Numerical Modeling of CO2, Water, Sodium Chloride, and Magnesium Carbonates Equilibrium to High Temperature and Pressure

energies

Article Numerical Modeling of CO2, Water, Sodium Chloride, and Magnesium Carbonates Equilibrium to High Temperature and Pressure

Jun Li * and Xiaochun Li

State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China; [email protected] * Correspondence: [email protected]

Received: 26 September 2019; Accepted: 27 November 2019; Published: 28 November 2019

Abstract: In this work, a thermodynamic model of CO2-H2O-NaCl-MgCO3 systems is developed. The new model is applicable for 0–200 ◦C, 1–1000 bar and halite concentration up to saturation. The Pitzer model is used to calculate aqueous species activity coefficients and the Peng–Robinson model is used to calculate fugacity coefficients of gaseous phase species. Non-linear equations of chemical potentials, mass conservation, and charge conservation are solved by successive substitution method to achieve phase existence, species molality, pH of water, etc., at equilibrium conditions. From the calculated results of CO2-H2O-NaCl-MgCO3 systems with the new model, it can be concluded that (1) temperature effects are different for different MgCO3 minerals; landfordite solubility increases with temperature; with temperature increasing, nesquehonite solubility decreases first and then increases at given pressure; (2) CO2 dissolution in water can significantly enhance the dissolution of MgCO3 minerals, while MgCO3 influences on CO2 solubility can be ignored; (3) MgCO3 dissolution in water will buffer the pH reduction due to CO2 dissolution.

Keywords: thermodynamic modeling; CO2 storage; MgCO3 minerals; phase behaviors; mineral solubility; CO2 solubility

1. Introduction

CO2 geological storage has been proved as an important option to reduce carbon emission and a clean way of using fossil energy resources [1]. When CO2 is injected into underground reservoirs, the reactions of CO2, water and various minerals are activated [2]. Magnesium carbonates are commonly found minerals in geological reservoirs. A reliable thermodynamic model of CO2, brine, and magnesium carbonate minerals is essential to understand phase behavior, water property changes, and mineral participation and dissolution [3]. Further, it will help us to understand the reservoir property (porosity and permeability) change after CO2 injected. Numerical dynamic simulation of the ﬂuid migration process is usually an important tool to analyze the whole procedure and helps the decision making of a real CO2 storage project [4]. The thermodynamic model is one of the basic components in a simulation framework. Both magnesium and carbon are commonly found underground in terms of various kinds of minerals. Researchers started experimental work on the H2O-MgCO3 system in 1867 [5]. Wagner [5] measured magnesite solubility at 5 ◦C and with CO2 partial pressure from 1 to 6 atm. The followers conducted magnesite solubility measurements with temperature up to 91 ◦C and CO2 partial pressure up to about 10 atm [5–12]. Cameron and Seidel [12] measured magnesite solubility in NaCl solutions with NaCl molality up to 6.5 molal. Nesquehonite solubility in water was ﬁrst measured by Engel et al. [13]. The most recent measurements were carried out by Konigsberger et al. [14]. The temperature range of

Energies 2019, 12, 4533; doi:10.3390/en12234533 www.mdpi.com/journal/energies Energies 2019, 12, 4533 2 of 16

