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Calcite and barite solubility measurements in mixed electrolyte solutions and the development of a comprehensive model for water-mineral-gas equilibrium of the Na-K-Mg-Ca-Ba-Sr-Cl-SO4CO3-HCO3-CO2(aq)-H2O system at up to 250 oC and 1,500 bars Zhaoyi Dai, Amy T. Kan, Wei Shi, Fei Yan, Fangfu Zhang, Narayan Bhandari, Gedeng Ruan, Zhang Zhang, Ya Liu, Hamad A. Alsaiari, Alex Yi-Tsung Lu, Guannan Deng, and Mason B. Tomson Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 23 May 2017 Downloaded from http://pubs.acs.org on May 28, 2017

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Industrial & Engineering Chemistry Research

Calcite and Barite Solubility Measurements in Mixed Electrolyte Solutions and The Development of A Comprehensive Model for Water-Mineral-Gas Equilibrium of the Na-K-Mg-Ca-Ba-Sr-Cl-SO4-CO3-HCO3-CO2(Aq)-H2O System at Up To 250 OC and 1,500 Bars Zhaoyi Daia*, Amy T. Kana1, Wei Shia, Fei Yana, Fangfu Zhanga, Narayan Bhandaria, Gedeng Ruana, Zhang Zhanga, Ya Liua, Hamad A. Alsaiaria, Yi-Tsung Lua, Guannan Denga, Mason B. Tomsona a

Department of Civil and Environmental Engineering, Rice University, 6100 Main Street, Houston, TX 77005, US * Corresponding Author contact information: E-mail address: [email protected] Tel: (713)348-2149 Abstract Calcite and barite are two of the most common scale minerals that occur in various geochemical and industrial processes. Their solubility predictions at extreme conditions (e.g., up to 250 oC and 1,500 bars) in the presence of mixed electrolytes are hindered by the lacks of experimental data and thermodynamic model. In this study, calcite solubility in the presence of high Na2SO4 (i.e., 0.0407 m Na2SO4) and barite solubility in a synthetic brine at up to 250 oC and 1,500 bars were measured using our high temperature high pressure geothermal apparatus. Using this set of experimental data and other thermodynamic data from a thorough literature review, a comprehensive thermodynamic model was developed based on the Pitzer theory. In order to generate a set of Pitzer theory virial coefficients with reliable temperature and pressure dependencies which are applicable to a typical water system (i.e., Na-K-Mg-Ca-Ba-Sr-Cl-SO4-CO3-HCO3-CO2H2O) that may occur in geochemical and industrial processes, we simultaneously fitted all available mineral solubility, CO2 solubility, as well as solution density. With this model, calcite and barite solubilities can be accurately predicted under such extreme conditions in the presence of mixed electrolytes. Furthermore, the 95% confidence intervals of the estimation errors for solution density predictions are within 4×10-4 g/cm3. The relative errors of CO2 solubility prediction are within 0.75%. The estimation errors of the saturation index mean values for gypsum, anhydrite, and celestite are within ± 0.1, and that for halite is within ± 0.01, most of which are within experimental uncertainties. 1

Contributed equally to this work with the first author

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1. Introduction Mineral solubility is an important thermodynamic property of water-mineral interactions. Such interactions are important in various geochemical and industrial processes 1, for example, fluid–rock interactions 2, secondary porosity in oil reservoir 3, scale and corrosion control in oil and gas production 4-6, deep sea oceanography 7-9, geologic carbon dioxide capture and sequestration 10-12, water cooling in geothermal energy production 13-15, and rock weathering and diagenesis 16, 17, to mention a few. Calcite and barite are two of the most common minerals that occur in the geochemical and industrial processes. Though having been heavily studied, they are continuing to be problematic due to unanticipated scale formations, especially when more extreme conditions are encountered in recent years 18, 19. For example, in oil and gas industry the expansion of offshore deep water oil and gas production leads to more occurrences of high temperature (150 to 250 oC), high pressure (1,000 to 1,500 bar), and high concentration of total dissolved solids (TDS, more than 300,000 mg/L) in the presence of mixed electrolytes 20, 21 . Therefore, accurate thermodynamic modeling based on solubility measurements are needed under such extreme conditions in the presence of mixed electrolytes. Mineral solubility measurement at both high temperature (up to about 250 oC) and high pressure (up to about 1,500 bars) is difficult, and few studies have made efforts in this measurement 22-25. However, these studies have usually failed to include mixed electrolytes in their measurements under such extreme conditions. For example, Lyachchenko and Churagulov (1981) have measured barite solubility at up to 250 oC and 1,000 bars only in pure water. Using a hydrothermal solution equipment (i.e., HSE) designed by Dickson et al. (1963), Blount (1977) has measured barite solubility at up to 253 oC and 1,403 bars with up to 6 m NaCl, but not in the presence of mixed electrolytes that might occur in the fields. Berendsen (1971) has also used HSE to measure calcite solubility at up to 200 oC and 1,000 bars under different CO2 partial pressure, but only in pure water. In the past few years, the authors have designed a novel apparatus which achieves mineral-water equilibrium when solution flows through the compacted mineral solids 26. Using this novel apparatus, the authors have measured barite solubility in NaCl solutions from 0 to 250 oC and up to 1,517 bars 26, and have extended calcite solubility measurements at up to 250 oC and 1,448 bars with up to 5.06 m NaCl and in presence of mixed electrolytes 27. In this study, more experiments were done to measure barite solubility in mixed electrolytes and calcite solubility in the presence of high SO42- ions, both under the extreme conditions mentioned above. In the past century, the Pitzer theory has become one of the most popular thermodynamic models in geochemical and industrial applications 2, 9, 28-41, and has been widely adopted 2 ACS Paragon Plus Environment

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by different geochemical software, such as Geochemist’s Workbench, PHRQPITZ 42, PHREEQC 43, ScaleSoftPitzer 19, 29, 44. Using virial coefficients which represent the short range interactions between species (i.e., ions or neutral compounds), the Pitzer theory is capable of predicting the thermodynamic properties of aqueous systems in the presence of mixed electrolytes over wide ranges of temperature, pressure and ionic strength 45-47. For example, Weare and his group members have derived the virial coefficients for related species interactions in H-Na-K-Ca-OH-Cl-HSO4-SO4-H2O system to predict the dissolved species activity coefficients and mineral solubilities up to 250 oC (usually called H-M-W model) 28, 30, 32, 48. Duan and his co-authors fitted the virial coefficients related to carbonic acid species (i.e., CO2,aq, HCO3-, CO32-) to predict CO2 partitioning in the gas and aqueous phase and calcite solubilities 2, 38, 49. In principle, these virial coefficients for different species interactions derived by various authors should be compatible of predicting the thermodynamic properties of all related species. However, the published virial coefficients from various sources usually have their specific applicable ranges of temperature or pressure, and are sometimes derived based on different functional forms and assumptions. Sufficient evidences suggest that these virial coefficients do not work as expected 50 and will be discussed below. Firstly, the limited pressure ranges of previously derived virial coefficients have hedged the applicability of the models at high pressures. For example, PHREEQC adopted the Na-SO4 virial coefficient derived by Holmes et al. (1986) without pressure dependence due to the lack of volumetric data 43, 51. At higher pressures, it will result in error in solution density prediction in the presence of high Na+ and high SO42- ions, and in solubility prediction for minerals composed of Na+ or SO42- ions. The Ca-Cl ion interactions fitted in the H-M-W model is valid up to 250 oC, but it has no pressure dependence beyond the vapor pressure of water and thus cannot be applied to calculate Ca2+ or Cl- ion activity coefficients at higher pressures nor can it be applied for solution density predictions 30, 32. In addition, Shi et al. (2013) found that the adoption of the virial coefficients without pressure dependence predicted the barite solubility 27% lower than measured value at 1,103 bars, 200 oC, in 6 m NaCl solutions 26. Therefore, it is necessary to extend the pressure dependence of the related virial coefficients by using more experimental data at higher pressures. Moreover, since the solution density is related to the first order pressure derivatives of the Gibbs free energy, this study also included solution density in the database to extend the applicable pressure ranges of various related virial coefficients. Secondly, many virial coefficients were derived in the models with different and incompatible functional forms. For example, Archer (1992) expanded the ternary ion interaction C term with two more ionic strength dependent terms for cation-anion 3 ACS Paragon Plus Environment


