27% 0.28% 0.19% 0.04% −681.74 735.56 53.82
0–10 d 21.49% 21.49% 47.45% 3.93% 3.19% 0.89% 0.44% 0.59% 0.14% 0.09% 0.14% 0.15% 0.01% −2124.24 2308.83 184.59
Re =3750
21.89% 21.89% 40.54% 4.86% 5.68% 1.62% 0.81% 0.00% 0.54% 1.62% 0.55% 0.00% 0.00% −49.15 52.13 2.98
30–40 d
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Fig. 12. Variations of the percentages of the total molar quantity of the chemical reactions with time for the two experiments at Re = 676 and Re = 3750.
Fig. 13. Variations of Ca2+ concentrations with time for the two experiments at Re = 676 and Re = 3750.
Fig. 14. Variations of reaction rates between sphene and the solutions after the corrections in terms of both the reaction surface area and the temperature.
sphene and the solutions was the dominating reaction out of the minerals. Fig. 13 shows the variations of Ca2+ concentrations with time in the two experiments at Re = 676 and Re = 3750. The Ca2+ concentrations increased granularly at the beginning and became stable at 2.45 and 1.88 mmol/L after 35 days in the experiments at Re = 676 and Re = 3750, respectively. Because the reaction surface areas of the two fractures were different and the temperatures varied with time in the two experiments, the chemical reaction rates were corrected. The correction of chemical reaction rates in terms of reaction surface area was performed. The correction of chemical reaction rates in terms of temperature was
11
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performed according to Eq. (11). Fig. 14 shows the variations of reaction rates between sphene and the solutions after the corrections in terms of both the reaction surface area and the temperature. The reaction rates decreased from 7.8e-6 and 5.9e-6 to about 0 for the two cases of Re = 676 and Re = 3750, respectively. It indicated that the higher flow rate, the lower chemical reaction rate was. This finding was consistent with the observations by Durham.35 They performed reactive transport through rough marble fracture. It was found that the rates of the reaction between calcite and acid solution on the fracture surface along the low flow rate channels were higher than those along the high flow rate channels. The correction coefficient fRe can be calculated according to Eq. (11). The correction coefficient fRe are 10896.7 and 8042.2 for the cases of Re = 676 and Re = 3750, respectively. It indicated that the effect of flow rate on the chemical reaction between sphene and solutions in the case of Re = 676 was 1.355 times of that in the case of Re = 3750.
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijrmms.2019.104105. References 1. MacQuarrie KTB, Mayer KU. Reactive transport modeling in fractured rock: a stateof-the-science review. Earth Sci Rev. 2005;72(3-4):189–227. 2. Qiao LP, Wang ZC, Huang AD. Alteration of mesoscopic properties and mechanical behavior of sandstone due to hydro-physical and hydro-chemical effect. Rock Mech Rock Eng. 2017;50(2):255–267. 3. Herman JS. The geochemical environment. Eng Geol. 1989;26(4):301–317. 4. Steefel CI, Lichtner PC. Multicomponent reactive transport in discrete fractures: I. Controls on reaction front geometry. J. Hydrol. 1998;209(1-4):186–199. 5. Moridis GJ. Semianalytical solutions of radioactive or reactive solute transport in variably fractured layered media. Water Resour Res. 2002;38(12) 46-1-46-24. 6. Sun Y, Buscheck TA. Analytical solutions for reactive transport of N-member radionuclide chains in a single fracture. J Contam Hydrol. 2003;62(1):695–712. 7. Kim JW, Baik MH, Jung H, Jeong JT. Reactive transport of uranium with bacteria in fractured rock: model development and sensitivity analysis. J Contam Hydrol. 2013;152:82–96. 8. Langer M. Safety concept and criteria for hazardous waste sites. Eng Geol. 1993;34(1):159–167. 9. Tian Z, Wang J. Lattice Boltzmann simulation of CO2 reactive transport in network fractured media. Water Resour Res. 2017;53(8):7366–7381. 10. Donato GD, Blunt MJ. Streamline-based dual-porosity simulation of reactive transport and flow in fractured reservoirs. Water Resour Res. 2004;40(4):W04203. 11. Zhan H, Wen Z, Gao G. An analytical solution of two-dimensional reactive solute transport in an aquifer-aquitard system. Water Resour Res. 2009;45(10):W10501. 12. Chen JS, Hsu SY, Li MH, Liu C. Assessing the performance of a permeable reactive barrier-aquifer system using a dual-domain solute transport model. J. Hydrol. 2016;543:849–860. 13. Raposo JR, Molinero J, Dafonte J. Quantitative evaluation of hydrogeological impact produced by tunnel construction using water balance models. Eng Geol. 2010;116(34):323–332. 14. Chigira M, Imai C, Hijikata H. Water percolating behavior indicated by the water chemistry within a decomposed granite slope, central Japan. Eng Geol. 2006;84(12):84–97. 15. Romanov D, Gabrovsek F, Dreybrodt W. Dam site in soluble rocks: a model of increasing leakage by dissolutional widening of fractures beneath a dam. Eng Geol. 2003;70(1):17–35. 16. Ko KS, Chang HW, Kim T, Lee K. Factors affecting the groundwater system around an underground LPG storage cavern. Q J Eng Geol Hydrogeol. 2002;35(3):279–290. 17. Jezerský Z. Hydrogeochemistry of a deep gas-storage cavern, Czech Republic. Hydrogeol J. 2007;15(3):599–614. 18. Wang ZC, Glais Y, Qiao LP, Huang AD. Hydro-geochemical analysis of the interplay between the groundwater, host rock and water curtain system for an underground oil storage facility. Tunn Undergr Space Technol. 2017;71:466–477. 19. Wang ZC, Li W, Bi LP, Qiao LP, Liu RC, Liu J. Estimation of the REV size and equivalent permeability coefficient of fractured rock masses with an emphasis on comparing the radial and unidirectional flow configurations. Rock Mech Rock Eng. 2018;51(5):1457–1471. 20. Steefel CI, Lasaga AC. A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems. Am J Sci. 1994;294(5):529–592. 21. Edson W, Thomas H. Transport simulation with stochastic aperture for a single fracture comparison with a laboratory experiment. Water Resour Res. 2002;25(1):19–32. 22. Yasuhara H, Elsworth D. A numerical model simulating reactive transport and evolution of fracture permeability. Int J Numer Anal Methods Geomech. 2006;30(10):1039–1062. 23. Chaudhuri A, Rajaram H, Viswanathan H. Alteration of fractures by precipitation and dissolution in gradient reaction environments: computational results and stochastic analysis. Water Resour Res. 2008;44(10):253–270. 24. Zhao Z, Liu L, Neretnieks I, Jing L. Solute transport in a single fracture with timedependent aperture due to chemically medicated changes. Int J Rock Mech Min Sci. 2014;66:69–75. 25. Berkowitz B, Zhou J. Reactive solute transport in a single fracture. Water Resour Res. 1996;32(4):901–913. 26. Dijk P, Berkowitz B. Precipitation and dissolution of reactive solutes in fractures. Water Resour Res. 1998;34(3):457–470. 27. Simpson MJ, Ellery AJ. Exact series solutions of reactive transport models with general initial conditions. J. Hydrol. 2014;513:7–12. 28. Chen K, Zhan H. A Green's function method for two-dimensional reactive transport in a parallel fracture-matrix system. J Contam Hydrol. 2018;213:15–21. 29. Berkowitz B. Characterizing flow and transport in fractured geological media: a review. Adv Water Resour. 2002;25(8):861–884. 30. Garcia-Rios M, Luquot L, Soler JM, Cama J. Influence of the flow rate on dissolution and precipitation features during percolation of CO2-rich sulfate solutions through fractured limestone samples. Chem Geol. 2015;414:95–108. 31. Dijk PE, Berkowitz B, Yechieli Y. Measurement and analysis of dissolution patterns in rock fractures. Water Resour Res. 2002;38(2) 5-1-5-12. 32. Detwiler RL, Glass RJ, Bourcier WL. Experimental observations of fracture
