Dissolution of Calcite at Up to 250 °C and 1450 bar and the Presence

The solubility of calcite (CaCO3) was measured for temperatures up to 250 °C and pressures up to 1450 bar (21 000 psi) in the presence of mixed elect...
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Dissolution of Calcite at Up to 250 °C and 1450 bar and the Presence of Mixed Salts Wei Shi,* Amy T. Kan, Nan Zhang, and Mason Tomson Department of Civil and Environmental Engineering, Rice University, MS 519, 6100 Main Street, Houston, Texas 77005, United States ABSTRACT: The oil and gas production from deepwater has been challenged due to limited knowledge of mineral solubility and inhibitor efficiency at the extreme conditions of ultrahigh temperature, pressure, and TDS (total dissolved solids) contributed by mixed salts. The solubility of calcite (CaCO3) was measured for temperatures up to 250 °C and pressures up to 1450 bar (21 000 psi) in the presence of mixed electrolytes. A set of stability constants was selected based upon experimental measurements, which, together with the current set of Pitzer coefficients for activity coefficients, produce predictions consistent with measured data for the NaCl system. Predictions for the system with high concentrations of mixed electrolytes, however, demonstrate deviation from the measurements due to the presence of SO42−. A need is therefore suggested to re-evaluate the pressure dependence of Pitzer coefficients corresponding to the interactions between various key species in the calcite system and SO42−.

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speciation of the CO2−H2O−NaCl system from 0 to 250 °C, from 0 to 1000 bar and from 0 to 5 m of NaCl.8 The literature has also accumulated voluminous experimental measurements of the solubility of calcite at different conditions. Because of the importance of the equilibrium between gas phase and aqueous CO2, all measured data can be separated into two categories depending upon whether a separate vapor phase exists in the system. In the studies by Malinin and Kanukov (1971)9 and Sharp and Kennedy (1965),10 for instance, CO2 is unsaturated in aqueous solution and therefore has a variable concentration in the solution phase that cannot be determined by its solubility. Other authors, such as Ellis11,12 and Segnit et al.,13 conducted the studies with CO2 saturated systems, in which its concentration can be calculated using Henry’s law. A summary of the calcite solubility data was presented by Duan and Li14 for the H2O−CO2−NaCl systems at temperatures up to 250 °C, pressures up to 1000 bar, and NaCl concentrations up to 6 m. The solubility reported in different sources, nevertheless, can sometimes differ substantially from each other.14 Measurements in the presence of other typical electrolytes associated with oil field brine, such as K+, Mg2+, SO42−, and Ca2+, however, are rare. Many models have been developed to calculate the solubility of different minerals (including calcite), such as PHREEQC, PHRQPITZ, WATEQ4F, and MINTEQ. However, most of these models are confined in terms of the range of applicable temperature and pressure, probably due to the inadequate understanding about the temperature and pressure dependence of various model components, including stability constants and activity coefficients over the wide range of temperature and pressure. The stability constants associated with various processes involved in calcite dissolution are available in the

INTRODUCTION The oil and gas industry is making firm strides in promoting production from unconventional sources, such as deep or ultradeep water. As pointed out in our previous study on dissolution of Barite at high temperature and high pressure, these environments, with temperatures of over 200 °C, pressures over 1500 bar, and total dissolved solids (TDS) over 300 000 mg/L, pose significant challenges to scale prediction and control due to limited knowledge of mineral solubility and inhibitor efficiency at these conditions.1−4 Prediction of mineral solubility, for instance, requires precise values of both equilibrium constants (including the solubility product and other association constants for complexes, if applicable) and activity coefficients. Calcite, essentially CaCO3, is one of the most common types of scale encountered in the oil and gas production.1 Because of its close connection to the carbonic acid system, the dissolution of calcite in complex oil field brine is controlled by several processes including the dissolution of CO2 in water (phase equilibrium), the dissociations of both carbonic acid (H2CO3) and bicarbonate ion (HCO3−), as well as the association and dissociation of any complex species present in the system (chemical equilibrium), all of which should be accounted for in both experimental measurement and model development for solubility determination. The equilibrium between gas-phase and aqueous CO2, for instance, is a complicated function of temperature, pressure, and solution composition. High salt concentration could substantially increase the size of the liquid−vapor region by raising the consolute temperature at a given pressure. Bowers and Helgeson showed that the effect of mixing H2O, CO2, and NaCl on equilibrium can be assessed quantitatively on the phase diagrams generated with the aid of a modified Redlich−Kwong equation of state.5 Duan and his colleagues have conducted systematic investigations of the liquid−vapor equilibrium at different temperature, pressure, and solution conditions and presented numerous models for solubility calculation,6,7 which, together with their examination of the chemical equilibrium processes, were consolidated in a model to calculate the © 2013 American Chemical Society

Received: Revised: Accepted: Published: 2439

August 15, 2012 January 3, 2013 January 7, 2013 January 8, 2013 dx.doi.org/10.1021/ie302190e | Ind. Eng. Chem. Res. 2013, 52, 2439−2448

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Figure 1. Solubility product of calcite (Ksp, CaCO3) at different temperatures and pressures from different sources.