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interactions to describe NaCl-H2O system over wide temperature and pressure ranges 37. Wang et al. (1998) added a cation-anion interactions term (denoted as D) to fit the properties of MgCl2 at from 250 to 600 K and up to 1,000 bars 36. Such modifications make Pitzer theory numerically more complex, subjective, and inconsistent with other models 34, 50, 52. In the H-M-W model, the calcium sulfate ion pair was explicitly treated with ion pair association constants, while some models implicitly treated 2-2 ion pair as a strong ion interaction using β(2) term in the Pitzer theory 46, 53. Duan and Li (2008) treated Ca-HCO3- ion pair as an individual species and assigned virial coefficients to represent its interaction with other species 38. Out of the common interests of geochemists and industrial engineers, calcite solubility in the presence of high Na2SO4 (i.e., 0.0407 m Na2SO4) and barite solubility in synthetic produced water at up to 250 oC and 1,500 bars were measured. Using this set of experimental data and other thermodynamic data from a thorough literature review, a comprehensive thermodynamic model was developed under the Pitzer theory formality through a simultaneous data regression. Thus, this model is able to predict the thermodynamic properties of a typical aqueous system (Na-K-Mg-Ca-Ba-Sr-Cl-SO4CO3-HCO3-CO2-H2O) that may occur in geochemical and industrial processes, for example, water produced during oil and gas and geothermal productions. In additional to accurately predict the scaling tendency of calcite and barite in mixed electrolyte solutions, this model can also predict the scaling tendencies of other minerals that may occur (i.e., halite, gypsum, anhydrite, and celestite), solubility of CO2, and solution density over wide ranges of temperature and pressure. The accuracy of density prediction reflects the reliability of the pressure dependence of related virial coefficients. The developed model has been incorporated into ScaleSoftPitzer 2017, an EXCEL based software package for aqueous solution thermodynamic property predictions, which has been widely adopted for geochemical applications and scale prediction and control in the oil and gas industry 54 . ScaleSoftPitzer 2017 is accessible to the members of Brine Chemistry Consortium and to those working with them in the website of https://bcc.rice.edu/. 2. Model descriptions 2.1. The Pitzer theory The reactions related to calcite and barite precipitation or dissolution in the aqueous system are listed below:  → CO2, aq , K H = CO2, g ← 

aCO2 ,aq f CO2 ,g


,

(1)

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 → H + + HCO3− , K1 = CO2,aq + H 2 O ← 

 → H + + CO32− , K 2 = HCO3− ← 

aH + aHCO− 3

aCO2,aq aH 2O

aH + aCO2− 3

,

,

aHCO−

(2)

(3)

3

 → Ca + CO3 , K sp ,calcite = CaCO3 ←  2+

2−

aCa2+ aCO2− 3

aCaCO3

 → Ba 2+ + SO42− , K sp ,barite = BaSO4 ← 

, and

aBa2+ aSO2− 4

aBaSO4

.

(4)

(5)

where a[] represents the activity of each aqueous species; fCO2,g is the fugacity of CO2 in the gas phase; Ksp is the solubility product of the mineral. The activities of the solids (e.g., calcite and barite) are assumed to be unity. The impacts of the occurrence of solid solutions in mixed electrolyte solutions need more future studies. The saturation index (SI) of a mineral (e.g., M m X x ) is the logarithm of the ratio of ion activity product over the solubility product, and represents the saturation status of the mineral considered:  am a x SI = log10  M X  K  sp

  mMm γ Mm mXx γ Xx = log  10   K sp  

  , 

(6)

where m[], and γ[] represent the molality, and activity coefficient of corresponding species, respectively. SI value is 0 at equilibrium, positive when the solution is supersaturated, and vice versa. Equation (6) shows that SI is related to the solubility products of minerals, the molality of aqueous ions, and the activity coefficients of each species. It deserves notice that the presence of mixed electrolytes can impact the activity coefficients of aqueous species, and the partitioning of CO2 can impact the molality of CO32- ion. The temperature and pressure dependencies of the solubility products of calcite and barite were fitted from the data listed in SOLMINEQ 88. 55, which were originally derived from the HKF (Helgeson-Kirkham-Flowers) theory 56-58. In a series of IUPAC-NIST papers, De Visscher and his co-authors reviewed the previous studies on earth metal carbonates solubilities and published the temperature and pressure dependences for K1, K2, and the temperature dependence of KH for CO2 59. This study adopted these fitted equilibrium constants for carbonic system and the pressure dependence of KH derived by Kaasa (1998) 41 .



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Based on the equation of excess Gibbs free energy, the activity coefficient of different species (γ), osmotic coefficient of water (ϕ), and water activity ( aH 2O ) can be calculated with its differentiation in terms of mole amount (n) or weight of water (ww), respectively: −1

   ∂ (G ex / RT )  , (φ − 1) = −  ∑ mi    ∂ww  i   T , P , ni

(7)

  aH 2O = exp  −φ M w ∑ mi  , i  

(8)

 ∂ (G ex / RT )  . ln γ i =   ∂ n i  T , P , ww , n j ≠i

(9)

The solution density is related to the volume of the solution which can be calculated as the sum of the volume of pure water (Vw), the total standard partial molar volume of the solute (

∑ mV i

0 i

), and the excess volume (Vex) due to the non-ideal interactions:

solute

Vsoln = Vw +

∑ mV i

0 i

+ V ex .

(10)

solute

Vw can be calculated by water density using the equations in the International steam 0

tables 60. V i can be fitted from the extrapolation of solution densities to infinite dilution. Vex can be calculated as the differentiation of excess Gibbs free energy in terms of pressure:

 ∂ ( G ex / RT )   . V / RT =    ∂P  ni ,T ex

(11)

Equations (10) and (11) illustrate the relationship between the solution density and the pressure dependence of the activity coefficients. In order to generate reliable pressure dependence for mineral solubility prediction, it is valuable to include the density of aqueous solutions in model regressions. The excess Gibbs free energy of the system can be represented by Pitzer theory as below 2, 9, 28, 32-34 :


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Nc Na    Nc  G ex 4 ⋅ I ⋅ Aφ =− ln (1 + b ⋅ I 1/2 ) + 2∑∑ mc ma  Bca +  ∑ mc zc  Cca  RT ⋅ ww b c =1 a =1  c    N c −1 Nc

Na Nc   N a −1 Na   + ∑ ∑ mc mc'  2Φ cc ' + ∑ maψ cc'a  + ∑ ∑ ma ma '  2Φ aa' + ∑ mcψ aa 'c  (12) c =1 c'= c +1 a =1 c =1   a =1 a '=a +1   Nn

Nc

N n Na

N n Nc

Na

n =1 a =1

n =1 c =1 a =1

+ 2∑∑ mn mc λnc + 2∑∑ mn ma λna + ∑∑∑ mn mc maξ nca n =1 c =1

1/2

1  2π Av ρ w  A =  3  1000  φ

 e2   DkT   

3/ 2

(13)

Bca = β ca(0) + β ca(1) g(α ca I ) + β ca(2) g(12 I )

Cca =

(14)

Ccaφ

(15)

2 | zc z a |

where ww is the weight of water; m is the molality of species in mol/kg H2O; R is the gas constant; k is the Boltzmann constant; T is temperature in Kelvin; ρw is the water density calculated based on the industrial formulation IAPWS-IF97 in the International steam tables 60; D is the dielectric constant of water and its equation was proposed by Bradley and Pitzer (1979) 61; e is the unit electron charge; Av is the Avogadro constant; z denotes the charge of an individual species; I is the ionic strength; b value is 1.2 (kg/mol)1/2; Aφ φ is the Debye-Huckel limiting slope, and the Aφ and ∂A / ∂P values calculated by this study are within ±0.6% relative deviations of those listed in Pitzer et al. (1984); B, Φ, λ

terms represent binary interactions, and C , ξ terms represent ternary interactions; c, a, n in the subscripts represent cation, anion, and neutral species, respectively; function g(x) = 1/2 2 ⋅ [1 − (1 + x) e− x ] / x2 is the ionic strength dependent function; α equals 2.0 (kg/mol) for