6. Conclusions The fundamentals of reactive flow through single rock fractures were reviewed and a correction coefficient was introduced to describe the effect of flow rate on the reaction rate. A set of experiment apparatus was designed and manufactured for the investigations on reactive flow through rock fractures. Two experiments at different flow rates of solutions (i.e., Reynolds numbers for the flow) were performed on granitic rock fractures with comparable hydraulic apertures. The alteration of minerals on the rock fracture and temporal evolution of solution were investigated according to simultaneous observations of mineral dissolution and precipitation on fracture surfaces and ion concentrations and pH values in solutions. The alteration of the minerals on fracture surfaces exhibited nonuniform feature induced by heterogeneity in soluble minerals and their nonuniform distribution on the rock fracture surfaces. The reaction areas of rock blocks in the experiments at Re = 676 and Re = 3750 were 15.83 and 14.48 cm2, respectively, which accounted for approximately 10% of the fracture surface area. The alteration depth was approximately 0.5–0.8 mm. The increment in the concentration of Ca2+ was much higher than those of other cations. Sphene was the dominating mineral in water-rock reactions for the granitic fractures. The reaction rate of minerals decreased with time. From the analysis of the characteristic dimensionless parameters, chemical reaction was the dominating mechanism for the reactive flow through the granitic rock fractures under the experiment conditions. According to the principles of mass and charge conservation, thirteen chemical reactions were identified between fracture surface minerals and solutions in the experiments and 3 out of the thirteen contributed more than 90% of the reactants in amount of substance. The total amount of substance of the chemical reactions was time-dependent. The mass changes of the fracture walls were higher than those measured from the experiments due to the settlement of the products on the tubing and in the tank, which was not collected and measured. The correction coefficient fRe were 10896.7 and 8042.2 for the cases of Re = 676 and Re = 3750, respectively. The effect of flow rate on the chemical reaction between sphene and solutions in the case of Re = 676 was 1.355 times of that in the case of Re = 3750. Acknowledgements The study was financially supported by the National Natural Science Foundation of China with Nos. 51579141 and 51779045, the Fundamental Research Funds for the Central Universities with No. N180104022, Liao Ning Revitalization Talents Program with No. XLYC1807029 and Research Fund of Liaoning Natural Science Foundation with Nos. 2019-MS114 and 2019-YQ-02. 12
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33. 34. 35. 36.
dissolution: the role of Peclet number on evolving aperture variability. Geophys Res Lett. 2003;30(12):1648. Durham WB, Bourcier WL, Burton EA. Direct observation of reactive flow in a single fracture. Water Resour Res. 2001;37(1):1–12. Deng H, Fitts JP, Crandall D, McIntyre D, Peters CA. Alterations of fractures in carbonate rocks by CO2-acidified brines. Environ Sci Technol. 2015;49(16):10226–10234. Qian J, Zhan H, Chen Z, Ye H. Solute transport in a filled single fracture under nonDarcian flow. Int J Rock Mech Min Sci. 2011;48(1):132–140. Yasuhara H, Kinoshita N, Ohfuji H, Lee DS, Nakashima S, Kishida K. Temporal
alteration of fracture permeability in granite under hydrothermal conditions and its interpretation by coupled chemo-mechanical model. Appl Geochem. 2011;26(12):2074–2088. 37. Berner RA. Rate control of mineral dissolution under earth surface conditions. Am J Sci. 1978;278(9):1235–1252. 39. Qiao L, Li S, Wang Z, Tian H, Bi L. Geotechnical monitoring on the stability of a pilot underground crude-oil storage facility during the construction phase in China. Measurement. 2016;82:421–431. 40. Brush DJ, Thomson NR. Fluid flow in synthetic rough-walled fractures: NavierStokes, Stokes, and local cubic law simulations. Water Resour Res. 2003;39(4):1085.
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Alteration of minerals and temporal evolution of solution in reactive flow through granitic rock fractures
T
Qiao Lipinga, Anda Huangb, Wang Zhechaoa,∗, Wenyuan Gaoc, Jie Liua a
Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang, Liaoning, 110819, P. R. China School of Civil Engineering, Shandong University, Jinan, Shandong, 250061, P. R. China c Department of Geology Sciences, School of Resources and Civil Engineering, Northeastern University, Shenyang, Liaoning, 110819, P. R. China b
ARTICLE INFO
ABSTRACT
Keywords: Reactive flow Alteration Granitic rock fracture Temporal evolution ion concentration Reaction rate
The alteration of minerals and temporal evolution of solution in reactive flow through granitic rock fractures were investigated. Two experiments at different flow rates of solutions (i.e., Reynolds numbers for the flow) were performed on granitic rock fractures with comparable hydraulic apertures. The fracture surface morphologies and masses of the fracture walls were measured before and after the experiments. The alteration of the minerals on fracture surfaces exhibited nonuniform features induced by heterogeneity in the soluble minerals and their nonuniform distribution on the rock fracture surfaces. The ion concentrations and pH values of the solutions were measured during the experiments. The variations of the ion concentrations in the solutions were complementary to the dissolution or precipitation of minerals on the fracture surfaces. The water-rock reaction was identified as the primary process dominating the reactive flow in the experiments. According to the principles of mass and charge conservation, thirteen chemical reactions were identified between the minerals on the fracture surfaces and solutions in the experiments and 3 out of the thirteen contributed more than 90% of the reactants in amount of substance. The dissolution rate of sphene for the experiment at Reynolds number 676 was higher than that at 3750 because of the higher reaction rate between the solutions and the rock minerals. A correction coefficient was introduced and calculated to describe the effect of flow rate on the reaction rate.