the experiments is from 0–90 ◦C and CO2 partial pressure ranges from about 0 to 56 atm [7,10,14–18]. Lansfordite solubility experiment work is less than magnesite and nesquehonite. The available literatures are Takahashi et al. [19], Ponizonvskii et al. [20], and Yanat’eva and Rassonskaya [21]. The temperature of the experiments is less than 15 ◦C and pressure is less than 10 atm. Numerical modeling of CO2-brine-salts-minerals was started in the 1980s. The pioneer work is from Harvie and Weare [22] and Harvie et al. [23]. They developed series thermodynamic models of sea water components based on the Pitzer model [24–27]. The models are able to accurately predict mineral precipitation and dissolution. The temperature and pressure are at standard condition (25 ◦C and 1 atm). Moller [28], Moller and Greenberg [29], and Christov and Moller [30] modeled temperature effects on the system. Duan and co-workers focused on the pressure effects and developed models on CO2-H2O-NaCl-CaCO3-CaSO4 systems from standard condition to high temperatures and pressures [31–34]. Thermodynamic models have been implemented in research or commercial software on reactive transport. The most famous reactive transport software packages are PhreeqC [35], TOUGHREACT [36], MIN3P [37], and EQ3/6 [38]. They have shown success in real project applications [39–41]. Some commercial reservoir simulators have coupled the reactive transport module (such as CMG-GEM [42] and MoReS-PhreeqC [43]) and were successfully applied in enhanced oil recovery research or real projects [44,45]. In this work, a new thermodynamic model of CO2-H2O-NaCl-MgCO3 systems is developed. The model is based on the existing experimental data and the consistency checking. The MgCO3 minerals of magnesite, nesquehonite, and lansfordite are considered in the system. In Section2, the methodology of the thermodynamic modeling is introduced. In Section3, model validations are made by comparing the model results and available experimental data of the systems. In Section4, the model is used to predict MgCO3 mineral solubility, aqueous solution properties (such as pH and various carbon ion concentrations) at various conditions. The influences of CO2 and MgCO3 on the speciation in the solutions are evaluated by the model.

2. Phenomenological Description and Geochemical Modeling

When a system of CO2-H2O-NaCl-MgCO3 approaches equilibrium at given temperature and pressure, phases of solids, vapor, and brine (aqueous phase) can appear. Minerals of magnesite (MgCO3), nesquehonite (MgCO 3H O), and lansfordite (MgCO 5H O) are considered in this modeling work. 3· 2 3· 2 The salt of sodium chloride (NaCl) can be precipitated when NaCl becomes saturated in the aqueous phase. In the vapor phase, the possible components are CO2 and H2O. In the aqueous phase, various cations, anions, and neutral particles can be dissolved. The following reversible reactions are considered for the modeling: H O(aq) H O(g), (1) 2 ↔ 2 CO (aq) CO (g), (2) 2 ↔ 2 (aq) (aq) 2 + CO + H O CO − + 2H , (3) 2 2 ↔ 3 + H O H + OH−, (4) 2 ↔ 2 + HCO − CO − + H , (5) 3 ↔ 3 (s) + NaCl Na + Cl−, (6) ↔ (s,Magnesite) 2 2+ MgCO CO − + Mg , (7) 3 ↔ 3 (s,Nesquehonite) 2+ 2 MgCO 3H O Mg + CO − + 3H O, (8) 3 · 2 ↔ 3 2 (s,Lans f ordite) 2+ 2 MgCO 5H O Mg + CO − + 5H O, (9) 3· 2 ↔ 3 2 (aq) 2+ 2 MgCO Mg + CO −, (10) 3 ↔ 3 2+ + + Mg + H2O = MgOH + H , (11) Energies 2019, 12, 4533 3 of 16 where (aq) denotes aqueous species; (s) denotes solid phase; (g) denotes gaseous phase species. When the whole system reaches equilibrium state, each of the above reactions will have: X νriµri = 0, (12) r where µri is the chemical potential for reaction r and species i; νri is the stoichiometric coefficient of species i in reaction r. For aqueous species, 0 µi = µi + RT ln(miγi). (13) For gaseous species, 0 µi = µi + RT ln(xiPϕi), (14) 0 where µi is standard chemical potential at the reference state; mi is the molality of aqueous species i; γi is the activity coefficient of aqueous species i; xi is mole fraction of gaseous species i; ϕi is fugacity coefficient of gaseous species i; P is total gas pressure; R is gas constant; T is temperature. More details about the parameter definition can be found from Duan and Li [32] and Li and Duan [34]. With Equations (12)–(14), equilibrium constant is usually defined for each chemical reaction as follows:

P 0 νriµri i ln Kr = . (15) − RT Combined with deﬁnition of chemical potential, we have:

νri Kr = Πari (16)

Here, ari is activity for aqueous species (mriγri) and fugacity for gaseous phase (xriPϕri). The thermodynamic modeling of the system is to determine the equilibrium constants, activity, and fugacity of each reaction. We follow the model from our previous work from Li et al. [46] for reactions (1) and (2), and from Li and Duan [34] for reactions (3) to (6).