1-1, 1-2, 2-1 ion interactions, 1.4 (kg/mol)1/2 for 2-2 ion interactions 2.0 − 0.00181⋅ (T (K ) − 298.15)

for

Mg/Ca/Ba/Sr-Cl

interactions

46

, and α equals to

with

temperature

dependence suggested by Holmes and his co-authors 34, 35. In Equation (12), the virial coefficients are represented by semi-empirical functions of temperature and pressure. Error! Reference source not found. lists the virial coefficients and the standard partial molar volumes that were adopted in this study. The virial coefficients or the standard partial molar volume were adopted if they were fitted based on experimental thermodynamic data of more categories (e.g., freezing point, vapor pressure, dilution enthalpy, heat capacity, solubility, solution density) for simple electrolyte solutions 33-35, 38, 59, 62-64. For example, many researchers have fitted Ca-Cl 7 ACS Paragon Plus Environment


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virial coefficients in the past decades using different experimental data 30, 32, 65-73. Phutela and Pitzer (1983) included Ca-Cl ion interactions in Pitzer theory, but only based on data up to 200 oC and at water vapor pressure 65. The H-M-W model didn’t include pressure dependence for Ca-Cl interactions either 28, 30, 32, 48. Holmes et al. (1994) built a comprehensive thermodynamic model for Ca-Cl-H2O system at up to 523 K, 400 bars, and 4.75 mol CaCl2/kg H2O based on enthalpy, heat capacity, solubility, activity coefficient, osmotic coefficient, and solution density 34. This study adopted the virial coefficient for Ca-Cl and standard partial molar volumes of CaCl2 fitted by Holmes et al. (1994), and similarly for Mg/Ba/Sr-Cl2 solutions 34, 35, 74. Note that the equations for standard partial molar volume calculations appear to be in error. The necessary modifications were discussed in the Supporting information. 2.2. Regression model In order to accurately determine the lattice ion activity coefficients of calcite and barite in the presence of mixed electrolytes, related virial coefficients need to be determined. Furthermore, to ensure that the virial coefficients and standard partial molar volumes are applicable to the typical geochemical and industrial water system mentioned before, more thermodynamic data of different categories needs to be included. In addition to the solubilities of calcite and barite, the thermodynamic database included the solubilities of other related minerals (i.e., halite, gypsum, anhydrite, celestite), the solubility of CO2, and the density of various solutions (i.e., NaCl, KCl, MgCl2, CaCl2, SrCl2, BaCl2, Na2SO4, K2SO4, and MgSO4). The reliability of the experimental data was evaluated before they were included in the database. The data was rejected if they were significantly inconsistent with other studies, or if they were rejected by previous research papers. For example, celestite solubility data from Gallo (1935) was rejected since they were up to 85% higher than other data sources at 0 to 100 oC and 1 bar 75; A recent study by IUPACNIST have done thorough reviews on calcite solubility 76 and only the references with additional calcite data are listed in Error! Reference source not found.. These adopted data are listed in Error! Reference source not found. and Error! Reference source not found.. The undetermined virial coefficients (i.e., related to SO4, Na, and HCO3) and standard partial molar volumes (i.e., SO4) were fitted with the least-square method using a genetic algorithm. The optimization was done on the super computer, DAVinCI, at Rice University. In the least-square method model, the objective function of this study was set as the equation below:


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f min

 SI = ∑ i   i , j  σ SIi 

2

 ∆ρ j  +   σ ∆ρ j

2

2 2  ∆ ρ SI   j i = .   +∑  ∑ i  0.031  j 0.001 

(16)

In the objective function, the residual variance of each data is weighted by the reciprocal of measurement variance of the data (i.e. 1 / σ i2 ), which means that the more reliable experimental data (with less measurement variance) are more weighted, and vice versa. However, it is hard to determine the experimental uncertainties for each data points which were measured with different methods using different apparatus under different conditions. This study assumed that the same type of adopted experimental data (i.e., solubility or solution density data) have the same uncertainties, as was done in the IUPAC-NIST paper 59, while the solution density measurements were assumed to have smaller relative standard deviation than the solubility measurements. According to the error propagation equation below, the standard deviation of a function f, which is dependent on other variables (i.e., x, y, and etc.), can be calculated from the standard deviations of these variables as below: 2

2

σ f ( x , y ,...)

 ∂f   ∂f  =   σ x2 +   σ y2 + ... .  ∂x   ∂y 

(17)

Based on Equations (6), (16) and (17), if assuming the relative error of solubility measurement is around 5% which is the general accuracy (see detailed discussion in later sections), σ SI is about 0.031. If the relative error of density measurement is about 0.070.14%, σ ρ is about 0.001 g/cm3.

3. Experiments 3.1. Chemicals All chemicals used in the experiments were of ACS reagent grade. Calcite and barite particles (99+%, Sigma-Aldrich) were packed with about 50% porosity in a stainless steel column (SS316, outer diameter 1.43 cm, inner diameter 0.48 cm, High Pressure Equipment Company). A 0.2 µm filter was placed at the end of the column. The ethylenediaminetetraacetic acid (EDTA) solution (0.2 mol/L) was prepared by dissolving the EDTA disodium salt (> 99%) in DI water, followed by adjusting the pH value to 10 with sodium hydroxide (> 99%, solid pellets). High SO42- or synthetic brines are prepared according to their compositions. In barite solubility measurements, high purity NaCl (99.999% trace metals basis, SigmaAldrich) was used to avoid the interferences from impurities. 9 ACS Paragon Plus Environment


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3.2. Calcite solubility measurement in solutions with 0.0407 m SO42+

Error! Reference source not found. plots the schematic of the apparatus for mineral solubility testing at high temperature and high pressure used in our previous research and this study 26, 27, 29, 44. The prepared feeding solution was composed of 4.951 m NaCl and 0.0407 m Na2SO4. The feeding solution was sparged with pure CO2 until the pH became constant so that the solutions contained a fixed amount of dissolved CO2. Then the feeding solution was pumped by the high pressure pump (ISCO Teledyne 65 HP, up to 1,700 bar, 24,000 psi) into the system. At desired temperature and pressure (i.e., listed in Table 1), the feeding solution flowed through the column and interacted with the calcite solids packed inside. The EDTA solution was injected at the end of the column using a second syringe pump (ISCO Teledyne 65 HP) to prevent precipitation of calcite due to the temperature or pressure drop. After the solution was cooled down in a cooling coil outside the oven, the effluent was collected for ion concentration analysis. The concentration of Ca2+ in the effluents was measured using inductively coupled plasma optical emission spectrometry (ICP-OES, Perkin-Elmer 4300DV). The concentrations of − 2− the carbonate species (i.e., CO2,aq , HCO3 , CO3 ) were calculated according to the

reactions shown below: CO2,aq + H 2O + CaCO3 ↔ Ca 2+ + 2 HCO3− ,

(

)

(18)

∆mAlkalinity = ∆ mHCO− + 2mCO2− + mOH − − mH + = 2∆mCa2+ ,

(19)

∆mTotal carbonate = ∆mCa2+ .