As pointed out in our previous paper on Barite solubility,24 prediction of scale solubility for deepwater development is currently limited by inadequate knowledge about the thermodynamics of common minerals at high temperature, high pressure, and high concentrations of mixed electrolytes. This study continues our investigation of mineral dissolution at high temperature and pressure. Solubility of calcite was measured at various temperatures, pressures, and ionic strengths in the NaCl−CO2−H2O system, up to 250 °C, 1450 bar (21 000 psi), and 4 m NaCl. Stability constants from different sources and Pitzer coefficients for activity coefficients were evaluated using the experimental data. The model was also tested and verified using solubility measured in synthetic solutions that contained elevated concentrations of mixed electrolytes typically present in oil field brines.

literature, although significant difference exists between values from different sources, especially at extreme conditions of high temperature and high pressure. The solubility products of calcite (Ksp, CaCO3) from different sources8,15−18 (Figure 1), for instance, agree well with each other at pressure lower than 500 bar, but deviate from each other as pressure increases. The deviation between Nordstrom’s recommended values15 and those calculated by SUPCRT 9217 is as high as one logarithm unit at 200 °C and 1,650 bar. Among the various approaches for estimating ionic activity coefficients in complex aqueous electrolyte solutions, Pitzer ion interaction theory has been widely and successfully applied in many systems to study calcite solubility.19−21 Pitzer and his coworkers22−24 parametrized the Na−K−Ca−Mg−HCO3−CO3−OH system at 25 °C and have extended part of it to the temperature range of 0 to 50 °C. Harvie et al.25 presented a model to predict mineral solubility in natural water for the Na−K−Mg−Ca− H−Cl−SO4−OH−HCO3−CO3−CO2−H2O system up to high ionic strength at 25 °C based upon Pitzer equation. He et al.26 re-evaluated the Pitzer coefficients corresponding to the interactions between carbonate species and other ions including Na+, K+, Ca2+, Mg2+, Cl−, and SO42− and presented a model that was able to provide accurate prediction of calcite solubility between 0 and 90 °C at 1 atm. More recently, the temperature and pressure ranges of model prediction has been expanded by Duan and Li,14 who developed a comprehensive model for the calculation of coupled phase and aqueous species equilibrium in the H2O−CO2−NaCl−CaCO3 system from 0 to 250 °C and 1 to 1000 bar with NaCl concentration up to saturation of halite. The temperature and pressure dependence of Pitzer coefficients for most interactions that involved other species typically present in the oil field brine, nevertheless, usually remains unavailable, or at the most, limited to below 100 °C and at atmospheric pressure.

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MATERIALS AND METHODS Chemicals. All chemicals used in the testing were of ACS reagent grade. Calcite particles (99+%, Sigma−Aldrich) were packed in a stainless steel column (SS316, outer diameter 1.43 cm, inner diameter 0.48 cm, High Pressure Equipment Company) with a length of 10.2 cm and a pore volume of approximately 1 mL (corresponding to a porosity of 50%). NaCl (Fisher Chemical) was use as background electrolyte in the solubility measurement. EDTA solution (0.2 M) at 10 pH was made by dissolving EDTA disodium salt (Fisher Chemical) in DI water, followed by adjusting pH to 10. CaCl2 (EMD Chemicals) and NaHCO3 (EMD Chemicals) were used to prepare feed solutions saturated with CaCO3 at temperature of interest. NaHCO3 (EMD Chemicals), NaBr (Fisher Chemical), Na2B4O7·10H2O (Fisher Chemical), and Na2SiO3 solution (26.5% SiO2, Sigma− Aldrich) were used to prepare a synthetic brine with elevated concentrations of mixed electrolytes. 2440

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CO2 in the gas and solution phases, respectively. γCO2(g) has a value of 0.994 at 25 °C and 1 atm according to the Peng− Robinson equation of state. γCO2(aq) is calculated using Pitzer ion interaction theory (eq 11). On the other hand, the possible formation of ion pair, such as CaCO30, CaOH+, and CaHCO3+, is theoretically accounted for in the Pitzer ion interaction theory as by certain coefficients 0 (such as β(2) CaCO3 for CaCO3 ion pair) as a special form of ion interaction and therefore does not need to be treated separately . Therefore, mCa2+ represented only the total calcium concentration measured by ICP-OES and was used in the modeling process, while the concentration of free calcium ion was not important. The dominant processes for our system are expressed in eqs 5−7, along with the stability constant for each process. a H+mHCO−3 γHCO− 3 CO2 + H 2O ↔ HCO−3 + H+, K1 = a H2OmCO2(aq)γCO (aq)