1. Introduction Flow and transport processes in fractured rock masses have received considerable attention in recent years.1 The processes alter the physical and chemical properties of groundwater and rock masses.2 The transport of solutes through fractured geological media is of critical importance for evaluating the impacts of nuclear waste disposal3–7, general hazardous waste disposal8, CO2 geological sequestration9, oil and gas development10, aquifer protection11,12, tunnel construction13, landslides14, dam foundations15 and underground oil/gas storage16–18 on the geological environment. Rock fractures dominate the flow and transport processes in fractured rock mass.19 Reactive flow in fractures has been extensively investigated using numerical and analytical methods. Deterministic and stochastic numerical simulations of reactive flow processes have been performed for rock fractures in numerous studies.20–24 Analytical methods have been used to describe the processes with simple boundary conditions in fractures.25–28 In the above numerical and
∗
analytical studies, various aspects of reactive flow have been investigated qualitatively. However, experimental data are required to validate the findings from these numerical and analytical studies. Predicting changes in the flow and transport properties of fractures is still a challenge due to the complexity of water-rock interactions and the uncertain role of fracture heterogeneity.29,30 Experiments conducted at the laboratory scale are needed for this kind of characterization. In the literature, experiments have been conducted to address the effects of the Damköhler number31, Peclet number32, flow rate and dissolution pattern30,33, and solution contents34 on the hydraulic conductivity of rock fractures. For reactive flow in rock fractures, the minerals on the fracture surfaces dissolve and the components and concentrations of solutes evolve in the process.35,36 A simultaneous observation of the alteration of fracture surface minerals and temporal evolution of solutions would provide a comprehensive understanding of reactive flow in rock fractures. In addition, fractures in rocks consisting of single minerals such as limestone, marble or rock salt were used in most of the existing studies. The experimental studies are few on
Corresponding author. School of Resources and Civil Engineering, Northeastern University, 11#, 3rd Ave, Wenhua Rd, Shenyang, 110819, P. R. China. E-mail address: [email protected] (Z. Wang).
https://doi.org/10.1016/j.ijrmms.2019.104105 Received 14 January 2019; Received in revised form 6 July 2019; Accepted 4 September 2019 1365-1609/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. (a) Skecth of the experiment apparatus (b) Longitudinal profile of the rock fracture (part 7) (c) Cross-sectional profile of the rock fracture (part 7).
reactive flow in rock fractures consisting of several minerals, where the alterations of the minerals on fracture surfaces would exhibit heterogeneous behavior. In this study, the fundamentals of reactive flow in single rock fracture were reviewed and a correction coefficient was introduced to describe the effect of flow rate on the reaction rate. A set of experiment apparatus was designed and manufactured for the investigations on reactive flow in rock fractures. Two experiments at different flow rates of solutions (i.e., Reynolds numbers (Re) for the flow) were performed on granitic rock fractures with comparable hydraulic apertures. The fracture surface morphologies and masses of the fracture walls were measured before and after the experiments. The ion concentrations and pH values of the solution were measured during the experiments. Based on the experiment results, the alteration of the minerals on fracture surfaces and the temporal evolution of the solute in reactive flow through granitic rock fractures were simultaneously investigated.
2. Fundamentals of reactive flow in single rock fractures 2.1. Governing equations For reactive flow in single fractures, the solute concentration and fracture aperture are to be solved under the specified initial and boundary conditions. The governing equations for solute concentration and fracture aperture are respectively expressed as37:
C = t
(Dm C )
b = rMs / t
s
(uC ) + R c
(1) (2)
where C is the solute concentration, [mol·L−1]; t is the time, [s]; Dm is the coefficient of diffusion, [m2·s−1]; u is the flow rate, [m·s−1]; Rc is the rate of solute concentration change induced by the chemical 2
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Fig. 2. (a) Rectangular plate samples with a size of 50 × 50 × 10 mm (b) Rock fracture consisting of 6 small rectangular plate samples and silicone pad formed as illustrated in Fig. 1
soluble minerals, [g·mol−1]; and ρs is the mass density of soluble minerals, [kg·m−3].
1.0
H y d ra u lic a p ertu re (m m )
Re=2500 Re=3750 Re=676 0.8
2.2. Characteristic dimensionless parameters
Re=500 Re=676 Re=3750
In reactive flow, advection, molecular diffusion and chemical reaction processes are coupled. To compare the influences of the mechanisms of the three processes, two dimensionless parameters are widely used, namely, the Pelect number and Damköhler number. The Pelect number describes the effect of advection relative to that of molecular diffusion on solute transport and is expressed as26:
0.6 0.4 0.2
Pe =
0.0 0
5
10
15
20 Time (d)
25
30
35
40
ub 2Dm
(3)
The Damköhler number describes the effect of chemical reaction relative to that of molecular diffusion on solute transport and is expressed as26:
Fig. 3. Variations of hydraulic apertures with time for the fractures in the two experiments.
Da =
reaction between the solution and fracture surface mineral, [mol·L−1·s−1]; b is the fracture aperture, [m]; r = bRc is the reaction rate of surface soluble minerals, [mol·m−2·s−1]; Ms is the molar mass of
kk b2 4Dm
where kk is the [mol·m−2·s−1]. 3
(4) first-order
kinetic
reaction
rate
coefficient,
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Fig. 5. Variations of ion concentrations with time in the solution for the experiment at Re = 3750.
Fig. 4. Variations of ion concentrations with time in the solution for the experiment at Re = 676.