(20)

3

3

where the symbol ∆ indicates the concentration change of each species. The increase of the alkalinity of the solution equals twice of the increase of Ca2+ ion concentration. The increase of total carbonate species concentration equals the increase of Ca2+ ion concentration. The initial concentration of CO2,aq and the equilibrium concentrations of carbonate species after calcite dissolution are calculated using our model. The pH of the solution also changes with the temperature, pressure, and the composition of the solutions. Based on Equations (19) and (20), pH values can be calculated at different conditions. In this set of experiments, the pH range of the effluent is around 5.83 to 6.70. The retention time was adjusted by changing the flow rate of the feeding solution to make sure the calcite-solution equilibrium was achieved. Similar Ca2+ concentrations in the effluent were achieved when retention time ranged from 0.5 to 10 minutes, indicating retention time longer than 0.5 minutes was sufficient to reach equilibrium. 3.3. Barite solubility measurement in mixed electrolytes solution 10 ACS Paragon Plus Environment

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In Table 2 is listed the composition of the synthetic brine (I) for barite solubility measurement. The ion concentrations of the synthetic brine represent the extremely high electrolyte concentrations (95% percentile) of the produced water in the oil and gas industry 77. Using the same apparatus, the prepared feeding solution is pumped through the barite column. The retention time longer than 2 minutes was used to make sure the equilibrium was achieved. The Ba2+ concentration in the effluent was measured using ICP-OES following the same procedures. The change of SO42+ concentration was assumed to be the same as that of Ba2+ concentration.

4. Results and Discussions The solubilities of calcite in high Na2SO4 (i.e., 0.0407 m Na2SO4) solutions and barite in the synthetic brine (I) are plotted in Figure 1 (a) and (b), respectively. Figure 1 (a) shows that calcite solubility increases with pressure but decreases with temperature. Figure 1 (b) shows that barite solubility increases with pressure and temperature. The dotted lines in Figure 1 shows that the comprehensive model developed in this study can accurately describe the temperature and pressure dependencies of calcite and barite in their background solutions. Furthermore, Table 3 summarizes the prediction results of all mineral solubilizes included in our thermodynamic database. The accuracy of mineral solubility prediction was evaluated by the saturation index (SI) which is defined in Equation (6) and has a theoretical value of zero at equilibrium. The SI values of different minerals have the mean values close to zero and the standard error of SI mean less than 0.01 log units, and that for halite is 0.0017. Table 4 lists the prediction accuracies of solution densities under various conditions. The accuracies of the solution density predictions were evaluated with the relative error, of which the ranges were mostly within ± 1%. The 95% confidence intervals of the absolute solution prediction error were less than 1.3 × 10-3 g/cm3. The details were discussed below. 4.1. Solution density Since solution density is related to the first order pressure derivative of Gibbs free energy, the inclusion of density data helps ensure the reliability of the pressure dependence of related virial coefficients. Table 4, Figure 2 and Error! Reference source not found. compare the solution densities calculated in this study with the experimental data, showing the excellent solution density predictions for different solutions by our model. This study compared the NaCl solution densities predicted by this study and those listed in Pitzer et al. (1984) under different conditions. The 95% confidence interval of prediction error of this study is 3.3E-5 g/cm3 which is 21 times smaller than that in 11 ACS Paragon Plus Environment


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Rogers and Pitzer (1982) (7.0E-4 g/cm3). It means that this study can predict NaCl solution density as accurately as Pitzer et al. (1984). Most of the 95% confidence intervals of solution density prediction errors shown in Table 4 are less than 1.3E-3 g/cm3, which corresponds to the relative error ranges of within ±1%. The 95% confidence interval of KCl solution predictions is slightly larger. However, the accuracy of the experimental results is not known because only one reference on KCl solution density is available. A larger relative error is observed in CaCl2 solution density predictions high concentrations over 2.5 m and temperatures over 150 oC, and in Na2SO4 solution density predictions at concentration larger than 0.605 m and about 250 oC. For MgSO4 system, only one out of 456 data points has a relative error larger than 1% data 78. This data is evidently a bad measurement since the 0.084 m MgSO4 solution density was measured to be 0.9250 g/cm3 at 175 oC, 21.85 bars, which is larger than the density of same solution at same temperature but at higher pressures (i.e., 0.9203 and 0.9239 g/cm3 at 31.05 and 36.48 bars, respectively). The accuracies in solution density prediction of this model reflect the reliability of the pressure dependence of the related virial coefficients adopted in this study. 4.2. CO2 solubility As mentioned above, the accurate prediction of CO2 partitioning is needed for the calcite saturation status determination. The CO2 solubility prediction strongly depends on the Henry’s constant (KH) and species interactions between CO2,aq with aqueous ions (e.g., Na+, Ca+, and Cl-). Various values of KH and the related virial coefficients have been proposed in different studies 2, 38, 41, 49, 59, 76. In the following, four models that use different combination of KH and virial coefficients were compared. The first model uses the IUPAC-NIST model 59, 76 with the pressure dependence of KH fitted by Kaasa (1998) and is denoted as model “IUPAC&K”. Duan and Sun (2003) studied CO2 solubility over wide ranges and their model is denoted as model “D&S”. Li and Duan (2007) and Duan and Li (2008) fitted KH and related virial coefficients for the NaCl-calcite-H2O-CO2 system and their model is denoted as model “D&L” 2, 38. This study used KH in “IUPAC&K” and virial coefficients in “D&L”, and shows the best prediction results among all these four models (denoted as “Our Model”). The CO2 solubilities predicted by these four models versus the measured solubilities were plotted in Figure 3 with different background electrolytes: (a) in pure water at up to 250 o C and 1,400 bars, (b) in 0.02 – 6.54 m NaCl solutions at up to 1,400 bars, 250 oC, and (c) in 1.00 – 3.90 m CaCl2 solutions at from 75 to 121 oC, from 16 to 700 bars. Figure 3 (a) shows that the CO2 solubility in pure water is accurately predicted by “IUPAC&K” and “Our Model”, which indicates the accuracy of Henry’s constants adopted in these two 12 ACS Paragon Plus Environment

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models. However, “D&L” underestimated the CO2 solubility at over 200 oC and over 500 bars, because the Henry’s constant adopted by “D&L” is much larger than that from “IUPAC&K” under these conditions (Figure 4) 2, 38, 41, 59. On the contrary, “D&S” overpredicts CO2 solubility in pure water for the same set of data since their Henry’s constants are smaller under these conditions (Figure 4). Figure 3 (b) shows the large deviations of CO2 solubilities in NaCl solutions predicted by “IUPAC&K” versus the measured data indicating that the adopted virial coefficients for CO2,aq-Na and CO2,aq-Cl interactions ( λCO2,aq − Na and λCO2,aq −Cl ) are not accurate

59

. The

underestimation of CO2 solubility by “D&L” when CO2,aq concentration is larger than 3 m, at 200 and 250 oC, over 500 bars, and less than 1.2 m NaCl can be attributed to the inaccurate KH or CO2,aq-CO2,aq interactions ( λCO2,aq −CO2,aq )

79

. Figure 3 (b) also shows that

except for overestimating the same set of data due to the relatively smaller KH in “D&S”, it can accurately predict CO2 solubility in NaCl solutions. “Our Model” can accurately predict CO2 solubility in NaCl solutions, except at 250 oC in the presence of more than 4.29 m NaCl 79. Figure 3 (c) shows that the CO2 solubility predicted by “Our Model” and “D&L” match well with the experimental data. However, large deviations are observed when using “IUPAC&K” and “D&L” in Figure 3 (c). Since the KH values adopted by these models are similar under these conditions, the errors are mainly attributed to the inaccurate CO2,aq-Ca virial coefficients ( λCO2,aq −Ca ) adopted in these models. In fact,

λCO

2,aq − Ca

from “IUPAC&K” and “D&L” are both fitted for calcite solubility but not for

CO2 solubility predictions. It clearly demonstrates the requirement of simultaneously fitting all related equilibrium constants and virial coefficients in one regression model for all systems. 4.3. Calcite solubility Generally, calcite solubility is hard to predict due to the presence of carbonic acid species, especially at high pressures when CO2 partition becomes less well understood. With the improvements made in CO2 solubility predictions (Section 4.2) and virial coefficients related to the carbonic system and Ca2+ ions, our model can predict calcite solubility accurately over wide ranges of temperature and pressure in the presence of mixed electrolytes. De Visscher and Vanderdeelen (2012) collected a comprehensive database of calcite solubility data at low pressures in the IUPAC-NIST paper 76. In that paper, the authors found equally good fit of models for calcite solubility by either treating CaHCO3+ ion 13 ACS Paragon Plus Environment


