Article pubs.acs.org/est
Determining pH at Elevated Pressure and Temperature Using in Situ 13 C NMR J. Andrew Surface,† Fei Wang,‡ Yanzhe Zhu,† Sophia E. Hayes,† Daniel E. Giammar,*,‡ and Mark S. Conradi§,† †
Department of Chemistry, ‡Department of Energy, Environmental, and Chemical Engineering, and §Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, United States ABSTRACT: We have developed an approach for determining pH at elevated pressures and temperatures by using 13C NMR measurements of inorganic carbon species together with a geochemical equilibrium model. The approach can determine in situ pH with precision better than 0.1 pH units at pressures, temperatures, and ionic strengths typical of geologic carbon sequestration systems. A custom-built high pressure NMR probe was used to collect 13C NMR spectra of 13 C-labeled CO2 reactions with NaOH solutions and Mg(OH)2 suspensions at pressures up to 107 bar and temperatures of 80 °C. The quantitative nature of NMR spectroscopy allows the concentration ratio [CO2]/[HCO3−] to be experimentally determined. This ratio is then used with equilibrium constants calculated for the specific pressure and temperature conditions and appropriate activity coefficients for the solutes to calculate the in situ pH. The experimentally determined [CO2]/[HCO3−] ratios agree well with the predicted values for experiments performed with three different concentrations of NaOH and equilibration with multiple pressures of CO2. The approach was then applied to experiments with Mg(OH)2 slurries in which the change in pH could track the dissolution of CO2 into solution, rapid initial Mg(OH)2 dissolution, and onset of magnesium carbonate precipitation.
■
INTRODUCTION Geologic carbon sequestration, a process wherein CO2 is injected at elevated pressure and temperature deep underground, has been proposed as a strategy for reducing large-scale CO2 emissions from energy generation and other industrial processes. Understanding the physical and chemical implications of CO2 injection for site geology and environmental chemistry is crucial to ensuring that sequestration sites are chosen that can withstand the physical and chemical changes that CO2 injection imposes. Knowledge of chemical reactions of CO2 with the aqueous phase and with the minerals of the formations into which it is injected can also improve estimates of a geologic formation’s storage capacity and the dominant mechanisms responsible for storage. As described in detail elsewhere,1−3 geologic storage of CO2 is accomplished through one or more possible entrapment mechanisms. These include stratigraphic (physically trapped CO2), solubility (CO2 dissolved in the brine), and mineral trapping (CO2 reacted with a divalent metal, such as Mg2+, Ca2+, or Fe2+). The most permanent and long-term storage mechanism is mineral trapping, the chemical conversion of CO2 into a thermodynamically stable solid form, a mineral carbonate. The divalent metal ions are supplied by the dissolution of the minerals in the geologic formation; the mineral dissolution is driven by the decrease in pH caused by the introduction of of CO2. Mineral trapping is most important © 2015 American Chemical Society
for geologic sequestration in magnesium- and iron-rich formations like basalts and peridotites.4−6 Pilot-scale injections into basalt have been performed,7,8 and the use of peridotites for either in situ or ex situ mineral carbonation has been proposed.9−11 Olivine, most often studied as the magnesium end-member form of forsterite (Mg2SiO4), is 34.5% Mg by weight, and serpentine (Mg3Si2O5(OH)4) is 26.3% Mg by weight. These target minerals have the highest carbonation potential of rocks in the earth’s crust and occur in vast quantities worldwide.9,12 The dissolution of magnesium-containing minerals and the subsequent precipitation of carbonate minerals have been extensively studied in batch experiments at pressures and temperatures relevant to carbon sequestration. Many experiments have been performed with pure minerals such as olivine,13−21 and others have been conducted with basalt and peridotite rocks.22−30 Reactions 1−3 describe the three important reaction steps involved in CO2 mineral trapping. CO2(g) ⇌ CO2(aq) Received: Revised: Accepted: Published: 1631
(1)
November 9, 2014 December 18, 2014 December 29, 2014 January 14, 2015 DOI: 10.1021/es505478y Environ. Sci. Technol. 2015, 49, 1631−1638
Article
Environmental Science & Technology CO2(aq) + H 2O ⇌ HCO3− + H+ ⇌ CO32 − + 2H+
(2)
Mg 2 + + CO32 − ⇌ MgCO3(s)
(3)