To incorporate the effect of variable aperture during the processes, Dijk and Berkowitz26 introduced the effective fracture aperture, effective flow rate, effective Pelect number and effective Damköhler number. The initial effective fracture aperture (beff ,0 ) is expressed as:
1
beff ,0 =
1 x=l 1 dx l x = 0 b03
1/3
(5)
where b0 is the initial fracture aperture, [m]; l is the fracture length, [m]; and x is the coordinate along flow direction. The initial effective maximum flow rate (ueff ,0 ) is expressed as: 2 1 pbeff ,0 8 lµ
(6)
Fig. 6. Variations of pH values with time in the solutions for the two experiments.
where Δp is the pressure difference along the fracture, [Pa], and μ is the dynamic viscosity of fluids, [Pa·s]. Then, the dimensionless initial effective Pelect and Damköhler numbers are expressed, respectively, as:
on the reactive flow of sodium sulfate solution through granitic rock fractures.
ueff ,0 =
Peeff ,0 =
ueff ,0 beff ,0 2Dm
2.3. Reaction rates
(7)
and
Daeff ,0 =
In general, the reaction rates between minerals and solutions depend on the solute concentrations in the solution. For a dilute solution, the reaction rate of a mineral can be expressed as36:
2 kk beff ,0
4Dm
(8)
r = ks (1
These dimensionless initial effective Pelect and Damköhler numbers are used in Section 5 to compare the influences of the three mechanisms
C /Csat )
(9)
where Csat is the concentration of a solute in the equilibrium state, 4
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caverns18,39, the concentration of Na+ is 0.9–3.9 mmol/L, and that of SO42− is 0–1.7 mmol/L in the real underground water. The concentrations of Na+ and SO42− in the experimental solution were in the range of the field underground water. 3.2. Experiment apparatus A set of experiment apparatus was designed and manufactured for the investigations on the reactive flow through rock fractures. The experiment apparatus mainly consists of rock fracture, pump, flow meter, pressure transducer and data recording system. The flow rate was measured by flow meter and ranged from 0.04–0.4 m3/h with an accuracy of 1%. The pressure was measured by pressure transducer and ranged from 0–0.5 MPa with an accuracy of 0.5%. The sketch of the experiment apparatus is shown in Fig. 1(a), and the rock fracture as the critical part of the apparatus is illustrated in Fig. 1(b) and (c) . As shown in Fig. 1, the characteristics of the system are as follows: (1) the flow rate of solutions can be specified and the transport characteristics of solutions in different flow regimes can be obtained; (2) a single rock fracture surface was formed to investigate the alteration of minerals and temporal evolution of solution in reactive flow through granitic rock fractures. 6 pieces of rectangular plate samples were arrayed in the socket made of steel plate as the rock fracture surface, while the rock fracture aperture was determined by the thickness of the positioned silicone pad, as shown in Fig. 1(b) and (c).
Fig. 7. Mass changes of rock blocks before and after the experiments.
[mol·L−1] and ks is the first-order static reaction rate coefficient, [mol·m−2·s−1]. Considering the effect of temperature on the reaction rate, ks can be expressed as:
ks = ks25 exp
Ea 1 R T
1 298.15
(10) −2 −1
where ks25 is the static reaction rate coefficient at 25 °C, [mol·m ·s ]; Ea is the reaction activation energy, [kJ·mol−1]; R is the universal gas constant, [kJ·mol−1·K]; and T is the absolute temperature, [K]. For a specified solute, ks25, Ea and R are constant and ks considering the temperature effect can be determined. In Eq. (9), the reaction rate is determined for the solution in a static state. The flow of the solution will alter the reaction rate as a consequence of the flow of reactants in solution. In this study, a correction coefficient (fRe) is introduced to describe the effect of flow on the reactive rate, and the reaction rate for a mineral considering reactive flow can be revised as:
r = kk (1
C / Csat ) = ks fRe (1
C /Csat )
3.3. Experiment procedure The experiment procedure includes experiment preparation and observation of minerals alteration and solution temporal evolution. To investigate the effect of flow regime on the minerals alteration and solution temporal evolution, two experiments were conducted with specified Reynolds number of 676 and 3750. The flow rates were controlled by regulating the pump pressure. At the preparation stage, 6 rectangular plate samples with the size of 50 × 50 × 10 mm were manufactured for each experiment, and the samples were polished using sander, as shown in Fig. 2(a). The fracture length was the sum of 6 samples and the gaps between each sample, and the total value was 0.36 m. The rock fracture apertures were determined by the positioned silicone pad for two experiment types as shown in Fig. 2(b). A digimatic micrometer with an accuracy of 0.001 mm was used to measure the thickness of the silicone pad. Considering that the silicone pad can be compressed after fixed by the screw, the heights of the apparatus without silicone pad and with silicone pad after fixed were both measured, and the difference between the two values was determined as the fracture aperture. The fracture apertures were 1.857 mm and 1.664 mm for the two experiments, respectively. During the experiment process, observations of minerals alteration and solution temporal evolution were performed. To investigate the mineral alteration on the rock fracture surface, the masses, the topographies, and the mineral compositions of the rock samples were obtained before and after the experiments. The masses of the samples were weighed using an electronic balance with an accuracy of 0.01 g. The initial topography of the fracture surface was measured using 3D digital microscope Keyence VHX-2000E. The SEM analyses were performed on the samples with the size of 1 × 1 cm using Zeiss Ultra plus Scanning Electron Microscope. The Electron Probe X-ray Microanalyser (EPMA) was used to investigate the mineral alteration of the rock fracture surface, and it can quantify the mineral contents of rocks. To obtain the solution temporal evolution, 100 ml aqueous chemical solution was sampled every 5 days and the initial solution with the same volume was added into the experiment apparatus. The ion composition and concentrations of the sampled solution were analyzed via wholespectrum direct-reading ICP-AES. The pH value of the sampled solution was measured using a PHS-25 digital pH meter.
(11)
In the following calculation, the reaction rate of surface soluble minerals r is determined from the experiment result. The first-order static reaction rate coefficient ks is determined according to Eq. (10) considering the effect of temperature. The solute concentration C is obtained from the experiment result, and the concentration of a solute in the equilibrium state Csat is a constant for a specified solute. Thereby, the proposed correction coefficient fRe can be calculated, as well as the parameter of kk. 3. Experiment method 3.1. Materials The rock specimens used in the experiments were granitic rocks from the Cretaceous and Proterozoicus ages and collected from Huangdao underground oil storage caverns which is the first large-scale underground water-sealed crude oil storage cavern project constructed in China. A sodium sulfate solution was chosen to be the experimental solution. Sodium hydroxide and sulphuric acid were used to prepare the sodium sulfate solution, and 6 L distilled water was used. The planed ion concentrations of Na+ was 1.5 mmol/L for the two experiments (Re = 676 and Re = 3750), respectively. However, the measured original ion concentration of Na+ for the two experiments (Re = 676 and Re = 3750) were 1.527 mmol/L and 1.274 mmol/L, respectively, while the measured concentration of SO42− for the two experiments (Re = 676 and Re = 3750) were 1.031 mml/L and 1.010 mmol/L, and the pH value for the two experiments (Re = 676 and Re = 3750) were 4. The error in the concentration of Na+ was considered as the test error. According to the field study of Huangdao underground oil storage 5
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Fig. 8. Surface topography of the 6 rectangular plate samples before and after the experiments measured using 3D digital microscope Keyence VHX-2000E with an amplification time of 200 (samples #1~#6 from top to bottom).