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pair explicitly with stability constants, or treating the complex implicitly with β(2) term. For same set of calcite solubility data in pure water, the standard deviation of calcite SI values predicted by this study is about 0.098, while that predicted in IUPAC-NIST paper is 0.149 or 0.103, using their two models respectively. Furthermore, this study also performs well for calcite solubility predictions in pure water at higher pressures, and with mixed electrolytes over wide ranges of pressures and temperatures published before or measured in this study 25, 27, 80-82. For example, Figure 1 (a) shows the calcite solubility (represented as Ca2+ concentration, listed in Table 1) in the presence of 4.951 m NaCl and 0.0407 m Na2SO4 solutions measured and predicted by our model. The good match indicates the virial coefficients related to SO42- ions derived in this study are reasonably accurate. Figure 5 (a) shows the measured calcite solubility in synthetic brine (II) (4.952 m Na+, 0.0534 m HCO3-, 0.0152 m BO33-, 0.0488 m Br-, 0.0523 m SO42-, 4.722 m Cl-) by Shi et al. (2013); in Figure 5 (b) is plotted the calcite solubility in synthetic brine (III) (Error! Reference source not found.) measured by He and Morse (1993); Figure 5 (c) shows the calcite solubility in the presence of 0.13 to 1.14 m KCl 82. The synthetic brine (II) in Figure 5 (b) was prepared according to the USGS produced water database to represent the extremely high electrolyte concentrations (95% percentile) of the produced water in the oil and gas industry 27, 77, and the composition of the synthetic brine (III) in Figure 5 (b) are prepared to simulate the produced water in two real oilfields 81. The good match of calcite solubility under these conditions shows the applicability of this model to scale prediction for oil and gas industry. In Figure 6 is plotted the solubility of calcite in 0.1 m and 4.0 m NaCl solutions at up to 250 oC and 1,440 bars. It shows that under these conditions our model can give much better predictions than PHREEQC, especially at higher pressures and with larger NaCl concentrations 43. This might be because the virial coefficients adopted by Appelo (2015) cannot accurately represent the pressure dependence of the corresponding species interactions (e.g., Ca-HCO3, Ca-CO2, Ca-Na, Ca-Na-Cl, Na-CO2, and etc.). Larger deviations are observed for calcite solubilities in 4.0 m NaCl at 0 oC (Figure 6 (b)), and with mixed electrolytes at high pressures (Figure 5 (a)). Such deviations are possibly due to errors in analysis under such extreme conditions or the lack of pressure dependence of several ion interaction virial coefficients (e.g., Ca-BO33-/Br-, Ca-Na). 4.4. Barite solubility Barite solubilities have been measured by many studies. Table 3 shows that our model gave an accurate barite solubility prediction with the standard deviation of SI values equaling to 0.078 (corresponding to 9% relative error). For example, Figure 1 (b) shows the good match between the barite solubility in mixed electrolytes brines (Table 2) 14 ACS Paragon Plus Environment

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measured in this study and predicted by our model. Figure 7 shows that the barite solubility in solutions with high SO42- or high Ba2+ concentrations predicted by our model agreed with that measured by Shi et al. (2013). Most of the errors in barite solubility predictions shown in Table 4 can be attributed to inconsistent solubility data. For example, Templeton (1960) measured barite solubility to be 0.018, 0.030, 0.039, 0.052 mm in the presence of 0.01, 0.05, 0.1 and 0.2 m NaCl at 25 o C and 1 atm, respectively 83. While Collins and Davis (1971) reported much smaller solubilities, i.e. 0.015, 0.018, 0.023, 0.031 mm, respectively at the same NaCl solutions 84. There are numerous examples of such inconsistency in literature reporting barite solubility data. Before more analyses are made available, the issue of large variance of solubility data cannot be resolved. The SI values of barite solubility data at temperatures from 110 to 250 oC and in the presence of 0.02 m to 1.02 m MgCl2 range from -0.24 to -0.65 85. The negative SI values indicate an over estimation of the barite solubility or, the under estimation of the activity coefficients of Ba2+ or SO42-. Since the Mg-SO4 and Ba-Cl ion interactions have been accurately predicted in the single electrolyte systems under these conditions, the errors may be due to the inaccurate temperature dependence of other related ion interactions, such as Mg-Ba, Mg-Cl-SO4, Ba-Cl-SO4, poor experimental measurements or other mechanisms unexplainable (e.g., solid solutions or ion exchange). 4.5. Solubility of other minerals In additional to calcite and barite, two of the most common scale minerals, this study also considered other common minerals (i.e., halite, gypsum, anhydrite, and celestite) that may occur in the typical natural and produced water system (i.e., Na-K-Mg-Ca-Ba-Sr-ClCO3-HCO3-SO4-CO2-H2O). The accurate solubility predictions for these minerals can not only extend the applicable area of the thermodynamic model developed in this study, but also reflect the reliability of this model. Halite has much larger solubilities comparing with other minerals, and thus a small SI difference corresponds to a relatively larger amount of salt that can be dissolved or precipitated. Pitzer et al. (1984) didn’t include halite solubility data in regression and didn’t explicitly report the halite solubility product 33. This study fitted the temperature dependence of K sp , halite based on the Na-Cl virial coefficients and the halite solubility data listed in Pitzer et al. (1984). Error! Reference source not found. compares the temperature dependence of K sp , halite from different studies. At temperature below 75 oC, 15 ACS Paragon Plus Environment


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the equations from different studies match well with each other, while the deviations are bigger at higher temperatures. For example, at temperatures higher than 150 oC, SOLMINEQ.88. gives higher Ksp values while those from Appelo (2015) and Kaasa (1998) give lower Ksp values. The pressure dependence of K sp , halite is calculated from the change of standard partial molar volume ( ∆Vrφ ) and compressibility ( ∆κ rφ ) of halite dissolution. Kaasa (1998) has fitted ∆Vrφ up to 280 oC and ∆κ rφ up to 45 oC based on Millero (1971)

41

. However, Error! Reference source not found. shows that at

temperature higher than 45 oC the fitted equation for ∆κ rφ deviates from the experimental data measured by Millero et al. (1987) up to 95 oC. In this study, a new polynomial equation fitted from the ∆κ rφ data from Millero et al. (1987) is plotted in Error!

Reference source not found.. Using the modified K sp , halite and the virial coefficients for Na-Cl interactions derived by Pitzer et al. (1984), halite SI values predicted by our model are within ±0.01. In detail, Figure 8 (a) shows that at 1 atm or water vapor pressures, our model can accurately predict halite solubility up to 250 oC. Exceptions are the data measured by Keevil (1942), which gave systematically larger solubility than those from Liu and Lindsay (1972) and Schroeder et al. (1935). Garcia (2005) also suggestted that Keevil’s measurements is not accurate enough 4. Figure 8 (b) shows that our model can provide excellent prediciton for halite solubility up to 1,500 bars at 24.05, 25, and 30 oC. For higher temperatures, no high pressure data is available for testing. This model gives very accurate halite solubility predictions for all available experimental data within experimental errors. Accurate solubility predictions for gypsum and anhydrite can be used to check the reliability of Ca-SO4 ion interactions, which are important to other aqueous systems, for example, calcite in the presence of SO42- ions, and barite with Ca2+ ions. This study fitted Ca-SO4 virial coefficients simultaneously for all systems with Ca-SO4 ion interactions present. Thus the fitted Ca-SO4 virial coefficients in our model is optimized for gypsum, anhydrite, barite and calcite solubility predictions in mixed electrolytes. Figure 9 shows that most of the SI values of gypsum and anhydrite are within ±0.1 ranges. In detail, the standard deviation of SI values of gypsum is 0.04 (corresponding to about 5% relative error in molality), and that of anhydrite is 0.08 (about 10% relative error in molality), which are within the general experimental uncertainties especially for high temperature and high pressure experiments. Lyashchenko & Churagulov (1981) measured the anhydrite solubility at temperatures from 100 to 250 oC, and pressures from water vapor pressure to 1,000 bars in pure water (open circles in Figure 9) 22. But the data measured at 200 and 250 oC cannot be accurately modeled by this study. Calcium sulfate experiments at such high temperatures are difficult to perform, but it may also indicate that additional 16 ACS Paragon Plus Environment