Their cost and inability to calibrate while pressurized also discourage their use.44,51,52 Recently Shao et al. demonstrated a spectrophotometric application in which they calculated pH from spectroscopicallydetermined concentrations of pH-sensitive chromophores.44 In their paper they discussed three different spectrophotometric methods of measuring concentration ratios from a pH indicator in a heated solution pressurized with CO2. They were able to accurately measure in situ pH based on comparison of their results with output of four different modeling packages. Additional methods for measuring pH at elevated pressures and temperatures include yttria-doped zirconia electrodes53,54 and specialized high pressure potentiometric measurement cells.55,56 One particular study used the carbonate equilibrium to elucidate the effect of pH in a high pressure solution via NMR.57 13 C NMR can provide quantitative ratios of concentrations of reactants and products in solution from which pH values can be derived if the equilibrium constants of the reactions at the elevated temperatures and pressures are known. The three carbon-containing aqueous species that form in solution after CO2(g) dissolves in water, CO2(aq), HCO3−, and CO32−, have distinct 13C NMR chemical shifts and nuclear spin relaxation properties.41,58−61 Using the first equilibrium step (CO2 ⇌ HCO3−) in Reaction 2, pH under standard conditions can be calculated using the ratio of [CO2]/[HCO3−] obtained from the 13C NMR intensities and the standard pKa of 6.35.20 The pH is obtained from the ratio of the activities of CO2, HCO3−, and CO32−, denoted by the braces, {}, in eqs 6 and 7:
While magnesium silicate dissolution (e.g., Reaction 4 for forsterite) will be the principal source of magnesium in actual formations, brucite (MgOH2) dissolution (Reaction 5) has also been investigated15,31−36 as a model phase with high reaction rates that enables investigation of trapping mechanisms. Mg 2SiO24(s) + 4H+ ⇌ 2Mg 2 +(aq) + H4SiO4(aq)
(4)
Mg(OH)2(s) + 2H+ ⇌ Mg 2 +(aq) + 2H 2O
(5)
In Reactions 4 and 5 the release of Mg2+ is accompanied by an increase in pH (consumption of H+) that neutralizes some of the acidity from the injected CO2. In most experiments the reaction products were analyzed ex situ only after depressurizing and cooling the batch reactor from higher experimental pressures and temperatures (>50 bar, and >70 °C). These ex situ methods have provided valuable chemical insight into net products formed but do not provide explicit information about the in situ pH or evidence for how and when the products form. In situ analysis methods for characterization of reaction products have recently been developed by modifying traditional bench-top methods for operation under carbon sequestration conditions. XRD,36−38 NMR,14,39−42 spectrophotometry,43,44 IR,45 and Raman46,47 studies of sequestration reactions in situ have been completed. These studies have provided additional information regarding the mechanisms, rates, and direct effects of changing reaction variables like pressure, temperature, and reactant concentrations. In situ Raman and elevated-pressure magic-angle spinning (HP-MAS) NMR, for example, each allowed the observation of thermodynamically unstable intermediate carbonate phases (e.g., hydromagnesite) and their subsequent slow kinetic conversion into more stable carbonates.14,46 These techniques have also enabled the monitoring of relative concentrations of species in solution throughout the reactionscontributing to a better understanding of mineral dissolution and precipitation at sequestration conditions. In addition to having in situ analysis of the products of a reaction, direct measurements of pH at the elevated pressure and temperature of geologic carbon sequestration are valuable to interpreting the processes occurring in batch experiments because the equilibria and rates of CO2-mineral-water reactions are heavily pH-dependent. As described in Reaction 2, the available HCO3− and CO32− for mineralization depend on pH. Additionally, mineral dissolution rates that supply Mg2+ are controlled by the pH.15,48−50 As recently described by Shao et al.,44 measuring pH during sequestration reactions has many challenges. One cannot simply take samples of the solution from a reacting system and then measure their pH using a traditional benchtop meterpH is dictated by how much CO2 is in the solution, and [CO2] depends on temperature and pressure. Thus, the pH will change as the sample is brought to ambient conditions. For accurate assessments of pH, measurements must be made in situ at elevated temperatures and pressures relevant to CO2 sequestration. While elevated pressure and temperature pH electrodes are commercially available, they require physical contact with the solution being observed. Consequently, measurements of the pH within porous media are impossible with the standard pH electrode.