2.1. Equilibrium Constant The equilibrium constant can be further expressed as [33,34]:   Vm,i(P Pre f )  K = K(T, P ) exp − , (17) i re f  RT  where K(T, Pre f ) is equilibrium constant at reference pressure Pre f ; the reference pressure is usually 1 bar at temperature under 373.15 K, and vapor pressure of water above 373.15 K; Vm,i is molar volume of aqueous species i. For K(T, Pre f ), we follow the empirical equation from Appelo [47]:

A2 A4 2 log(KH(T, P )) = A0 + A T + + A3 log(T) + + A5T . (18) re f 1 T T2

For reactions (7) to (9), we regressed the parameters in Equation (17) and Vm,i from the related mineral solubility in water or brine. Vm,i is calculated as follows:

4 ! 100a2,i a3,i 10 a4,i V = 41.84 0.1a + + + ω QBrn , (19) m,i 1,i 2600 + P (T 288) (2600 + P)(T 288) − i × − − where a1,i–a4,i and ωi are the parameters found in Appelo [47], and QBrn is the Born function, which can be found in Helgson et al. [48]. For magnesium carbonate dissolution reactions (7–9), we assume Energies 2019, 12, 4533 4 of 16

Vm,i is set as a constant value. For reactions (10) and (11), Vm,i is calculated following Helgson et al. [48]. Table1 shows the parameters used in this model.

Table 1. Parameters of equilibrium constants for magnesium carbonate dissolution reactions.

Reaction A0 A1 A2 A3 A4 A5 Vm (7) 7.267 0.033918 1476.604 0 0 0 28.3 − − (8) 6.008 0.00688 873.4 0 0 0 74.789 − − (9) 4.85 0 0 0 0 0 100.81 − (10) 0.5837 9.2067 2.3984 0.03 0 0 Helgson et al. [48] − − − − (11) a 11.809 0 0 0 0 0 0 − a From Appelo [47].

2.2. Activity Model and Fugacity Model From Equation (13), the activity coefficient describes the deviation of an aqueous species in a real solution from that in ideal solution. Pitzer [24] proposed an accurate model framework that can accurately estimate the activity coefficients of aqueous species and osmotic coefficients of H2O in solutions to high salinity. Science 1980s, the Pitzer model [24] framework began to be used to model water–salt–mineral equilibria with various kinds of aqueous species (Harvie and Weare [22]; Harvie et al. [23]; Greenburg et al. [29]; Moller [28]; Christov and Moller [30]; Li and Duan [33]) and shows its success in applications. Li and Duan [34] and many other literatures [29–33] provided the expressions of the model in details. In this work, we use the Pitzer model to calculate the activity coefficients. The (0) (1) ϕ Pitzer parameters includes cation and anion binary interaction parameters βc,a , βc,a , Cc,a, cation and cation binary interaction parameters θc,c, anion and anion interaction parameters θa,a, triple particle interaction parameters Ψc,c,a, Ψc,a,a, and neutral-ion interaction parameters λn a, λn c. The selection of − − the Pitzer parameters can be found from Table2.

Table 2. The Pitzer parameters of the system.