Calcite Solubility Measurement at High Temperature and High Pressure. The same apparatus introduced in our previous paper on Barite dissolution at high temperature and high pressure was used in this study.27 Calcite dissolution tests were conducted at temperatures of 0, 25, 100, 200, and 250 °C, pressures of 34.5 (about 69 bar for tests at 250 °C), 483, 965, and 1448 bar (500, 7000, 14 000, and 21 000 psi) and background NaCl concentrations of 0.1 and 4 mol/kg-H2O (m). All feed solutions were sparged with pure CO2 until the pH became constant so that the solutions contained a fixed amount of dissolved CO2 in equilibrium with 97% of CO2 in the gas phase, taking into consideration approximately 3% of water vapor. The pH values were 6.00 and 5.70 for feed solutions with 0.1 and 4m NaCl, respectively, consistent with the calculations by our model. For tests at each temperature, CaCl2 and NaHCO3 were dosed in the feed solution in 1:2 molar ratio in such concentrations that the solution would be saturated with CaCO3 at 97% CO2 at the temperature of interest and one atmosphere. The feed solution was then delivered into the column for the interaction between the solution phase and calcite particle to take place at the temperature of interest and different pressures. The effect of retention time on dissolution equilibrium was examined by varying the flow rate of the feed solution. Similar effluent concentrations were observed at retention time ranging from 0.5 to 10 min, suggesting equilibrium was achieved in less than 0.5 min. A feed flow rate of 0.5 mL/min was therefore chosen for the convenience of sample collection, corresponding to a retention time of 2 min in the column. The concentration of Ca2+ in the effluents from the back pressure regulator was measured using inductively coupled plasma optical emission spectrometry (ICP-OES, Perkin-Elmer 4300DV), and the concentrations of HCO3− and aqueous CO2 were calculated based upon the stoichiometry of the following dominant dissolution reaction. CO2 + H 2O + CaCO3 → Ca 2 + + 2HCO−3

(1)

Δm HCO−3 = 2ΔmCa 2+

(2)

ΔmCO2(aq) = −ΔmCa 2+

(3)

2

(5)

HCO−3 ↔ CO32 − + H+,

K sp ,CaCO3 = mCa 2+γCa 2+mCO32−γCO2− 3

(7)

The saturation index (SI), defined as logarithm of the ion activity product divided by the solubility product, can be calculated by combining eqs 5−7 (eq 8). The theoretic value of SI is zero at dissolution equilibrium, so the deviation of SI values from zero calculated by the model using experimentally measured Ca2+ concentration and concentrations of HCO3− and CO2 calculated by eqs 2 and 3 can be used as the criterion to evaluate the model prediction; the closer SI is to zero, the better the match between model calculation and experimental measurements. ⎛ m 2 +m 2 − ⎛ aCa 2+aCO2− ⎞ 3 ⎟⎟ = log ⎜ Ca HCO3 SICaCO3 = log10⎜⎜ 10⎜ ⎝ K sp ,CaCO3 ⎠ ⎝ mCO2(aq) ×

2 γCa 2+γHCO − 3

γCO (aq)a H2O 2

×

⎞ ⎟ K1K sp ,CaCO3 ⎟⎠ K2

(8)

2+

where mCa2+ is the measured Ca molal concentration. mHCO3− and mCO2(aq) are the molal concentrations of HCO3− and aqueous CO2 calculated by eqs 2 and 3, respectively. K1, K2, and Ksp,CaCO3 are equilibrium constants defined in eqs 5−7. aH2O is the activity of water as calculated using Pitzer theory.21 γCa2+, γHCO3− and γCO2(aq) are the activity coefficients of Ca2+, HCO3−, and aqueous CO2, respectively. The activity coefficients of various species were calculated using Pitzer specific ion interaction theory. The derivation of Pitzer working equations for activity coefficients can be found in a variety of sources, including his textbook on thermodynamics21 and many papers published in the 1980s.19,22,23 A brief summary about the application of these equations to the calculation of activity coefficients of ions in a simple NaCl−H2O system has been presented in our previous paper.27 The activity coefficients of various aqueous species were calculated using the same approach in this study, except that extra terms corresponding to interactions with aqueous CO2, a neutral species, should be