4. Experiment result
The variations of hydraulic apertures with time for the two experiments are shown in Fig. 3. The hydraulic apertures remained basically unchanged during the experiments. The average hydraulic aperture was 0.53 mm for the experiment with Re = 676, while the average hydraulic aperture was 0.57 mm for the experiment with Re = 3750. Therefore, the hydraulic apertures are comparable in the two experiments.
4.1. Hydraulic apertures In this study, the hydraulic aperture can be obtained using cubic law40:
Q=
we3 P 12µl
(12)
4.2. Temporal evolution of solutions
where Q is the volumetric flow rate, [m3/s], and e, l and w are the hydraulic aperture, length and width of fracture, respectively, [m].
The variations of ion concentrations in the solutions with time for 6
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Fig. 9. (a) Surface topography of the rock sample #6 (b) Slightly alterated zones (saz) (c) Intensively alterated zones (iaz) on the surface after the experiment at Re = 3750.
the cases of Re = 676 and Re = 3750 are shown in Figs. 4 and 5, respectively. The variations of pH values in the solutions with time are shown in Fig. 6. From the results, the concentrations of Ca2+, K+ and Mg2+ in the solutions increased with time. The concentration of Ca2+ increased at the beginning of the experiment and then tended to be stable. The concentration of Na+ first increased to some extent and then decreased slightly and tended to be stable. The concentrations of Al3+, Fe2+, and SiO32− were close to 0 mmol/L and had no obvious variation. The large fluctuations were observed for SO42−, and this may be caused by the addition of 100 ml original solution and some unknown reason. The pH values of the solutions increased to approximately pH = 8 at the first 5 days and then tended to be stable at pH = 8, and the reason was explained in the following discussion. The variations of pH values were similar in the two experiments.
two representative zones are analyzed as shown in Fig. 9. Fig. 9(b) and (c) show the images of the two zones on the rock sample #6 after the experiment at Re = 3750 magnified by 2000 times. As shown in Fig. 9(b), only slight corrosion occurred in the light-flesh zone considered as slightly alterated zone (the zone labeled saz in the figure), while obvious corrosion holes and cavities were observed in the darkgray zone considered as intensively alterated zone (the zone labeled iaz in the figure). The two representative zones of #6 rock sample after the experiment at Re = 3750 were magnified for different times as shown in Fig. 10. Fig. 10(b) and (c) show the microstructures in the slightly alterated zone magnified by 1000 and 3000 times, respectively. A slight alteration of minerals, e.g., corrosion and erosion holes in the zone can be observed due to the reactive flow of the solution. Fig. 10(d)-(f) show the microstructures in the intensively alterated zone magnified by 300, 3000 and 10000 times, respectively. Intensive mineral dissolution, e.g., inter-granular and intra-granular holes, was observed on fracture surface. There were some precipitate minerals observed on the fracture surface although the solution flowed at the specified rate. The heterogeneity in minerals on the fracture surface induced the difference in alteration degree in different zones. EPMA analysis was conducted to quantify the alteration of the rock minerals. Fig. 11 shows the microscopic electron micrographs and atomic spectrograms of #6 rock sample after the experiment at Re = 3750. The point analysis of spectral element content and mineral composition at different locations of #6 rock sample after the experiment at Re = 3750 can be obtained by the EPMA analysis as listed in Table 1. The major elements of the minerals in locations of #7, 9, 10 and 11 were Si, O, Al, K and Na, which was consistent with the composition of potassium feldspar, albite, quartz and mica. The elements Fe appeared in location of #13, and it indicated that there was a large quantity of magnetite. The element contents of Ca, Ti, Si and O were existed in locations of #18 and 19, and this was consistent with the composition of sphene. The element contents of Ca in locations of #18 and 19 were higher than those in the other locations.
4.3. Alteration of minerals of rock fractures 4.3.1. Mass of fracture walls The mass of rock walls changed in the rock fracture alteration process. Fig. 7 shows the mass changes of the 6 pieces rock samples before and after the experiments. In the case of Re = 676, the mass variations in the 6 pieces rock samples from #1 to #6 were −20, −20, 10, 20, 0 and −30 mg, respectively, with a total mass decrease of 40 mg. In the case of Re = 3750, the mass variations in the 6 pieces of the rock samples from #1 to #6 were −40, 30, 10, 50, 20 and −30 mg, respectively, with a total mass increase of 40 mg. 4.3.2. Fracture surface topography The topography of the 6 rectangular plate samples before and after the experiments were measured using 3D digital microscope Keyence VHX-2000E with an amplification factor of 200 as shown in Fig. 8. The visible changes, including the color and the border, can be seen on the rock samples before and after the experiments. In general, there are two main zones on the rock samples, i.e., the dark-gray zones on the fracture surfaces (as marked in the pictures after the experiments) and the lightflesh zones. In the case of Re = 676, the areas of dark-gray zones (marked zones) of the 6 rock samples from #1 to #6 were measured to be 3.38, 1.37, 1.23, 1.94, 5.98, and 1.93 cm2, respectively, with a total area of 15.83 cm2. In the case of Re = 3750, the areas of dark-gray zones (marked zones) of the 6 rock samples from #1 to #6 were 2.53, 2.39, 1.55, 2.45, 2.37 and 3.18 cm2, respectively, with a total area of 14.47 cm2. The alteration depths in the intensively alterated zones were estimated from 0.5 to 0.8 mm.