(0) (0) (0) (1) (1) (1) (0) β , β , β , β , β , β , β , 2 + HCO ,Na+ Cl ,Na+ Cl ,Na+ 2 + HCO ,Na+ OH ,Na+ CO3−,Na 3− − − CO3−,Na 3− − (1) ϕ ϕ ϕ ϕ Li and Duan [33], Duan and Li [32] β + , C , C + , C + , C + , Ψ + , OH ,Na 2 + HCO ,Na Cl ,Na OH ,Na Cl−,HCO3−,Na − CO3−,Na 3− − − + + + ΨCl−,OH−,Na , ΨCl−,H ,Na (0) (0) (0) (1) (1) (1) β , β , β , β , β , β , 2 2+ HCO ,Mg2+ Cl ,Mg2+ Cl ,Mg2+ 2 2+ HCO ,Mg2+ CO3−,Mg 3− − − CO3−,Mg 3− (0) (1) ϕ ϕ ϕ ϕ Greenburg et al. [29]; Moller 1988 β , β , C , C , C , C , OH ,Mg2+ OH ,Mg2+ 2 2+ HCO ,Mg2+ Cl ,Mg2+ OH ,Mg2+ [28] Christov and Moller [30]; − − CO3−,Mg 3− − − Ψ 2+ , Ψ 2+ , Ψ + 2+ Cl−,HCO3−,Mg Cl−,OH−,Mg Cl−,H ,Mg (0) (1) + + ΨCl ,OH ,Mg(OH) , ΨCl ,H+,Mg(OH) , β + , β + , − − − Cl−,Mg(OH) Cl−,Mg(OH) (0) (1) Set to 0.0 β , β ( )+ 2 ( )+ HCO3−,Mg OH CO3−,Mg OH λ + , λ 2+ , λ 2 , λ CO2,Na CO2,Mg CO2,CO3 − CO2,HCO3− Duan and Sun [31]; Duan et al. [49]

To calculate the fugacity coeﬃcient of gaseous component (CO2 and H2O), the Peng–Robinson (PR) model [50] is used. The details of the PR model and the methodology of the application are discussed in our previous work [2,46]. The equation for PR model is as follows:

RT a(T) P = (20) Vm b − Vm(Vm + b) + b(Vm b) − − where a(T) = a(Tc)α(Tr, ω); a(Tc) is the Van der Waals’ attraction factor at a critical temperature R2T2 deﬁned as a(T ) = 0.45724 c , where P is critical pressure; b = 0.07780 RTc ; T is reduced temperature c Pc c Pc r Energies 2019, 12, 4533 5 of 16

T = T ; T is critical temperature; ω is acentric factor; α(T , ω) is a dimensionless function of relative r Tc c r temperature and acentric factor. When gaseous phase has more than one component, the mixing rule is considered for parameters “a” and “b”: X X a = yi yjaij, (21) i j X b = bi yi, (22) i where aij = √aiaj(1 δij) and δij is binary interaction coeﬃcient of species i and j; yi is mole fraction of − species i in gaseous phase. The PR parameters are adopted from Li et al. [46].

2.3. Calculation Routine The equilibrium of the whole system is described by equations of chemical potentials, charge and mass conservation. The equations are non-linear. In this work, we use successive substitution method (Li and Duan [34]; Michealson and Mollerup [51]). The calculation routine is as follows.

(1) Initialize the system with molality of each component and species at given pressure and temperature. (2) Calculate the equilibrium constant of each reaction. (3) Calculate activity coefficient of each aqueous species and fugacity coefficient of each gaseous species with current molality of each species of the system. (4) Solve mass and charge conservation equations and linearized reaction equilibrium equations. Update the molality and activity/fugacity coefficient of each species. (5) Calculate the absolute relative difference of molality of each species and activity coefficient. If both are smaller than tolerance, stop the calculation and output the final results. Otherwise, go to step (3).