⎛ {CO2 } ⎞ pH = − log10{H+} = − log10⎜K a1· ⎟ {HCO3−} ⎠ ⎝
(6)
⎛ {HCO3−} ⎞ ⎟ pH = − log10{H+} = − log10⎜K a2· {CO32 −} ⎠ ⎝
(7)
If the solution is sufficiently dilute that activity coefficients of the solutes (γ) can be assumed to equal 1, then [CO2] =[HCO3−] at pH of 6.35. (Note: here we have simplified this first equilibrium step and pKa as the combination of two reactions CO2 + H2O ⇌ H2CO3 and H2CO3 ⇌ HCO3− + H+. The concentration of H2CO3 is negligible, allowing the two reactions to be combined.) When solutions have higher ionic strengths, as is typically the case for brines selected to represent waters in target geologic sequestration formations, then activity coefficients must be included in the equations so that the pH can then be determined from the ratios of the concentrations of the inorganic carbon species (eq 8). ⎡ ⎤ ⎛ γ ⎞⎛ [CO2 ] ⎞⎥ CO2 ⎢ ⎜ ⎟ pH = − log10{H } = − log10 K a1·⎜ − ⎟⎥ ⎟·⎜ ⎢ ⎝ γHCO3− ⎠ ⎝ [HCO3 ] ⎠⎦ ⎣ +
(8) 13
C NMR has previously been used, by our group and others, as an unobtrusive, quantitative spectroscopic method to measure the [CO2]/[HCO3−] and [HCO3−]/[CO32−] ratios nondestructively.40,41,58,59,61 The evolution of these quantities over time can therefore be evaluated in a reacting system. In one biological study,62 a group was able to image pH in vivo using spatially resolved [CO2]/[HCO3−] ratios in a living cell. A common practice in these previous studies has been to use 1632
DOI: 10.1021/es505478y Environ. Sci. Technol. 2015, 49, 1631−1638
Article
Environmental Science & Technology the ideal pH assumption, where pH = −log[H+], instead of pH = −log{H+}. The objective of this study was to extend the 13C NMR approach to determine the in situ pH of systems reacting at conditions relevant to geologic carbon sequestration. A custombuilt elevated pressure and high temperature NMR probe was used to investigate reactions of high pressure CO2 with NaOH solutions and Mg(OH)2 suspensions of known compositions. A geochemical equilibrium model was used to calculate the pH from concentration ratios of carbon species determined from the NMR measurements, and the model was also used to compare the measured and predicted equilibrium speciation.
reaction kinetics, making it ideal for study in the laboratory setting.31,40 The molar ratio of mineral/H2O for the experiment was 23% (7.42 × 102 g Mg(OH)2/L H2O); there was enough water to cover the mineral powder. After mixing, the solution was allowed to settle so that a heterogeneous slurry formed with the wet mineral settled on the bottom and a thin water layer at the top of the tube. Static in Situ 13C NMR. All 13C NMR results reported in this paper were conducted at an NMR Larmor frequency of 89.07 MHz without 1H decoupling, with a typical π/2 pulse of 15 μs. All NMR experiments were either acquired using a Bloch decay pulse sequence with a π/2 pulse or a 16-row phase cycled Hahn echo using a 100 μs delay. Recycle delays for the NMR experiments varied between 1 and 120 s, depending on the T1 relaxation time constants of the species being observed. All 13C NMR spectra were referenced to the 13CO2(aq) resonance at 126.0 ppm at our conditions.39,40,58,59 A single data point is attained by 32 NMR scans separated by at least 60 s of time these NMR parameters are required to attain adequate signalto-noise and to maintain the quantitative nature to the data. Temporal resolution was therefore limited to 30 min intervals. NMR data integrations were completed using the peak fitting program DMFIT.63 A static CSA line shape function was used to fit all powder patterns, and a Voigt function (a combination of an exponential and a Gaussian function) was used for fitting all narrow resonances (shimming constraints in the probe due to the presence of a solid gave the solution NMR lineshapes Gaussian characteristics). Fitting was necessary to calculate integrated intensities since the broad solid carbonate powder pattern sometimes extended into the region of the CO2(aq) (126 ppm) and HCO3−(aq) (161.5 ppm) peaks and thus needed to be separated for accurate calculation of [CO2]/[HCO3−] from the NMR data. The 13C NMR spectrum has two separate peaks for CO2 and HCO3− because the rate of exchange between CO2 and HCO3− is much slower than the NMR time scale. The individual peak fits had the same error as the inverse of the signal-to-noise ratio of the peak. For the CO2(aq) signals, this was around ±0.6% relative error as the CO2(aq) signal had a signal-to-noise ratio that averaged 450:1. The bicarbonate signals generally had an error of ±3.6% as the bicarbonate S/N averaged 85:1. (Here we have defined error as ±3 × σnoise, and signal-to-noise ratio as Integralpeak/σnoise.) Where possible, fitted integrations were compared to numerical integrations and found to be in agreement within the signal-to-noise