2

2

(6)

CaCO3(s) ↔ Ca 2 + + CO32 − ,

K gw,CO2PCO2γCO (g) γCO (aq)

3

m HCO−3 γHCO− 3

where ΔmCa2+, ΔmHCO3−, and ΔmCO2(aq) are the changes in molal concentrations of Ca2+, HCO3−, and CO2(aq) during the dissolution process, respectively. The initial CO2 concentration is calculated for the feed solution in equilibrium with 97% of CO2 gas at room temperature using Henry’s law. Data Processing and Model Calculation. According to Duan and Li,14 as many as 10 possible processes and 11 possible species are involved in the calcite dissolution process at the presence of gas phase CO2. For our system, however, because the feed solution contained only dissolved CO2, which would be partially consumed in the subsequent calcite dissolution process, a separate gas phase did not exist. Therefore, the equilibrium between gas phase and aqueous CO2 needs to be considered only for calculation of the initial CO2 concentration of the feed solution at room temperature and one atmosphere as a function of only solution composition. According to Henry’s law, mCO2(aq) =

K2 =

a H+mCO32−γCO2−

(4)

where Kgw,CO2 is the Henry’s constant of CO2 with a value of 0.0336 m/bar at 25 °C and 1 atm. PCO2 is the partial pressure of CO2 of 0.97 atm. γCO2(g) and γCO2(aq) are the activity coefficients of 2441

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temperatures ranging from 0 to 250 °C and pressures from 34.5 to 1448 bar, all at 0.1 m NaCl. Also listed in the table are the SI values calculated using the measured experimental data and three sets of stability constants. The closest match to the experimental data is attained using K1 and K2 from Li and Duan8 and Ksp,CaCO3 from Kharaka;18 the SI values are within plus or minus 0.1 units for most conditions. The deviation with Nordstrom’s recommended values, on the contrary, was as high as 0.82 logarithm units. The accuracy of the combination of constants that included K1 and K2 from Li and Duan,8 and Ksp,CaCO3 from Kharaka18 was confirmed by measurement of calcite solubility in 4 m NaCl (Table 2). The calculated SI values are within plus or minus 0.1 unit for all conditions tested, whereas Nordstrom’s recommended values generated errors as great as two logarithms units at 250 °C and 1448 bar. Another implication of this close agreement between model prediction and experimental measurement at ionic strength as high as 4 m, on the other hand, is that there is negligible inaccuracy in the model calculation of activity coefficients as well, suggesting that the current set of virial coefficients for the Pitzer equations for activity coefficients of all species involved in this system are valid at the full ranges of temperature and pressure explored. Li and Duan8 (2007) evaluated the activity coefficients of all species using Pitzer equation for the H2O−CO2−NaCl system, and a list of the corresponding virial coefficients can be found in their paper. For our system, with the saturation of CO2, the concentrations of both OH− and CO32− in the solution are extremely low, so any interaction that involves these species does not need to be taken into account. The concentrations of Ca2+, HCO3−, and CO2(aq) are all on the magnitude of 0.01 m, meaning that any interaction that involves two of these species would be negligible compared to those associated with Na+ or Cl−. A list of virial coefficients used in this study is summarized in Table 3, together with the corresponding sources. Those not listed are set to zero because the corresponding interactions are not important in this study. Application to Mixed Electrolytes. Challenges associated with applying Pitzer model to concentrated solutions with mixed electrolytes at high temperature and pressure, which is commonly encountered in deep water production, result from the need to account for not only various interactions among different species, but also possible formation of ion pairs between solutes exhibiting strong association. Our model employs Pitzer approach by using a specific coefficient β(2) to account for the association between divalent cations and anions (Ca2+ and SO42−, for instance), although it has been suggested by other authors that an explicit ion pair term (for instance, CaSO40) should be included in the model.28 A synthetic brine was prepared with the composition listed in Table 4 that represented the maximum concentrations of typical constituents (95% CI) encountered in the oil and gas field according to the USGS database (USGS 2002)29 as the feed solution for calcite dissolution tests. Cations such as Ba2+ and Sr2+ were not included in the feed to eliminate complexion due to precipitation of Barite and celestite. Model deviation from experimental data was observed at all conditions, especially at lower temperatures (0, 25, and 100 °C), as indicated by the SI values calculated based on experimental data (Table 5). The fact that the calculated SI values appear negative for these conditions suggests that the model is overpredicting the interaction (including ion pair formation) that might have contributed to the overall nonideality. It is well-known that both HCO3− and

included. As a result, the activity coefficients in eq 8 can be calculated using the following relationships: 2 F + m −(2B ln γCa 2+ = z Ca 2+ Cl CaCl + ZCCaCl)