3. Results

3.1. Comparisons of MgCO3 Mineral Solubility: Model Calculations and Experiments

The experimental work of MgCO3 mineral solubility started very early by previous researchers [5–8]. However, the reliable experimental data of this system is not sufficient for modeling. To test the model behavior, we compared the model results with the existing experimental data of MgCO3 mineral solubility. Visscher et al. [52] carefully compared the experimental data and checked the reliability of the data. We defined average absolute deviation (AAD) to measure the difference between model results and experimental work:

1 X scal sexp AAD% = − 100%, (23) N sexp × where N denotes the number of data points; Scal denotes calculated solubility; Sexp denotes experimental solubility. Table3 shows the experimental data of magnesite (MgCO 3) in water and the average absolute deviation of the calculated results from this model. The experimental data of magnesite are usually at temperature from normal temperature to 91 ◦C and CO2 partial pressure to about 1 atm. More recent work is from Benezeth et al. [3] who conducted experiments of magnesite solubility with temperature from 120 to 200 ◦C and CO2 partial pressure from 12–30 bar. From the comparison, the AAD% is usually less than 10% with some of them up to 13.17%. Figure1 shows the magnesite solubility trend with temperature at various CO2 partial pressure calculated by this model. The trend shows that the model results are reliable compared with the experimental data. Energies 2019, 12, x FOR PEER REVIEW 6 of 16 at temperature from normal temperature to 91 °C and CO2 partial pressure to about 1 atm. More recent work is from Benezeth et al. [3] who conducted experiments of magnesite solubility with temperature from 120 to 200 °C and CO2 partial pressure from 12–30 bar. From the comparison, the AAD% is usually less than 10% with some of them up to 13.17%. Figure 1 shows the magnesite Energiessolubility2019 trend, 12, 4533 with temperature at various CO2 partial pressure calculated by this model. The trend6 of 16 shows that the model results are reliable compared with the experimental data.

Table 3. Average absolute deviation of magnesite solubility in water between model calculation by this Table 3. Average absolute deviation of magnesite solubility in water between model calculation by model and the experimental results. this model and the experimental results.

Reference Data Points T (◦C) PCO2 (atm) AAD% Reference Data Points T (°C ) PCO2 (atm) AAD% Wells [7]Wells [7] 11 2020 0.00029 0.00029 3.8 3.8 Bar [8]Bar [8] 22 1818 0.00031 0.00031 13.3 13.3 Halla [9]Halla [9] 22 25–38.825–38.8 0.932 0.932–0.955–0.955 8.75 8.75 Berg and BorisovaBerg and [10 Borisova] [10] 1 1 2525 0.987 0.987 11.6 11.6 Christ and Hostetler [11] 3 90.3–91 0.0274–0.312 9.61 Christ and Hostetler [11] 3 90.3–91 0.0274–0.312 9.61 Benezeth et al. [3] 11 120–200 12–30 13.17 Benezeth et al. [3] 11 120–200 12–30 13.17

0.040 Pco₂=0.31 atm, this model 0.035 Pco₂=0.95 atm, this model 0.030 Pco₂=0.0003 atm, this model Christ and Hostetler (1970) 0.025 Halla (1936) & Berg and Borisova (1960) Wells (1915) & Bar (1932) 0.020

0.015

0.010

Magnesite solubility (molality) solubility Magnesite 0.005

0.000 273 293 313 333 353 373 Temperature (K)

Figure 1. Comparison of magnesite solubility in water at various temperatures and pressures.pressures. Lines are calculated results byby thisthis model,model, andand dotsdots areare fromfrom experiments.experiments.

The experimental data of nesquehonite solubility in water is more than that of magnesite, but is with limitedlimited TPTP range.range. TheThe temperaturetemperature is is from from 0 0 to to 60 60◦C °C and and CO CO2 partial2 partial pressure pressure is fromis from 0.00029 0.00029 to 21to 21 atm. atm. Table Table4 shows 4 shows the comparisonthe comparison between between experimental experimental data data and theand calculatedthe calculated results results by this by model.this model. The The average average absolute absolute deviations deviations are all are under all under 10%. 10%. Figure Figure2a posts 2a posts all of all the of experimental the experimental data (whichdata (which are judged are judged as reliable as reliable by Visscher by Visscher et al. [52 et]) al. and [52 the]) and calculated the calculated results with resu dots,lts with most dots, of which most areof which quite are close quite to theclose equal to the line equal (y = linex). (y Figure = x). 2Figureb shows 2b theshows nesquehonite the nesquehonite solubility solubility varying varying with COwith2 partialCO2 partial pressure pressure at various at various temperature. temperature. The comparison The comparison shows a shows reliable a nesquehonite reliable nesquehonite solubility trendsolubility with trend CO2 partialwith CO pressure2 partial with pressure this modelwith this calculations. model calculations.