error. Geochemical Equilibrium Calculations. Equilibrium calculations were performed to calculate the in situ pH from the experimentally measured [CO2]/[HCO3−] ratio that was determined from the 13C NMR spectra. For use in eq 8 for calculating the pH, the concentrations of CO2 and HCO3− were used with activity coefficients determined using Pitzer equations to determine the ratio of the activities of CO2 and HCO3−. The value of Ka1 at nonstandard temperature and pressure was determined using the SUPCRT9264 software with the dslop98 thermodynamic database.65 Calculations were performed using PHREEQC66 with the accompanying Pitzer database (pitzer.dat). The pH values determined from the experimental measurements were compared with predicted values for the compositions of the NaOH solutions in equilibrium with elevated pressure CO2. The pH was determined in PHREEQC for the known total Na+ concentration and the CO2 solubility. The CO2 solubility for the fixed headspace pressure of CO2 and ionic strength was determined from published equations of
■
MATERIALS AND METHODS Materials. Reactions were investigated in solutions prepared in ultrapure water and then contacted with elevated pressure 99% 13C-labeled 13CO2 gas (Sigma-Aldrich). Chemicals used in preparing solutions included NaOH pellets (Alfa Aesar, Stock #A16037) of 98% purity and brucite with purity exceeding 98% (used as received from Alfa Aesar). The small amounts of impurities in the brucite are soluble salts (as described in the Mg(OH)2 purity report from Alfa Aesar). Elevated Pressure Experiments. Reactions were performed in a custom-built NMR probe with an yttria-stabilized zirconia pressure vessel which is suitable for use up to 250 °C and 300 bar (yttria-stabilized zirconia has relatively little loss of tensile strength at higher temperatures and is electrically nonconductive, making it an ideal sample holder inside an NMR coil). Reactants were loaded into a glass tube (10 mm in diameter and 4.13 cm in length) designed to fit into the high pressure vessel. The glass tube prevents crystallization on the zirconia walls of the pressure vessel. Other details of the probe are described elsewhere.40 The reactor was pressurized with 13 C-labeled CO2 gas at 107 bar and heated at 80 °C for 4 days in the NMR apparatus. 13C NMR spectra were obtained throughout this time to monitor changes in the [CO2]/ [HCO3−] ratio. Experiments with NaOH solutions were performed to examine the ability of the approach to determine pH from measured [CO2]/[HCO3−] ratios in solutions of known composition and in which no precipitation reactions would occur. NaOH pellets were added to deionized water to make a standard solution from which 0.0948, 0.288, and 1.041 molal solutions were prepared by diluting three different aliquots with additional ultrapure water. Each of the three samples was “titrated” with 13CO2 gas at different pressures and allowed to equilibrate. Approximately 2 mL of each aliquot was added to the high pressure reaction tube in the 13C NMR apparatus after first being put under modest vacuum (0.1 bar) to remove most air. The solutions were allowed to equilibrate with the pressurized 13CO2 gas (without being stirred) at each pressure set point for 12 h before NMR data were acquired. Experiments using in situ 13C NMR monitoring indicated that CO2 dissolution in these unstirred systems takes approximately 12 h to come to equilibrium, depending on the initial pressure of gas and the affinity of CO2 with the solution. In subsequent experiments with a slurry of brucite (1.15 g mixed with 1.15 g of deionizd water), the potential reactions were more complex with initial brucite dissolution (Reaction 5) and the possible precipitation of magnesium carbonates (Reaction 3). Brucite served as a model source of Mg2+ for sequestration targets such as olivine and serpentine. Brucite has high magnesium content (42% Mg by weight) and favorable 1633
DOI: 10.1021/es505478y Environ. Sci. Technol. 2015, 49, 1631−1638
Article
Environmental Science & Technology
experimental NaOH data (in Figure 1) corresponds to ±0.1 pH units overall. Brucite−CO2−Water Reactions at Elevated Pressure and Temperature. The [CO 2]/[HCO 3−] ratios were measured by 13C NMR based on integrated intensities of the 13 CO2 and H13CO3− resonances. Figure 2 shows an in situ 13C
Duan and Sun.67−70 The values of the relevant equilibrium constants (Ka1 and Ka2 for CO2 and Kw for the dissociation of water) were determined using SUPCRT92. For experiments with the brucite suspensions, the pH was determined from the [CO2]/[HCO3−] ratio as in the experiments with the NaOH solutions, but the speciation could not be predicted because the system was likely not in equilibrium as brucite was dissolving and a magnesium carbonate phase was precipitating.