+ m HCO−3 (2BCaHCO3 + ZCCaHCO3) + m Na+(2ΦNaCa + mCl−ΨCaNaCl) + |z Ca 2+|(m Na+mCl−C NaCl + m Na+mHCO−3 C NaHCO3 + mCa 2+mCl−CCaCl) + mCO2(aq)(2λCO2Ca) + mCO2(aq)mCl−ξCO2CaCl

(9)

2 −F + m ln γHCO− = z HCO Na +(2B NaHCO3 + ZC NaHCO3) 3 3

+ mCa2+(2BCaHCO3 + ZCCaHCO3) + mCl−(2ΦClHCO−3 + m Na+ ΨNaHCO3Cl) + |z HCO−3 |(m Na+mCl−C NaCl + m Na+mHCO−3 × C NaHCO3 + mCa 2+mCl−CCaCl) + mCO2(aq)(2λCO2HCO3) + mCO2(aq)m Na+ ξCO2NaHCO3

(10)

ln γCO (aq) = m Na+(2λCO2Na) + mCa 2+(2λCO2Ca) 2

+ mCl−(2λCO2Cl) + m HCO−3 (2λCO2HCO−3 ) + m Na+mCl−(ζCO2NaCl) + m Na+mHCO−3 (ζCO2NaHCO3) + mCa 2+mCl−(ζCO2CaCl) + mCa 2+m HCO−3 (ζCO2CaHCO3)

(11)

where γ is the activity coefficient of aqueous species and m is the concentration in molality. B and C are coefficients that denote the interactions between two oppositely charged ions. Φ stands for the interaction between two like-charged ions. λ denotes the binary interaction between neutral species and ions. Ψ represents the ternary interactions among three ions, while ξ and ζ are for those among one neutral species, one cation and one anion. Z is the total molality of charges in the system, and z denotes the charge of an individual species.

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RESULTS AND DISCUSSION Calcite Solubility in the NaCl−CO2−H2O System. Significant difference exists between values reported by different sources for all three stability constants related to our system, K1, K2, and Ksp,CaCO3 (Figures 1−3), especially at extreme conditions of high temperature and high pressure. Calcite dissolution tests with 0.1 m NaCl solution were conducted to examine the constants from different sources and select appropriate values for model construction. The activity coefficients of various aqueous species could be determined with confidence at such a low ionic strength, so that any deviation between model calculation and experimental data can be attributed to inaccuracies in stability constants. Table 1 shows the measured Ca2+ concentrations as well as the calculated concentrations of HCO3− and CO2(aq) in the effluent from the column at different testing conditions with 2442

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Figure 2. Dissociation constant of carbonic acid (K1) at different temperatures and pressures from different sources.

Figure 3. Dissociation constant of bicarbonate ion (K2) at different temperatures and pressures from different sources.

SO42− exhibit strong interactions with Ca2+ in aqueous solutions, and therefore, the corresponding virial coefficients for Pitzer equations are likely the major contributors to the error in modeling.

Two other feed solutions were then prepared to investigate the effects of the two species separately, one with 3000 mg/L of HCO3− and no SO42− and the other with 4500 mg/L of SO42− and no HCO3−, both having the same NaCl concentration as the 2443

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Table 1. SI Calculated Using Experimentally Measured Data at 0.1 m NaCl and Stability Constants from Different Sources concn. in the effluent (mmol/kg-H2O)

SI calcd using stability constant group

temp. (°C)

pressure (bar)

Ca2+

HCO3−

CO2(aq)

a

b

c

0 0 0 0 25 25 25 25 100 100 100 100 200 200 200 200 250 250 250 250 Mean SI Std. Dev.

34.5 483 965 1448 34.5 483 965 1448 34.5 483 965 1448 34.5 483 965 1448 69 483 965 1448

12.85 17.61 20.84 27.47 12.22 14.81 19.29 24.68 5.82 7.40 9.55 11.35 1.32 1.98 2.81 3.71 0.65 1.07 1.45 2.34

25.70 35.22 41.67 54.95 24.44 29.62 38.59 49.36 11.64 14.80 19.11 22.69 2.63 3.96 5.61 7.42 1.30 2.14 2.91 4.68

30.63 25.87 22.64 16.01 31.26 28.67 24.19 18.80 32.12 30.52 28.34 26.53 32.27 31.60 30.76 29.85 32.27 31.84 31.45 30.55

0.05 −0.03 −0.14 −0.27 0.12 −0.10 −0.24 −0.37 0.05 −0.19 −0.45 −0.82 0.03 −0.01 −0.20 −0.49 0.37 0.39 0.15 0.11 −0.102 0.292