Table 4.4. AverageAverage absoluteabsolute deviation deviation of of nesquehonite nesquehonite solubility solubility in in water water between between model model calculation calculation by thisby this model model and and the the experimental experimental results. results.

Reference Data Data Points T (°C ) PCO2 (atm) AAD% Reference T(◦C) PCO2 (atm) AAD% Engel [13] Points 14 3.5–50 0.878–5.986 2.09 Engel [13]Wells [7] 142 3.5–5020 0.878–5.9860.00029 9.41 2.09 Wells [7]Mitchell [16] 26 2025 0.000296–21 5.22 9.41 Mitchell [16Haehnel] [17] 612 255–60 6–211 1.13 5.22 HaehnelYanat and [17] Rassonskaya [21] 12 10 5–600–53.5 1 1 2.91 1.13 Yanat and Rassonskaya [21] 10 0–53.5 1 2.91

Energies 2019, 12, 4533 7 of 16 Energies 2019, 12, x FOR PEER REVIEW 7 of 16

0.7

0.6

0.5

0.4

Engel (1988)

0.3 (molality) Mitchell (1923) 0.2 Haehnel (1924)

0.1 Berg et al. (1960) & Yanat and Rassonskaya (1961)

Nesquehonite Nesquehonite solubility from this model Konigsberger et al. (1999) 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Nesquehonite solubility from experiments (molality)

(a) 0.7

0.6

0.5

0.4

0.3 289.15K, this model 0.2 298.15K, this model 333.15K, this model 0.1 289.15K, Engel (1888)

298.15K, Kline (1923) & Mitchell (1923) Nesquehonite Nesquehonite solubility (molality) 333.15K, Haehnel (1924) 0 0 10 20 30 40 CO partial pressure (atm) 2 (b)

Figure 2. 2.Comparison Comparison of of nesquehonite nesquehonite solubility solubility in water in water at various at various temperatures temperatures and pressures and pressures between calculatedbetween calculated results by results this model by this and model experiments. and experiments. Dots are experimental Dots are experimental data from referencesdata from [references10,13–17], and[10,13 lines–17], are and calculated lines resultsare calculated by this model. results (a ) by comparison this model. of experimental (a) comparison nesquehonite of experimental solubility innesquehonite water and the solubility calculated in water results and by thisthe calculated model. (b) results Nesquehonite by this m solubilityodel. (b) varyingNesquehonite with CO solubility2 partial pressurevarying with at various CO2 partial temperatures. pressure at various temperatures.

Compared with magnesite and nesquehonite, the experimental data of lansfordite solubility in water is even less. The experimental work covers the temperature range from 1.8 to 20 C and CO water is even less. The experimental work covers the temperature range from− −1.8 to 20 ◦°C and CO22 partial pressure fromfrom 1–101–10 atm.atm. Table5 5 shows shows the the averageaverage absoluteabsolute deviationdeviation of of thethe calculatedcalculated resultsresults with thisthis modelmodel fromfrom thethe currentcurrent availableavailable experimentalexperimental data.data. From the comparison,comparison, the calculatedcalculated results are are close close to to the the experimental experimental data. data. Figure 3 3 showsshows the the lansfordite lansfordite solubility solubility varying varying with with temperature atat variousvarious COCO22 partial pressures.pressures. The available experimental data points are also post on the ﬁgure.figure. The model results show its reliability toto predictpredict thethe solubilitysolubility trend.trend.