■
RESULTS AND DISCUSSION NaOH Solution Experiments. The experimentally determined and predicted equilibrium compositions of the three NaOH solutions were compared on the basis of the measured [CO2]/[HCO3−] ratios. The initial comparison on this basis− and not the measured pH−was done because the [CO2]/ [HCO3−] ratios are the directly measured result from 13C NMR. The differences between the model predictions and experimental measurements of [CO2]/[HCO3−] shown in Figure 1 are relatively small. Figure 1 also shows the pH values
Figure 2. In situ 13C NMR data with all of the 13C-containing species in system noted. Data are shown for the reaction of brucite with 107 bar CO2 at 80 °C for three reaction times and for a 0.095 M NaOH solution that was equilibrated with 52 bar CO2 for 12 h. The feature labeled as sc-CO2 is a resonance from a supercritical CO2 artifact in the space between the glass sample holder and the zirconia pressure vessel.
NMR spectrum obtained 87 h into the reaction with brucite. The aqueous and gaseous 13C NMR signals (CO2(aq), HCO3−, and sc-CO2) are motionally narrowed, unlike the solid carbonate precipitate, which shows a typical static solid-state “powder pattern”. The breadth of the solid carbonate feature is due to its large chemical shift anisotropy, and its shape is typical of axially symmetric solid carbonate crystallites (randomly oriented).15,71−73 The solid carbonate 13C NMR line shape is indicative of carbonate type, and in principle the exact mineral could be identified; however, the possible presence of multiple mineral components limited identification from the spectra collected in situ. Ex situ analysis (magic angle spinning NMR and Raman spectroscopy) of the reacted materials showed that the largest amount of the carbonate mineral formed in the top layers of the sample, including the region within the NMR coil. In the experiments with brucite suspensions, the speciation of the solution evolved with time as brucite dissolved and magnesium carbonate solids precipitated. This temporal variation is in contrast to the experiments with NaOH solutions in which equilibrium was reached on time scales more quickly than the duration of the measurements. For the brucite suspensions, the [CO2]/[HCO3−] ratio initially increased (i.e., pH decreases) as the CO2 dissolved into the solution (Figure 3). After 12 h the dissolution of the brucite led to substantial decreases in the [CO2]/[HCO3−] ratio (i.e., increases in pH) and continued for 20 h. After about 32 h, the rate of pH increase slowed, which was probably caused by carbonate mineral precipitation. In the 13C NMR spectrum for the in situ reactor after 87 h, the broad peak corresponding to a solid carbonate mineral is clearly evident (Figure 2). Brucite
Figure 1. Experimentally measured [CO2]/[HCO3−] ratios from elevated pressure 13C NMR (diamonds) and pH values (circles) calculated from those ratios for solutions with three different initial NaOH concentrations and varying CO2 pressure. Predicted equilibrium pH values are shown with the solid line. The experimental error of the ratios from S/N in the 13C NMR experiments is smaller than the size of the data points.
calculated from the measured [CO2]/[HCO3−] ratios. The largest disagreement in the “high concentration” 1.041 m data set was a 0.19 model versus 0.10 experimental value for [CO2]/ [HCO3−] which corresponds to 0.3 pH units in error. The largest disagreement in the “low concentration” 0.0948 m data set was 11.99 versus 13.68 corresponding to a difference of 0.05 pH units error. The average model agreement with the 1634
DOI: 10.1021/es505478y Environ. Sci. Technol. 2015, 49, 1631−1638
Article
Environmental Science & Technology
Figure 3. [13CO2]/[H13CO3−] ratios (diamonds) monitored by 13C NMR and the pH (circles) determined from those ratios over time in a brucite slurry reacting with 104−107 bar CO2 at 80 °C. The line connecting the pH points is just included as a visual guide. The error in the NMR-measured [13CO2]/[H13CO3−] ratios is smaller than the size of the data points.