0.05 0.05 −0.10 0.06 0.12 −0.03 0.00 0.03 0.06 −0.03 −0.05 −0.19 0.04 0.13 0.19 0.16 0.35 0.27 0.22 0.38 0.085 0.145

0.05 0.07 −0.06 0.04 0.13 −0.02 0.00 0.02 0.09 0.00 −0.04 −0.18 0.05 0.10 0.13 0.09 0.11 0.11 0.02 0.17 0.044 0.081

a

K1, K2, and Ksp, CaCO3 from Nordstrom’s recommended data.15 bK1 and K2 from Kaasa,16 and Ksp, CaCO3 from Kharaka.18 cK1 and K2 from Li and Duan,8 and Ksp, CaCO3 from Kharaka.18

Table 2. SI Calculated Using Experimentally Measured Data at 4 m NaCl and Stability Constants from Different Sources concn. in the effluent (mmol/kg-H2O)

SI calcd using stability constant group

temp. (°C)

pressure (bar)

Ca2+

HCO3−

CO2(aq)

a

b

c

0 0 0 0 25 25 25 25 100 100 100 100 200 200 200 200 250 250 250 250 mean SI std. dev.

34.5 483 965 1448 34.5 483 965 1448 34.5 483 965 1448 34.5 483 965 1448 69 483 965 1448

17.05 22.70 27.22 31.12 13.26 17.10 19.44 23.59 7.90 9.88 12.89 16.39 4.31 5.36 6.79 7.37 3.30 3.94 5.16 5.82

34.10 45.39 54.45 62.25 26.52 34.21 38.87 47.18 15.81 19.75 25.78 32.78 8.61 10.73 13.58 14.75 6.60 7.87 10.31 11.64

18.43 12.78 8.25 4.35 17.90 14.06 11.72 7.57 18.59 16.62 13.61 10.11 18.17 17.11 15.68 15.10 18.54 17.90 16.68 16.02

−0.11 −0.06 −0.17 −0.25 0.02 −0.02 −0.29 −0.37 −0.10 −0.26 −0.38 −0.52 −0.02 −0.10 −0.31 −0.91 0.11 0.13 −0.38 −1.99 −0.299 0.464

−0.13 −0.03 0.01 0.06 0.02 0.06 −0.05 0.02 −0.09 −0.10 0.01 0.11 −0.02 0.05 0.15 −0.02 −0.09 0.10 0.20 0.15 0.021 0.091

−0.12 −0.02 0.01 0.07 0.03 0.07 −0.05 0.02 −0.06 −0.07 0.03 0.11 0.00 0.03 0.09 −0.08 0.09 −0.03 0.11 −0.04 0.009 0.067

a

K1, K2, and Ksp,CaCO3 from Nordstrom’s recommended data.15 bK1 and K2 from Kaasa,16 and Ksp,CaCO3 from Kharaka.18 cK1 and K2 from Li and Duan,8 and Ksp,CaCO3 from Kharaka.18

synthetic brine. Model prediction agrees well with measured data at the presence of HCO3− at select conditions tested (Table 6), whereas SO42− results in the same level of deviation as it causes for the synthetic brine system that contains similar SO42−

concentration, suggesting that the virial coefficients corresponding to interactions involving HCO3− might be valid and the majority of the errors in modeling the synthetic system might be associated with coefficients for SO42− related interactions. 2444

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Table 3. Calcite-Related Virial Coefficients for Pitzer Equations for Activity Coefficients virial coefficients

source

(1) φ β(0) CaCl, βCaCl, CCaCl θHCa (0) (0) βNaHCO3, βNaHCO3, CφNaHCO3, λCO2Na, λCO2Cl

Christov and Moller30(2004) He and Morse26 (1993)

(1) φ β(0) NaCl, βNaCl, CNaCl θNaCa, θClHCO3, ψHCaCl, ψNaClHCO3

Pitzer et al.20 (1983) Harvie et al.25 (1984)

θHNa, ψNaCaCl (1) (2) β(0) CaSO4, βCaSO4, βCaSO4

He and Morse26 (1993) Kaasa16 (1998)

Table 6. SI Values Calculated for Calcite Dissolution in Feed Solution with High Concentrations of HCO3− and SO42− at Select Temperatures and Pressures composition of the feed solution with high HCO3−

concn. (mg/L)

concn. (mol/L)

Na HCO3 B Br SO4 Si Cl TDS

102000 3000 150 3500 4500 30 150000 ∼262000

4.44 0.0492 0.0136 0.0438 0.0469 0.001 4.23 −

concn. (mg/L)

concn. (mol/L)