5. Discussion 5.1. Dominating mechanism The initial effective Pelect number and initial effective Damköhler number Peeff,0 and Daeff,0 were determined for the cases of Re = 676 and Re = 3750 using Eqs. (5)–(8), respectively. The parameters used in the determination were presented in Table 2. In the case of Re = 676, the values of Peeff,0 and Daeff,0 were 1.87 × 105 and 6.25 × 10−5, respectively. In the case of Re = 3750, the values of Peeff,0 and Daeff,0 were 9.25 × 105 and 3.70 × 10−5, respectively. The effect of advection was an order of 105 that of molecular diffusion on solute transport, while the effect of reaction was an order of 10−5 that of molecular
4.3.3. Alteration of minerals on fracture surfaces SEM analyses with different magnification factors were conducted on the two representative zones to investigate the mineral alteration. Taking #6 rock sample of the experiment at Re = 3750 for an example, 7
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Fig. 10. SEM images of fracture surface on the #6 rock sample after the experiment at Re = 3750 showing mineral alteration.
Ca2+ was much higher than those of other cations. In addition, the EPMA result can tell that the mineral with Ca2+ was sphene. Therefore, it was considered that sphene was the dominating mineral in water-rock reactions for the granitic rock fractures and solutions. From Figs. 4 and 5, the concentration of Ca2+ increased quickly within the first 10 days and the rate was slow in the following 20 days. Eventually, the concentration of Ca2+ tended to become stable in the last 10 days. This result indicated that the water-rock reaction rate was time-dependent. According to the alteration of minerals on rock fracture surfaces and the temporal evolution in the solutions, the chemical reaction equations
diffusion on solute transport. Under the experiment conditions, convection had the greatest influence on the flow of reactive solutes, and chemical reaction had the lowest influence. Therefore, chemical reaction was the dominating mechanism for the alteration of minerals and temporal evolution of solution in reactive flow through the granitic rock fractures under the experiment conditions. 5.2. Chemical reaction equations As shown in Figs. 4 and 5, the increment in the concentration of 8
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#12: H4SiO4→H2O + H2SiO3→H2O + H++HSiO3−
can be identified using the conservations of mass and charges. For this study, the chemical reaction equations were determined as: +
#1: CaTiSiO5+4H →TiO #2: TiO
2+
2+
#13: KFe3AlSi3O10(OH)2+10H+→Al3++K++2H4SiO4+3Fe2+
2+
+H4SiO4+Ca
Table 3 presents Molar fractions of chemical reactions and masses of dissolution and precipitation minerals during different periods of time. According to the data in Table 3, the major 3 chemical reactions in the experiments are as follows:
+2H2O→H2TiO3↓+2H+
#3: H2O + CO2↔HCO3− + H+ #4: Ca2++SO42−→CaSO4↓
#1: CaTiSiO5+4H+→TiO2++H4SiO4+Ca2+
+
#5: 2NaAlSi3O8+2H +2H2O→Al2(Si2O5)(OH)4↓+4SiO2+ 2Na+Al2(Si2O5)(OH)4↓+4SiO2+2Na+
#2: TiO2++2H2O→H2TiO3↓+2H+ #3: H2O + CO2↔HCO3− + H+
#6: Fe3++3H2O↔Fe(OH)3↓+3H+
The reactants in the major 3 chemical reactions accounted for 90% of the total reactants in all the chemical reactions by the amount of substance. At the beginning, the sodium sulphate was acidic with pH value of 4, and sphene can dissolute under the acidic condition. The dissolution of sphene tended to be stable while the solution tended to be neutral. This is also in accordance with the variation of pH value. As the above mentioned, the pH values of the solutions in the two experiments increased to approximately pH = 8 at the first 5 days and then tended
#7: Fe3O4+8H+→2Fe3++Fe2++4H2O #8: Fe2++2H2O↔Fe(OH)2↓+2H+ #9: Al3++3H2O↔Al(OH)3↓+3H+ #10: 2KAlSi3O8+2H++2H2O→Al2(Si2O5)(OH)4↓+4SiO2+2K+ #11: KAlMg3Si3O10(OH)2+10H+→Al3++K++2H4SiO4+3Mg2+
Fig. 11. Microscopic electron micrographs and atomic spectrograms of #6 rock sample after the experiment at Re = 3750. 9
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Fig. 11. (continued)
chemical reaction #1. This was in accordance with the increase of the concentration of Ca2+.
Table 1 Point analysis of spectral element content and mineral composition at different locations of #6 rock sample after the experiment at Re = 3750.
5.3. Temporal evolution of reactions
oxide contents (wt%)
Locations #7
#9
#10
#11
#13
#18
#19
Na2O Al2O3 SiO2 K2O CaO MgO FeO TiO2 Total Mineral
0.76 18.82 65.22 15.21 0.00 0.00 0.00 0.00 100.00 potassium feldspar
9.54 21.02 67.42 0.36 1.67 0.00 0.00 0.00 100.00 albite
0.00 0.00 100.00 0.00 0.00 0.00 0.00 0.00 100.00 quartz
0.52 35.82 47.32 12.25 0.00 0.56 3.53 0.00 100.00 mica
0.00 0.61 0.00 0.00 0.00 0.00 99.39 0.00 100.00 magnetite
0.00 1.39 30.67 0.00 28.69 0.00 1.54 37.71 100.00 sphene
0.00 3.18 30.88 0.00 28.33 0.00 1.35 35.15 98.89 sphene
Fig. 12 shows the variations of the percentages of the total amount of substance of the chemical reactions with time in the two experiments at Re = 676 and Re = 3750. In the first 5 days, the percentages were 37.04% and 37.40% for the cases of Re = 676 and Re = 3750, respectively. The percentages dropped to 16.88% and 14.5% for the two cases in the 5–10 days, 9.36% and 6.70% in 10–15 days. Eventually, the percentages were less than 1% in the last 5 days. Table 3 presents the changes in masses of dissolution and precipitation minerals. For the case Re = 676, the mass of the dissolution minerals was 3481.38 mg, and the mass of the precipitated minerals was 3756.51 mg with a gain in mass of 275.13 mg for rock sample. For the case Re = 3750, the mass of the dissolution minerals was 2855.13 mg, and the mass of the precipitation minerals was 3096.52 mg with a gain in mass of 241.39 mg for rock sample. The mass changes of the rock samples from the above analysis were higher than those measured from the experiments due to the settlement of the products on the tubing and in the tank, which was not collected and measured. The mass changes after the experiments at Re = 676 and 3750 are small, i.e., 275.13 mg and 241.39 mg. Then assuming a density of 3.5 g/ cm3 for reactive minerals, the geometrical aperture changes during the tests can be estimated 0.0052 mm and 0.0046 mm, respectively. Therefore, the permeability changes little for the two experiments.