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thermodynamic consideration may be needed at such high temperatures, for example the ion pairs are expected to be strong at high temperatures when the dielectric constant of water is smaller. Celestite solubility has been measured by different scientists at up to 250 oC and 576 bars. This study gave accurate predictions for celestite solubility with standard deviations of SI values equal to 0.14 (corresponding to about 17 % relative error). This predicted error is due to the large disagreement among reported celestite solubility data in different studies 4, 86 . The experimental data from Muller (1960) and Gallo (1935) are excluded in this paper because the reported celestite solubilities are much higher than those of other studies at 25 oC and 1 atm and up to 6 m NaCl solutions, and in pure water at 1 bars from 0 to 100 oC, respectively 75, 87. But there are still large inconsistencies among different sources of data. For example, 8 previous studies reported celestite solubility in pure water at 25 oC and 1 atm. The reported celestite solubility ranges from 0.620 to 0.822 mm, and the predicted SI values varies between -0.038 to 0.170 84, 88-94. At about 150 oC and water vapor pressure, Strubel (1966) reported a solubility of 0.26 mm in pure water, while Howell (1992) reported a solubility of 0.11 mm 91, 95. The celestite solubility at 25 oC, 3 m NaCl was measured by Howell (1992) to be 4.82 mm, while Lucchesi and Whitney (1962) reported a solubility of 4.07 mm at 25 oC in 3.22 m NaCl solutions 96. 4.6. Uncertainty estimations The solution composition measurements in practical applications usually have relatively larger uncertainties than those in laboratory. For example, in oil and gas fields, the accuracy of produced water composition analysis is impacted by the co-existence of oil phase, the high salinity, and the complicated sampling processes. According to Equation (17), if only considering the relative errors of the concentration measurement of the cation and anion composing the mineral to be 5%, σ SI of halite, gypsum, barite, gypsum, anhydrite and celestite are about 0.031, and that of calcite, expressed as follows 2  aCa 2+ aHCO  − K2 3  ), is about 0.049. σ SI is one order of magnitude ( SI calcite = log10   aCO aH O K1 K sp ,calcite  2 ,aq 2   larger than the standard error of the SI mean listed in Table 3. But it deserves notice that such error estimation neglects the contribution of the uncertainties in the measurements of temperature, pressure, total dissolved solids, other ion concentrations, CO2 partial pressure and etc. Kan and Tomson (2012) estimated that an overall error of about 0.083 SI units of calcite exist for a particular gas well in south Texas by considering most of these uncertainties 19. For the oilfield produced water, most metal ions can be measured by inductively coupled plasma atomic emission spectroscopy (ICP-OES) within ± 10%



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relative errors 19. The relative error of SO42- ion measurement can be more than 20% especially when its concentration is less than 10 mg/L limited by the accuracy of the methods at high salinity. The alkalinity measurement is often off by more than ± 30%, and the pH can be off by ± 0.5 log unit 19. It demonstrates that our model has the capability to predict the mineral scaling risks within analytical limits under most conditions in the oil and gas industry! Moreover, in many practical applications the change in mineral solubility due to temperature or pressure is often of more interest than the absolute solubility prediction under a certain condition. For example, in oil and gas production, the produced water is typically assumed to be in equilibrium with rock minerals in the reservoir. When the produced water flows from downhole to the surface, changes of temperature and pressure lead to the formation of mineral scales. Thus the scaling risk may be determined by the difference of mineral solubility or SI (∆SI = SI2 – SI1) between downhole and surface conditions, where the subscripts 1 and 2 represent surface and downhole conditions, or change in SI from one condition to another, such as drawn-down or change in temperature, respectively. If the solution composition doesn’t change during the process, the uncertainties resulted from inaccurate ion concentration measurements are mostly canceled out in ∆SI. For example, the SI and the ∆SI values of the produced water with a composition listed in Table 5 under downhole (171 oC, 483 bars) and surface (60 oC, 28 bars) conditions were listed in Table 6 with various measurement accuracies. It shows that the 5% relative errors in Ba or SO4 ion concentration measurements lead to the SI values varying from 0.1540 to 0.1974 at downhole and from 1.0164 to 1.0598 at surface both with 0.0434 SI unit range. But the ∆SI values vary from 0.8622 to 0.8625 of which the range is less than 1% of the absolute SI ranges. In addition, errors resulting from inaccurate measurements from Ca2+, IS, temperature, and pressure are also reduced by using ∆SI instead of the absolute SI values. This demonstrates that in practical applications, ∆SI has improved precision comparing with the absolute SI values in predicting changes in scale risks during such processes. Comparing with the experimental data, our model also shows good reliability in predicting ∆SI values. For instances, the halite solubility is predicted to increase by 2.838 m from 24.05 to 250 oC at water vapor pressure in this study, which matches well with the experimental results of 2.854 m 97, 98. Our model predicts celestite solubility to increase by 0.11 mm from 5 to 556 bars at 150 o C, which matches very well with the experimental measurements of 0.10 mm, even though the predicted SI values differ by -0.23 and -0.16 log units for each case, respectively 91.

5. Conclusions


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In summary, this study has measured calcite solubility in the presence of 0.0407 m Na2SO4 and barite solubility in synthetic brine at conditions of up to 250 oC and 1,500 bars. Using this set of data and other thermodynamic data from a thorough literature review, this study has also established a comprehensive thermodynamic model to predict the solubility of common scale minerals (e.g., halite, barite, calcite, gypsum, anhydrite, and celestite), solubility of CO2, and solution densities over wide ranges of temperature, pressure and ionic strength. This comprehensive model is applicable to the typical water system, Na-K-Mg-Ca-Ba-Sr-Cl- SO4-CO3-HCO3-CO2-H2O, which usually occurs in geochemical and industrial processes. The predicted thermodynamic properties are helpful for related geochemical researches and industrial applications. The simultaneous regression model including all thermodynamic data was done with a genetic algorithm running on DAVinCI, a supercomputer in Rice University. This simultaneous regression overcomes the disadvantage that the virial coefficients optimized for a certain system may not work for other systems. The inclusion of solution density data ensures the reliability of the pressure dependence of related virial coefficients since solution density is related to the first order pressure derivatives of excess Gibbs free energy. This model can predict solution densities accurately under most conditions and the 95% confidence intervals of most solution density prediction errors are within 4E-4 g/cm3 error. Comparing with other thermodynamic models, this model can predict CO2 solubility accurately within 0.75% relative error. The uncertainties of the SI mean values for most minerals are within ± 0.1, and that for halite is within ± 0.01, most of which are within experimental uncertainties, where as the standard deviation of the mean is much smaller. However, deviations still exist under certain conditions mainly due to two reasons: (1) the inconsistencies among the experimental data from different sources will force the model to compromise among these data sets during the fitting process, and (2) there is not enough data for fitting the virial coefficients in mixed electrolytes especially under extreme conditions. More statistical analysis is needed when dealing with such large amounts of data for data selection and error analysis. Before much more reliable and indepth statistical analysis is available, the simultaneous regression method adopted in this study is probably the best way to deal with mixed electrolyte solutions. This study is a good example of measuring necessary thermodynamic data, making the best use of the flexibility and capability of Pitzer theory, and using simultaneous regression method for studying the complex natural water systems. More efforts should be put toward expanding the experimental database, improving the data quality, and improving the regression methods.



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Acknowledgements This work was financially supported by Brine Chemistry Consortium companies of Rice University, including Baker Hughes, BWA, Carbo, Cenovus, Chevron, ConocoPhillips, Dow, EOG, GE, Halliburton, Hess, Italmatch, Kemira, Kinder Morgan, Lubrizol, Marathon, Nalco Champion, Occidental, Petrobras, RSI, Saudi Aramco, Schlumberger, Shell, SNF, Statoil, and Total.