Energies 2019, 12, 4533 8 of 16

Energies 2019, 12, x FOR PEER REVIEW 8 of 16 Table 5. Average absolute deviation of lansfordite solubility in water between model calculation by thisTable model 5. Average and the absolute experimental deviation results. of lansfordite solubility in water between model calculation by this model and the experimental results. Reference Data Points T (◦C) PCO2 (atm) AAD% Reference Data Points T (°C) PCO2 (atm) AAD% Takahashi et al. [19] 6 1.8–20 0.987 1.84 Takahashi et al. [19] 6 − −1.8–20 0.987 1.84 Ponizonvskii et al. [20] 4 0 1.93–9.68 3.92 Ponizonvskii et al. [20] 4 0 1.93–9.68 3.92 Yanat’eva and Rassonskaya [21] 3 0–15 1 7.11 Yanat'eva and Rassonskaya [21] 3 0–15 1 7.11

0.90 Pco₂=0.987 atm, this model 0.80 Pco₂=2atm, this model Pco₂=10 atm, this model 0.70 Pco₂=0.987 atm, Takahashi et al. (1927) Pco₂=1 atm, Yanat'eva and Rassonskaya (1961) 0.60

0.50

0.40

0.30

0.20 Lansfordite solubility (molality) solubility Lansfordite 0.10

0.00 270 290 310 330 350 370 Temperature (K)

FigureFigure 3.3. ComparisonComparison ofof lansforditelansfordite solubility solubility in in water water at at various various temperatures temperatures and and pressures. pressures. Line Line is theis the calculated calculated results results by by this this model model and and dots dots are are from from experiments. experiments.

3.2.3.2. CO2 SolubilitySolubility AA complexcomplex system model should be able to reproduce experimental results of simple systems. DuanDuan andand Sun Sun [ 31[31]] developed developed an an accurate accurate model model (DS (DS model) model) for CO for2 solubilityCO2 solubility in water in orwater brine or within brine awithin wide pressure, a wide pressure, temperature, temperature and salinity, and range. salinity DS model range. has DS been model comprehensively has been comprehensively examined with existingexamined experimental with existing data experimental and is usually data treated and is as usually a reliable treated model. as Wea reliable compared model. this We model compared results forthis CO model2 solubility results for with CO DS2 solubility model with with temperature DS model with from temperature 0–250 ◦C, pressure from 0–250 from °C 1–1000, pressur bar,e from and NaCl1–1000 molality bar, and from NaCl 0 to molality saturated from condition. 0 to saturated Figure4 shows condition. the comparisons Figure 4 shows between the results comparisons from thisbetween model results and the from DS this model. model From and the the comparison, DS model. From this modelthe comparison, can reproduce this model the DS can model reproduce results withthe DS wide model TP rangeresults at with different wide NaClTP range concentrations. at different NaCl concentrations. ToTo evaluate evaluate the the influences influences of MgCO of MgCO3 dissolution3 dissolution on CO2 solubility on CO2 solubility in brine, numerical in brine, experiments numerical areexperiments conducted are with conducted cases of MgCO with3 casessaturated of MgCO solutions3 saturated or MgCO solutions3 free solutions or MgCO at various3 free temperatures solutions at andvarious pressures. temperatures Figure5 andshows pressures. the CO 2 Figuresolubility 5 shows in water the with CO MgCO2 solub3 ilitysaturated in water or free with conditions. MgCO3 Fromsaturated the comparisons,or free conditions. it can From be concluded the comparisons, that dissolution it can be of concluded MgCO3 in that water dissolution has little influenceof MgCO3 on in COwater2 solubility. has little This influence is because on COof the2 solubility. limited solubility This is of because MgCO of3 minerals. the limited solubility of MgCO3 minerals.