Table 2 Parameters for the determination of initial effective Pelect number and initial effective Damköhler number. Re
b(mm)
u(m/s)
l(m)
Dm(m2•s−1)
μ(Pa•s)
ks(mol/ (m2•s))
kk(mol/ (m2•s))
676 3750
1.857 1.664
0.27 1.49
0.36 0.36
1.34E-09 1.34E-09
0.74E-03 0.66E-03
8.91E-12 8.91E-12
9.71E-8 7.17E-8
to be stable at pH = 8. This is because the chemical reaction of the mineral sphene was the main reaction following the chemical reaction #1. The ions H+ decreased in the whole process. Although some ions H+ generated, considering that the other 2 dominant chemical reactions #2 and #3, the generated H+ was quickly consumed in the
5.4. Chemical reaction rate As observed in the experiments, the chemical reaction between 10
Mineral mass
Mole fractions
Category
2+
2+
CaTiSiO5+4H →TiO +H4SiO4+Ca TiO2++2H2O→H2TiO3↓+2H+ H2O + CO2↔HCO3− + H+ Ca2++SO42−→CaSO4↓ 2NaAlSi3O8+2H++2H2O→Al2(Si2O5)(OH)4↓+4SiO2+2Na+Al2(Si2O5)(OH)4↓+4SiO2+2Na+ Fe3++3H2O↔Fe(OH)3↓+3H+ Fe3O4+8H+→2Fe3++Fe2++4H2O Fe2++2H2O↔Fe(OH)2↓+2H+ Al3++3H2O↔Al(OH)3↓+3H+ 2KAlSi3O8+2H++2H2O→Al2(Si2O5)(OH)4↓+4SiO2+2K+ KAlMg3Si3O10(OH)2+10H+→Al3++K++2H4SiO4+3Mg2+ H4SiO4→H2O + H2SiO3→H2O + H++HSiO3− KFe3AlSi3O10(OH)2+10H+→Al3++K++2H4SiO4+3Fe2+ Dissoluted minerals (mg) Precipitated minerals (mg) Mass changes (mg)
+
23.11% 23.11% 46.33% 3.93% 1.54% 1.18% 0.47% 0.12% 0.08% 0.00% 0.07% 0.05% 0.01% −2487.59 2717.38 229.79
0–10 d
Re = 676
Table 3 Molar fractions of chemical reactions and masses of dissolution and precipitation minerals during different periods of time.
22.30% 22.30% 46.97% 2.35% 0.53% 3.32% 1.66% 0.19% 0.08% 0.19% 0.05% 0.03% 0.03% −955.63 999.94 44.31
10–30 d 23.27% 23.27% 40.47% 2.53% 3.04% 2.02% 1.01% 1.01% 0.67% 2.02% 0.67% 0.01% 0.01% −38.16 39.19 1.03
30–40 d
10–30 d 24.08% 24.08% 44.93% 3.37% 0.18% 0.90% 0.45% 0.90% 0.33% 0.27% 0.28% 0.19% 0.04% −681.74 735.56 53.82
0–10 d 21.49% 21.49% 47.45% 3.93% 3.19% 0.89% 0.44% 0.59% 0.14% 0.09% 0.14% 0.15% 0.01% −2124.24 2308.83 184.59
Re =3750
21.89% 21.89% 40.54% 4.86% 5.68% 1.62% 0.81% 0.00% 0.54% 1.62% 0.55% 0.00% 0.00% −49.15 52.13 2.98
30–40 d
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Fig. 12. Variations of the percentages of the total molar quantity of the chemical reactions with time for the two experiments at Re = 676 and Re = 3750.
Fig. 13. Variations of Ca2+ concentrations with time for the two experiments at Re = 676 and Re = 3750.
Fig. 14. Variations of reaction rates between sphene and the solutions after the corrections in terms of both the reaction surface area and the temperature.
sphene and the solutions was the dominating reaction out of the minerals. Fig. 13 shows the variations of Ca2+ concentrations with time in the two experiments at Re = 676 and Re = 3750. The Ca2+ concentrations increased granularly at the beginning and became stable at 2.45 and 1.88 mmol/L after 35 days in the experiments at Re = 676 and Re = 3750, respectively. Because the reaction surface areas of the two fractures were different and the temperatures varied with time in the two experiments, the chemical reaction rates were corrected. The correction of chemical reaction rates in terms of reaction surface area was performed. The correction of chemical reaction rates in terms of temperature was
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performed according to Eq. (11). Fig. 14 shows the variations of reaction rates between sphene and the solutions after the corrections in terms of both the reaction surface area and the temperature. The reaction rates decreased from 7.8e-6 and 5.9e-6 to about 0 for the two cases of Re = 676 and Re = 3750, respectively. It indicated that the higher flow rate, the lower chemical reaction rate was. This finding was consistent with the observations by Durham.35 They performed reactive transport through rough marble fracture. It was found that the rates of the reaction between calcite and acid solution on the fracture surface along the low flow rate channels were higher than those along the high flow rate channels. The correction coefficient fRe can be calculated according to Eq. (11). The correction coefficient fRe are 10896.7 and 8042.2 for the cases of Re = 676 and Re = 3750, respectively. It indicated that the effect of flow rate on the chemical reaction between sphene and solutions in the case of Re = 676 was 1.355 times of that in the case of Re = 3750.