Na HCO3 Cl TDS

103000 3000 157000 263000 SI calculations

4.48 0.0492 4.43 −

concn. in the effluent (mmol/kg-H2O)

Table 4. Composition of the Synthetic Brine for Calcite Dissolution Tests constituents total

constituents total

temp. (°C) 100 100

The effect of SO42− on model calculation was further examined by dissolution tests at various SO42− concentrations. The SI values calculated using experimentally measured solubility, the selected set of stability constants and current set of Pitzer coefficients are shown in Figure 4 for different temperatures, pressures, and SO42− concentrations. At temperatures of 25 and 100 °C, calculated SI values are negative at most conditions, consistent with the results with the synthetic brine. The deviation of SI values from zero (equilibrium) generally increases with increasing SO42− concentration when temperature and pressure

pressure (bar)

Ca2+

HCO3−

CO2(aq)

483 1.24 56.06 15.17 965 2.12 57.82 14.11 composition of the feed solution with high SO42−

SI 0.04 0

constituents total

concn. (mg/L)

concn. (mol/L)

Na SO4 Cl TDS

104000 4500 157000 264000 SI calculations

4.51 0.0468 4.43 −

concn. in the effluent (mmol/kg-H2O) temp. (°C)

pressure (bar)

Ca2+

HCO3−

CO2(aq)

SI

100 100

483 965

7.27 8.08

14.54 16.16

6.96 6.15

−0.11 −0.23

are fixed and therefore indicates there is a greater impact on the modeling at higher SO42− concentration. The SI values also appear more negative at higher pressure at each certain

Table 5. SI Values Calculated for Calcite Dissolution in the Synthetic Brine with Composition Listed in Table 4a concn. in the effluent (mmol/kg-H2O)

a

temp. (°C)

pressure (bar)

Ca2+

HCO3−

CO2(aq)

SI w/o β(2) CaSO4 adjustment

SI w/ β(2) CaSO4 adjustment

0 0 0 0 25 25 25 25 100 100 100 100 200 200 200 200 250 250 250 250 mean SI std. dev.

34.5 483 965 1448 34.5 483 965 1448 34.5 483 965 1448 34.5 483 965 1448 69 483 965 1448

4.07 6.16 8.43 11.33 1.44 2.91 4.96 7.39 0.66 0.95 1.51 2.67 0.17 0.24 0.38 0.58 0.10 0.16 0.25 0.40

61.72 65.90 70.44 76.23 56.47 59.39 63.50 68.36 54.90 55.48 56.60 58.93 53.93 54.06 54.35 54.73 53.77 53.89 54.08 54.39

11.67 9.58 7.31 4.42 14.30 12.84 10.78 8.35 15.08 14.79 14.23 13.07 15.57 15.50 15.36 15.17 15.65 15.59 15.49 15.34

0.02 −0.14 −0.21 −0.20 −0.11 −0.11 −0.11 −0.13 0.05 −0.12 −0.21 −0.22 −0.09 −0.11 −0.13 −0.21 −0.11 −0.09 −0.03 −0.09 −0.117 0.073

0.00 −0.02 −0.04 −0.01 −0.08 −0.01 0.03 0.01 0.07 −0.05 −0.10 −0.08 0.01 −0.08 −0.07 −0.09 −0.10 −0.06 −0.01 −0.05 −0.037 0.048

Values are compared between with and without adjustment of the Pitzer coefficient β(2) CaSO4. 2445

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pressure (P, bar) using a format similar to that used in our previous study to describe the temperature and pressure dependence of various Pitzer coefficients (eq 12). z1 to z12 are listed in Table 7. SI values calculated with the adjusted β(2) CaSO4 are within ±0.1 for almost all conditions tested (Figure 5). Table 7. Values of z1 to z12 in Equation 12 coefficients in eq 12

value

z1 z2 z3 z4 z5 z6 z7 z8 z9 z10 z11 z12

3.03897298913545 × 103 −5.31302425888199 −4.85081374641688 × 105 52.1518281108391 987.226233606002 0.21053258199198 −3.03361894746869 × 104 −166.116005727064 −1.26988618990119 −2.78269558839499 × 10−4 39.2305939815086 0.214212784027518

(2) βCaSo = z1 + z 2T + z 3/T + z4 ln T 4

+ (z5 + z6T + z 7/T + z8 ln T )P + (z 9 + z10T + z11/T + z12 ln T )P 2

(12)