Supporting Information Details on the experimental data source, model parameter source, apparatus set up, and data comparisons.


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(117). Belfiori, P. The effect of alkali nitrites on several difficult soluble sulfates. Annali di chimica applicata 1940, 30, 233-237. (118). Harned, H. S.; Davis Jr, R. The ionization constant of carbonic acid in water and the solubility of carbon dioxide in water and aqueous salt solutions from 0 to 50 °C. J. Am. Chem. Soc. 1943, 65, 2030-2037. (119). Ellis, A.; Golding, R. The solubility of carbon dioxide above 100 degrees C in water and in sodium chloride solutions. Am. J. Sci. 1963, 261, 47-60. (120). Nighswander, J. A.; Kalogerakis, N.; Mehrotra, A. K. Solubilities of carbon dioxide in water and 1 wt.% sodium chloride solution at pressures up to 10 MPa and temperatures from 80 to 200. degree. C. J. Chem. Eng. Data 1989, 34, 355-360. (121). Rumpf, B.; Nicolaisen, H.; Öcal, C.; Maurer, G. Solubility of carbon dioxide in aqueous solutions of sodium chloride: experimental results and correlation. J. Solution Chem. 1994, 23, 431-448. (122). Prutton, C.; Savage, R. The Solubility of Carbon Dioxide in Calcium ChlorideWater Solutions at 75, 100, 120° and High Pressures. J. Am. Chem. Soc. 1945, 67, 15501554. (123). Ellis, A. Partial molal volumes of MgCl2, CaCl2, SrCl2, and BaCl2 in aqueous solution to 200 °C. J. Chem. Soc. A 1967, 660-664. (124). Obšil, M.; Majer, V.; Hefter, G. T.; Hynek, V. Volumes of MgCl2 (aq) at temperatures from 298 K to 623 K and pressures up to 30 MPa. J. Chem. Thermodyn. 1997, 29, 575-593. (125). Rodnyanskii, I.; Korobkov, V.; Galinker, I. S. Specific volumes of aqueous electrolyte solutions at high temperatures. In Mezhdunarodnaya Kniga: Moscow, Russia, 1962; Vol. 36, pp 2216-2219. (126). Kumar, A. Densities of aqueous strontium chloride solutions up to 200. degree. C and at 20 bar. J. Chem. Eng. Data 1986, 31, 347-349. (127). Azizov, N.; Akhundov, T. The bulk properties of the Na2SO4-H2O system in a wide range of the parameters of state. High Temp. 2000, 38, 203-209. (128). Ellis, A. Partial molal volumes in high-temperature water. Part III. Halide and oxyanion salts. J. Chem. Soc. A 1968, 1138-1143. (129). Chen, C.-T.; Emmet, R. T.; Millero, F. J. The Apparent Molar Volumes of Aqueous Solutions of NaCl, KCl, MgCl2, Na2SO4, and MgSO4 from 0 to 1000 Bars at 0, 25, and 50 oC. J. Chem. Eng. Data 1977, 22, 201. (130). Surdo, A. L.; Alzola, E. M.; Millero, F. J. The (p, V, T) properties of concentrated aqueous electrolytes I. Densities and apparent molar volumes of NaCl, Na2SO4, MgCl2, and MgSO4 solutions from 0.1 mol/kg to saturation and from 273.15 to 323.15 K. J. Chem. Thermodyn. 1982, 14, 649-662. (131). Abdulagatov, I.; Azizov, N.; Zeinalova, A. Viscosities, densities, apparent and partial molar volumes of concentrated aqueous MgSO4 solutions at high temperatures and high pressures. Phys. Chem. Liq. 2007, 45, 127-148.


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Contents of Tables Table 1. Calcite solubility in the presence of 4.951 m NaCl and 0.0407 m Na2SO4 measured with the same method and apparatus adopted in Shi et al. (2013)...................................................... 30 Table 2. Composition of the synthetic brine (I) for barite solubility measurements ..................... 31 Table 3. The ranges of temperature, pressure, compositions, and the saturation index (SI) of the minerals and CO2 predicted by this study. .................................................................................... 32 Table 4. The 95% confidence interval and relative error of the solution density predicted in this study. ............................................................................................................................................. 33 Table 5. The compositions of typical produced water and the temperatures and pressures at downhole and surface conditions. ................................................................................................ 34 Table 6. The SI values at downhole and surface conditions and their differences under different measurement accuracies for barite. ............................................................................................. 35

Contents of Figures Figure 1. The solubilities of (a) calcite in solutions with 4.951 m NaCl and 0.0407 m Na2SO4, and (b) barite in synthetic brine (I) measured in this study (solid symbols) and predicted by our model (dotted lines). ..................................................................................................................... 36 Figure 2. Comparisons of the measured and predicted solution densities (g/cm3) by this study for NaCl solutions. The density predictions for the solution of KCl, MgCl2, CaCl2, SrCl2, BaCl2, Na2SO4, K2SO4, and MgSO4 are plotted in Figure S2. .................................................................................. 37 Figure 3. The solubilities of CO2 in (a) in pure water, (b) in NaCl solutions, and (c) in CaCl2 solutions from experiments and from different models specified in the context. ....................... 38 Figure 4. The Henry’s constant of CO2 from 0 to 250 oC, from 1 bar or vapor pressure to 1500 bars from different models specified in the context..................................................................... 39 Figure 5. Calcite solubility (represented as Ca2+ concentration) (a) in synthetic brine (II), (b) in synthetic brine (III) (Table S5), and (c) in KCl solutions. The solid symbols are from experimental measurements 27, 81, 82, and the dotted lines are predicted by this study. .................................... 41 Figure 6. Calcite solubility (represented as Ca2+ concentration) in the presence of (a) 0.1 m NaCl, and (b) in 4.0 m NaCl solutions, measured by Shi et al. (2013) (solid symbols), predicted by this study (solid lines), and predicted by PHREEQC (dotted lines) 43. .................................................. 42 Figure 7. Barite solubility in solutions with high concentrations of SO4 (about 2.0 and 28 mm) or Ba (about 2.0 mm) 26. The solid symbols are from experimental measurements, and the dotted lines are predicted by this study. .................................................................................................. 43 Figure 8. The solubility of halite changing with (a) temperature at 1 bar or saturation pressure, and (b) pressure at 24, 25 and 30 oC. ............................................................................................ 44 Figure 9. SI of gypsum and anhydrite and its distributions predicted by this study. The open circles are data measured by Lyashchenko & Churagulov (1981)................................................. 45



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Table 1. Calcite solubility in the presence of 4.951 m NaCl and 0.0407 m Na2SO4 measured with the same method and apparatus adopted in Shi et al. (2013). Temperature (oC)

Pressure (bar)

Ca2+ (m)

25 25 25 25 100 100 100 100 200 200 200 200 250 250 250 250

34 483 965 1,448 34 483 965 1,448 34 483 965 1,448 34 483 965 1,448

1.164E-02 1.402E-02 1.662E-02 1.967E-02 7.610E-03 9.490E-03 1.072E-02 1.256E-02 4.280E-03 5.170E-03 6.340E-03 7.300E-03 3.650E-03 4.620E-03 5.310E-03 6.350E-03


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Table 2. Composition of the synthetic brine (I) for barite solubility measurements Constituents

Concentration (mg/L)

Concentration (mol/L)

Na

75000

3.26

K

1000

0.0256

Mg

3500

0.1458

Ca

20000

0.5

NH4

250

0.0139

Cl

~163000

4.598

TDS

~263000

-



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Table 3. The ranges of temperature, pressure, compositions, and the saturation index (SI) of the minerals and CO2 predicted by this study. Parameter

halite

calcite

barite

gypsum

anhydrite

celestite

CO2

No. of data (#)