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijrmms.2019.104105. References 1. MacQuarrie KTB, Mayer KU. Reactive transport modeling in fractured rock: a stateof-the-science review. Earth Sci Rev. 2005;72(3-4):189–227. 2. Qiao LP, Wang ZC, Huang AD. Alteration of mesoscopic properties and mechanical behavior of sandstone due to hydro-physical and hydro-chemical effect. Rock Mech Rock Eng. 2017;50(2):255–267. 3. Herman JS. The geochemical environment. Eng Geol. 1989;26(4):301–317. 4. Steefel CI, Lichtner PC. Multicomponent reactive transport in discrete fractures: I. Controls on reaction front geometry. J. Hydrol. 1998;209(1-4):186–199. 5. Moridis GJ. Semianalytical solutions of radioactive or reactive solute transport in variably fractured layered media. Water Resour Res. 2002;38(12) 46-1-46-24. 6. Sun Y, Buscheck TA. Analytical solutions for reactive transport of N-member radionuclide chains in a single fracture. 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Quantitative evaluation of hydrogeological impact produced by tunnel construction using water balance models. Eng Geol. 2010;116(34):323–332. 14. Chigira M, Imai C, Hijikata H. Water percolating behavior indicated by the water chemistry within a decomposed granite slope, central Japan. Eng Geol. 2006;84(12):84–97. 15. Romanov D, Gabrovsek F, Dreybrodt W. Dam site in soluble rocks: a model of increasing leakage by dissolutional widening of fractures beneath a dam. Eng Geol. 2003;70(1):17–35. 16. Ko KS, Chang HW, Kim T, Lee K. Factors affecting the groundwater system around an underground LPG storage cavern. Q J Eng Geol Hydrogeol. 2002;35(3):279–290. 17. Jezerský Z. Hydrogeochemistry of a deep gas-storage cavern, Czech Republic. Hydrogeol J. 2007;15(3):599–614. 18. Wang ZC, Glais Y, Qiao LP, Huang AD. Hydro-geochemical analysis of the interplay between the groundwater, host rock and water curtain system for an underground oil storage facility. Tunn Undergr Space Technol. 2017;71:466–477. 19. Wang ZC, Li W, Bi LP, Qiao LP, Liu RC, Liu J. Estimation of the REV size and equivalent permeability coefficient of fractured rock masses with an emphasis on comparing the radial and unidirectional flow configurations. Rock Mech Rock Eng. 2018;51(5):1457–1471. 20. Steefel CI, Lasaga AC. A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems. Am J Sci. 1994;294(5):529–592. 21. Edson W, Thomas H. Transport simulation with stochastic aperture for a single fracture comparison with a laboratory experiment. Water Resour Res. 2002;25(1):19–32. 22. Yasuhara H, Elsworth D. A numerical model simulating reactive transport and evolution of fracture permeability. Int J Numer Anal Methods Geomech. 2006;30(10):1039–1062. 23. Chaudhuri A, Rajaram H, Viswanathan H. Alteration of fractures by precipitation and dissolution in gradient reaction environments: computational results and stochastic analysis. Water Resour Res. 2008;44(10):253–270. 24. Zhao Z, Liu L, Neretnieks I, Jing L. Solute transport in a single fracture with timedependent aperture due to chemically medicated changes. Int J Rock Mech Min Sci. 2014;66:69–75. 25. Berkowitz B, Zhou J. Reactive solute transport in a single fracture. Water Resour Res. 1996;32(4):901–913. 26. Dijk P, Berkowitz B. Precipitation and dissolution of reactive solutes in fractures. Water Resour Res. 1998;34(3):457–470. 27. Simpson MJ, Ellery AJ. Exact series solutions of reactive transport models with general initial conditions. J. Hydrol. 2014;513:7–12. 28. Chen K, Zhan H. A Green's function method for two-dimensional reactive transport in a parallel fracture-matrix system. J Contam Hydrol. 2018;213:15–21. 29. Berkowitz B. Characterizing flow and transport in fractured geological media: a review. 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6. Conclusions The fundamentals of reactive flow through single rock fractures were reviewed and a correction coefficient was introduced to describe the effect of flow rate on the reaction rate. A set of experiment apparatus was designed and manufactured for the investigations on reactive flow through rock fractures. Two experiments at different flow rates of solutions (i.e., Reynolds numbers for the flow) were performed on granitic rock fractures with comparable hydraulic apertures. The alteration of minerals on the rock fracture and temporal evolution of solution were investigated according to simultaneous observations of mineral dissolution and precipitation on fracture surfaces and ion concentrations and pH values in solutions. The alteration of the minerals on fracture surfaces exhibited nonuniform feature induced by heterogeneity in soluble minerals and their nonuniform distribution on the rock fracture surfaces. The reaction areas of rock blocks in the experiments at Re = 676 and Re = 3750 were 15.83 and 14.48 cm2, respectively, which accounted for approximately 10% of the fracture surface area. The alteration depth was approximately 0.5–0.8 mm. The increment in the concentration of Ca2+ was much higher than those of other cations. Sphene was the dominating mineral in water-rock reactions for the granitic fractures. The reaction rate of minerals decreased with time. From the analysis of the characteristic dimensionless parameters, chemical reaction was the dominating mechanism for the reactive flow through the granitic rock fractures under the experiment conditions. According to the principles of mass and charge conservation, thirteen chemical reactions were identified between fracture surface minerals and solutions in the experiments and 3 out of the thirteen contributed more than 90% of the reactants in amount of substance. The total amount of substance of the chemical reactions was time-dependent. The mass changes of the fracture walls were higher than those measured from the experiments due to the settlement of the products on the tubing and in the tank, which was not collected and measured. The correction coefficient fRe were 10896.7 and 8042.2 for the cases of Re = 676 and Re = 3750, respectively. The effect of flow rate on the chemical reaction between sphene and solutions in the case of Re = 676 was 1.355 times of that in the case of Re = 3750. Acknowledgements The study was financially supported by the National Natural Science Foundation of China with Nos. 51579141 and 51779045, the Fundamental Research Funds for the Central Universities with No. N180104022, Liao Ning Revitalization Talents Program with No. XLYC1807029 and Research Fund of Liaoning Natural Science Foundation with Nos. 2019-MS114 and 2019-YQ-02. 12
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dissolution: the role of Peclet number on evolving aperture variability. Geophys Res Lett. 2003;30(12):1648. Durham WB, Bourcier WL, Burton EA. Direct observation of reactive flow in a single fracture. Water Resour Res. 2001;37(1):1–12. Deng H, Fitts JP, Crandall D, McIntyre D, Peters CA. Alterations of fractures in carbonate rocks by CO2-acidified brines. Environ Sci Technol. 2015;49(16):10226–10234. Qian J, Zhan H, Chen Z, Ye H. Solute transport in a filled single fracture under nonDarcian flow. Int J Rock Mech Min Sci. 2011;48(1):132–140. Yasuhara H, Kinoshita N, Ohfuji H, Lee DS, Nakashima S, Kishida K. Temporal
alteration of fracture permeability in granite under hydrothermal conditions and its interpretation by coupled chemo-mechanical model. Appl Geochem. 2011;26(12):2074–2088. 37. Berner RA. Rate control of mineral dissolution under earth surface conditions. Am J Sci. 1978;278(9):1235–1252. 39. Qiao L, Li S, Wang Z, Tian H, Bi L. Geotechnical monitoring on the stability of a pilot underground crude-oil storage facility during the construction phase in China. Measurement. 2016;82:421–431. 40. Brush DJ, Thomson NR. Fluid flow in synthetic rough-walled fractures: NavierStokes, Stokes, and local cubic law simulations. Water Resour Res. 2003;39(4):1085.
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