Figure 4. Calculated saturation indices (dimensionless) versus reaction time for experiments with a brucite suspension reacted at 104−107 bar CO2 and 80 °C in which the magnesium carbonate solids magnesite and hydromagnesite could form.
the entire vessel during the time frame sampled here. The rapid climb of the saturation index of hydromagnesite here suggests that it may precipitate at later times. These differences in the saturation indices for different phases could be one reason for a spatial gradient of products that was found to form in a similar reaction we reported previously,40 where magnesite preferentially precipitated in the top portion of the sample, hydromagnesite in the middle, and finally dypingite in the bottom. It is important to note that the data in Figure 3 are dependent on the position of the NMR coil relative to the sample. Gradients of species in the NMR sample holder may develop due to inadequate diffusive transport in these unmixed systems. In this experiment, the NMR coil was situated such that the top of the slurry is at the top of the NMR coil. The NMR coil is therefore monitoring the first 2 cm of CO2 penetration into the sample (4.13 cm long) and reporting an average ratio across that region. The pH below this 2 cm zone is likely higher than the average within the zone due to limited diffusion of inorganic carbon into and Mg2+ out of the deeper portions of the slurry. Environmental Implications. The elevated pressure and high temperature NMR probe is another tool available for in situ investigation of geochemical reactions relevant to carbon sequestration. By providing information on aqueous speciation, including pH, the technique complements in situ X-ray diffraction and spectroscopic techniques that probe the solid phases. The determination of pH is indirect, relying on the measured [CO2(aq)]/[HCO3−] ratio, and the calculated pH is therefore only as good as the estimation of pKa1 and activity coefficients at the temperature, pressure, and ionic strength of interest. The currently available geochemical equilibrium models and thermodynamic databases are sufficient for accurate determination of pH. With refinements to the hardware, the NMR approach may be able to also provide spatially resolved determinations of pH. The in situ NMR technique is limited to laboratory-scale investigations, and because of the interference of iron with NMR spectra, the technique is also limited to ironfree samples. The combination of NMR and a computational model provides additional analysis and calculation tools for the determination of pH in aqueous reactions of CO2 far removed from ideal conditions (i.e., in low ionic strength solutions and at standard temperature and pressure). This method is relevant to a variety of fields beyond geosequestration including but not limited to carbonate chemical production, CO2 capture, and any aqueous reaction system pressurized with CO2, such as
conversion to magnesite in CO2-rich slurries or in wet CO2 has previously been observed to be a relatively rapid process. Complete conversion at 200 °C and elevated CO2 pressures of approximately 15 bar was observed within 4 h,32 and a study at 75 °C and 82 bar found complete conversion to magnesite within 10 h in wet supercritical CO2.36 In our own previous work with the same elevated pressure NMR probe, we first detected magnesium carbonates after 58 h, a considerably longer time than seen here. The slower net carbonation reaction in the NMR probe observed in the previous study may be due to the higher brucite loading of the slurry (1 g/mL in the present study compared with 0.029 g/mL in the other experiment with a slurry32). The overall trend of increasing pH can be influenced by the rates of brucite dissolution, magnesite precipitation, and solute diffusion within the slurry. Equilibrium calculations indicate that magnesite precipitation is thermodynamically favorable based on the saturation index for magnesite. The saturation indexes of the solution with respect to magnesite (MgCO 3 ) and hydromagnesite (Mg5(CO3)4(OH)2·4H2O), where “act” means actual activity, are given in eqs 9 and 10. ⎛ {Mg 2 +} {CO 2 −} ⎞ act 3 act ⎟ SI MgCO = log10⎜⎜ ⎟ 3 K sp,magnesite ⎠ ⎝
(9)
⎛ {Mg 2 +}5 {CO 2 −}4 {OH−}2 ⎞ act 3 act ⎟ act SIMg (CO3)2 (OH)2 = log10⎜ ⎜ ⎟ 3 K sp,hydromagnesite ⎝ ⎠ (10)
For these calculations, the value of {Mg2+}act was estimated by finding the Mg2+ concentration that would satisfy charge balance for a solution in equilibrium with the fixed PCO2 at the pH determined from the NMR approach. This provides an upper limit on the Mg2+ concentration since the actual value cannot be determined precisely because the overall inorganic speciation may be affected by magnesite precipitaton and not just by the PCO2. The saturation indices calculated for magnesite as well as hydromagnesite and brucite are plotted in Figure 4. The production of magnesite is favorable in all time points of the reaction, suggesting that it will readily precipitate out of solution. Brucite is always undersaturated (having a SI value