32 10-254 1-1,517 5.6-9.0 0-0.41 6.1-9.0 0.000 0.01

625 0-258 1-1,448 0-6.2 0-1.14 0-0.66 0-6.2 0-0.07 0-0.05 0.006 0.088

406 0-250 1-1,517 0-6.0 0-0.25 0-1.02 0-0.55 0-6.0 0-0.03 -0.007 0.078

233 0-95 1-1,379 0-6.4 0-0.05 0-0.11 0-6.4 0-0.12 -0.016 0.038

126 94-247 1-1,410 0-6.3 0-0.039 0-6.3 0-0.04 0.023 0.08

357 0-253 1-576 0-5.0 0-1.4 0-0.12 0-0.05 0-5.0 0-0.05 -0.020 0.14

527 0-330 1-1,400 0-6.0 0-3.9 0-7.8 -

0.0035

0.0039

0.0028

0.0098

0.0074

-

T (°C) P (bar) Na+ (m) K+ (m) Mg2+ (m) Ca2+ (m) Cl- (m) alkalinity (m) SO42- (m) SI mean Standard deviation of SI Standard error of SI 0.0017 mean


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Table 4. The 95% confidence interval and relative error of the solution density predicted in this study. T range P range conc. range density range 95% confidence (o C) (bar) (m) (g/cm3) interval (g/cm3) NaCl 0 - 250 1 – 1,000 0.10 - 6.00 0.86 - 0.989 3.3E-05 KCl 25 - 250 1 - 40 0.25 - 3.00 0.805 - 1.239 1.3E-03 MgCl2 50 - 244 20 - 306 0.00 - 3.04 0.814 - 1.118 3.6E-04 CaCl2 25 - 250 1 - 417 0.05 - 6.44 0.819 - 1.173 3.5E-04 SrCl2 50 - 200 20 - 20 0.10 - 2.72 0.832 - 1.406 2.7E-04 17 - 250 3.3 - 399 0.10 - 1.00 BaCl2 0.880 - 1.317 3.9E-04 Na2SO4 0 - 250 1 – 1,000 0.00 - 1.62 0.821 - 1.168 1.2E-04 K2SO4 25 - 243 20 - 307 0.00 - 0.51 0.812 - 1.189 9.4E-05 MgSO4 0 - 203 1 - 995 0.02 - 2.54 0.872 - 1.263 1.2E-04 * relative error = (predicted density – experimental density)/experimental density Salts


Ranges of relative error* (%) -0.34 - 0.10% -0.94 - 0.43% -0.76 - 0.72% -1.98 - 0.69% -0.59 - 0.29% -0.21 - 0.34% -2.21 - 0.70% -0.26 - 0.16% -1.03 - 0.32%

No. of data (#) 1620 34 120 424 84 189 756 127 456


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Table 5. The compositions of typical produced water and the temperatures and pressures at downhole and surface conditions. Compositions Na+ K+ Mg2+ Ca2+ Sr2+ Ba2+ Fe2+ Zn2+ Pb2+ ClSO42FBrSilica Alkalinity CO2 Gas Downhole temperature Surface temperature Downhole pressure Downhole pressure

units mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L as Si mg/L as HCO3% o C o C bar bar

Concentration measured at surface 19,872 500 54 6,500 700 550 12 10 1 43,000 10 1 10 8 281 0.28 171 25 483 1


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Table 6. The SI values at downhole and surface conditions and their differences under different measurement accuracies for barite. Error source Accurate measurement Ba +5% Ba -5% SO4 +5% SO4 -5% Ca +5% Ca -5% IS +5% IS -5% T +5% T -5% P +5% P -5% Standard deviation

SI at downhole 0.1763 0.1970 0.1544 0.1974 0.1540 0.1582 0.1946 0.1696 0.1830 0.1392 0.2110 0.1669 0.1867 0.0212

SI at surface 1.0386 1.0596 1.0166 1.0598 1.0164 1.0298 1.0476 1.0294 1.0485 0.9978 1.0819 1.0378 1.0395 0.0219


∆SI 0.8624 0.8625 0.8622 0.8624 0.8624 0.8716 0.8530 0.8597 0.8654 0.8586 0.8708 0.8709 0.8528 0.0060


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Figure 1. The solubilities of (a) calcite in solutions with 4.951 m NaCl and 0.0407 m Na2SO4, and (b) barite in synthetic brine (I) measured in this study (solid symbols) and predicted by our model (dotted lines). 36 ACS Paragon Plus Environment

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Figure 2. Comparisons of the measured and predicted solution densities (g/cm3) by this study for NaCl solutions. The density predictions for the solution of KCl, MgCl2, CaCl2, SrCl2, BaCl2, Na2SO4, K2SO4, and MgSO4 are plotted in Error! Reference source not found..



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Figure 3. The solubilities of CO2 in (a) in pure water, (b) in NaCl solutions, and (c) in CaCl2 solutions from experiments and from different models specified in the context.


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Figure 4. The Henry’s constant of CO2 from 0 to 250 oC, from 1 bar or vapor pressure to 1500 bars from different models specified in the context.



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Figure 5. Calcite solubility (represented as Ca2+ concentration) (a) in synthetic brine (II), (b) in synthetic brine (III) (Error! Reference source not found.), and (c) in KCl solutions. The solid symbols are from experimental measurements 27, 81, 82, and the dotted lines are predicted by this study.



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Figure 6. Calcite solubility (represented as Ca2+ concentration) in the presence of (a) 0.1 m NaCl, and (b) in 4.0 m NaCl solutions, measured by Shi et al. (2013) (solid symbols), predicted by this study (solid lines), and predicted by PHREEQC (dotted lines) 43.


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Figure 7. Barite solubility in solutions with high concentrations of SO4 (about 2.0 and 28 mm) or Ba (about 2.0 mm) 26. The solid symbols are from experimental measurements, and the dotted lines are predicted by this study.



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Figure 8. The solubility of halite changing with (a) temperature at 1 bar or saturation pressure, and (b) pressure at 24, 25 and 30 oC.


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Figure 9. SI of gypsum and anhydrite and its distributions predicted by this study. The open circles are data measured by Lyashchenko & Churagulov (1981).



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Table of Contents


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Figure 1. The solubilities of (a) calcite in solutions with 4.951 m NaCl and 0.0407 m Na2SO4, and (b) barite in synthetic brine (I) measured in this study (solid symbols) and predicted by our model (dotted lines).

ACS Paragon Plus Environment


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Figure 2. Comparisons of the measured and predicted solution densities (g/cm3) by this study for NaCl solutions. The density predictions for the solution of KCl, MgCl2, CaCl2, SrCl2, BaCl2, Na2SO4, K2SO4, and MgSO4 are plotted in Error! Reference source not found..


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Figure 3. The solubilities of CO2 in (a) in pure water, (b) in NaCl solutions, and (c) in CaCl2 solutions from experiments and from different models specified in the context.



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Figure 4. The Henry’s constant of CO2 from 0 to 250 oC, from 1 bar or vapor pressure to 1500 bars from different models specified in the context.


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Figure 5. Calcite solubility (represented as Ca2+ concentration) (a) in synthetic brine (II), (b) in synthetic brine (III) (Error! Reference source not found.), and (c) in KCl solutions. The solid symbols are from experimental measurements 27, 81, 82, and the dotted lines are predicted by this study.


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Figure 6. Calcite solubility (represented as Ca2+ concentration) in the presence of (a) 0.1 m NaCl, and (b) in 4.0 m NaCl solutions, measured by Shi et al. (2013) (solid symbols), predicted by this study (solid lines), and predicted by PHREEQC (dotted lines) 43.



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Figure 7. Barite solubility in solutions with high concentrations of SO4 (about 2.0 and 28 mm) or Ba (about 2.0 mm) 26. The solid symbols are from experimental measurements, and the dotted lines are predicted by this study.


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Figure 8. The solubility of halite changing with (a) temperature at 1 bar or saturation pressure, and (b) pressure at 24, 25 and 30 oC.



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Figure 9. SI of gypsum and anhydrite and its distributions predicted by this study. The open circles are data measured by Lyashchenko & Churagulov (1981).


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Calcite and Barite Solubility Measurements in ... - ACS Publications

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