While the interaction between Ca2+ and SO42− (including the formation of CaSO40 ion pair) might be a major contributor to the deviation in model calculation, the adjustment to the β(2) CaSO4 term represents only one possible way to correct the model. According to eq 8, the activity coefficients of at least three species, Ca2+, HCO3−, and CO2 are involved in the calculation of SI value of CaCO3. Because of the complexity of the Pitzer equations that involves numerous virial coefficients for specific ion interactions, a thorough evaluation of the impact of SO42− on the calculation of each activity coefficient would require systematic testing and measurement in independent systems that can separate one species from the others. For instance, the Ca2+−SO42− interaction, including CaSO40 formation, can be examined more efficiently through measurement of the solubility of CaSO4 at full ranges of temperature and pressure, as well as the presence of different concentrations of Ca2+ and SO42−. These tests are currently planned and will be reported as a separate study on the dissolution of gypsum/hemihydrate/anhydrate at high temperature, pressure, and salt concentration. On the other hand, it has been reported by several authors30−32 that the presence of SO42− retards the kinetics of calcite dissolution, especially at low temperatures. The kinetics of calcite dissolution has been examined as described in the Materials and Methods section, and obvious retarding effects were not observed in the range of SO42− concentration and column detention time used in our testing. However, while it was not the focus of this study to examine the dissolution kinetics, it is worthwhile to conduct a systematic investigation of the kinetics at different temperatures, levels of SO42−, and other constituents, because in addition to equilibrium, kinetics is an equally, if not more, important aspect of the dissolution process. Understanding kinetics, moreover, will also support the validity of the solubility data obtained in this study.

Figure 4. Saturation indices of CaCO3 at different temperatures, pressures, and the presence of different concentrations of SO42−.

temperature and SO42− concentration, suggesting a need to reevaluate the pressure dependence of Pitzer coefficients relevant to interactions between SO42− and other species present in the solution at the low temperature range. The deviations in SI calculations at temperatures of 200 and 250 °C are lower compared to when the temperature is lower; the calculations are within plus or minus 0.1 at most conditions, although values as negative as −0.2 are observed at the pressure of 1448 bar. These deviations can mostly be eliminated by adjusting only β(2) CaSO4, the Pitzer coefficient corresponding to the association between Ca2+ and SO42−, as a function of temperature (T, K) and 2446

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unconventional sources such as ultradeep water. While the solubility of calcite has been measured in a few studies at elevated temperature and pressure, primarily in pure water or at the presence of only NaCl, the effect of high concentrations of mixed electrolytes has rarely been reported. The measurements conducted in this study therefore expands the current database to conditions that combines high temperature, pressure, and complicated solution composition with the flexibility to adapt to other types of mineral and other modes of high temperature and pressure testing. On the other hand, there also exists substantial deviation between predictions by different models due to the inconsistency between model parameters from different sources. We are confident, nevertheless, that our current model that incorporates the selected set of stability constants, including K1 and K2 from Duan and Li as well as Ksp,CaCO3 from Kharaka provide reliable calculation that closely matches the experimental measurements in the NaCl system. One of the major limitations of applying the current model to complicated solutions with high concentrations of mixed salts results from the presence of SO42−, especially at low temperature and high pressure, suggesting a need to reevaluate the pressure dependence of SO42− related Pitzer coefficients. The deviation between model calculation and experimental measurement can mostly be eliminated by adjusting Pitzer coefficients for the interaction between Ca2+ and SO42−. Due the complexity of the CaCO3 system where numerous key species are involved in determining the solubility, however, a thorough re-evaluation process would require additional testing in independent systems that can separate the effect of these species from each other. In the long term, we are planning to expand the current testing to additional types of minerals (CaSO4, for instance, with multiple phases), modes of testing (precipitation kinetics or scale inhibition), and the range of temperature, pressure, and brine composition to accommodate the growing demands from the oil and gas industry.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: 713-348-2149. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by Brine Chemistry Consortium companies of Rice University, including Baker Hughes, BP, Champion Technologies, Chevron, Clariant, ConocoPhillips, Dow, Halliburton, Hess, Kemira, Kinder Morgan, Marathon Oil, Multi-Chem, Nalco, Occidental, Petrobras, Saudia Aramco, Schlumberger, Shell, Shengli Engineering & Consulting Co., Statoil, Southwestern Energy, and Total, China−U.S. Center for Environmental Remediation and Sustainable Development.

Figure 5. Saturation indices of CaCO3 at different temperatures, pressures, and the presence of different concentrations of SO42− with the adjustment of β(2) CaSO4.

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CONCLUSION This study continues our exploration of the dissolution of minerals at ultrahigh temperature, pressure, and ionic strength in the presence of mixed electrolytes. With the previous success of the experimental measurement of Barite solubility, we are confident that our apparatus offers a reliable and efficient method for conducting studies on mineral dissolution under extreme conditions encountered in the oil and gas production from

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