Energies 2019, 12, 4533 9 of 16 Energies 2019, 12, x FOR PEER REVIEW 9 of 16 Energies 2019, 12, x FOR PEER REVIEW 9 of 16 4.0 4.0 This model, mNaCl=0 3.5 This model, mNaCl=0mNaCl = 2 molal 3.5 This model, mNaCl = 24 molal 3.0 ThisDuan model, and Sun mNaCl (2003), = 4 mNaCl=0 molal 3.0 Duan and Sun (2003), mNaCl=0mNaCl=2 molal 2.5 Duan and Sun (2003), mNaCl=2mNaCl=4 molal 2.5 Duan and Sun (2003), mNaCl=4 molal 2.0

solubility 2.0 455.15K 2

solubility 1.5 455.15K

2 CO

1.5 CO 1.0 1.0 0.5 0.5 0.0 0.0 0 200 400 600 800 1000 0 200 400 Pressure (bar)600 800 1000 Pressure (bar) Figure 4. 4. COCO22 solubilitysolubility varying varying with with pressure pressure at di atﬀ erent different NaCl NaCl concentration concentration calculated calculated by this by model this (lines)Figuremodel and(lines) 4. CO DS 2and modelsolubi DS lity (dots).model varying (dots). with pressure at different NaCl concentration calculated by this model (lines) and DS model (dots). 2.5 2.5

2 393.15 K 2 393.15 K

1.5 1.5

1 MgCO3 free solubility solubility (molal)

2 1 MgCO3 free

solubility solubility (molal) 2

CO MgCO3 saturated

CO 0.5 MgCO3 saturated 0.5

0 0 0 200 400 600 800 1000 0 200 400Pressure (bar)600 800 1000 Pressure (bar)

Figure 5. CO2 solubility varying with pressure at 393.15 K in solutions with MgCO3 saturated (dots) Figureor free 5.(line) CCOO 2conditions. solubility varying withwith pressurepressure at at 393.15 393.15 K K in in solutions solutions with with MgCO MgC3Osaturated3 saturated (dots) (dots) or orfree free (line) (line) conditions. conditions. 3.3. Model Predictions 3.3. Model Predictions 3.3. Model Predictions With the new model, the following results can be calculated: (1) the solubility of MgCO3 minerals With the new model, the following results can be calculated: (1) the solubility of MgCO3 (i.e., Withlansfordite, the new magnesite model, the, and following nesquehonite) results canat various be calculated: conditions; (1) the (2) solubility solutions of properties MgCO3 minerals such as minerals (i.e., lansfordite, magnesite, and nesquehonite) at various conditions; (2) solutions properties (i.e.pH,, lansfordite,various ion magnesiteconcentrations, and nesquehonite)and carbonate atconcentrations various conditions; at various (2) solutions conditions properties of H2O such-NaCl as- such as pH, various ion concentrations and carbonate concentrations at various conditions of pH,MgC variousO3-CO2 systems.ion concentrations and carbonate concentrations at various conditions of H2O-NaCl- H2O-NaCl-MgCO3-CO2 systems. MgCO3-CO2 systems. 3.3.1. MgCO3 Mineral Solubility 3.3.1. MgCO3 Mineral Solubility MgCO3 mineral solubilities (i.e., lansfordite, magnesite, and nesquehonite) at various temperatures,MgCO3 mineral pressures solubilities, and NaCl (i.e. molalities, lansfordite, are calculated magnesite by, thisand model. nesquehonite) Figure 6 a at shows various the temperatures,solubility of magnesite pressures at, temperatureand NaCl molalities ranging between are calculated 0 and 200 by °C, this and model. pressure Figure rang 6aing shows between the solubility of magnesite at temperature ranging between 0 and 200 °C, and pressure ranging between

Energies 2019, 12, 4533 10 of 16

3.3.1. MgCO3 Mineral Solubility

MgCO3 mineral solubilities (i.e., lansfordite, magnesite, and nesquehonite) at various temperatures, pressures, and NaCl molalities are calculated by this model. Figure6a shows the solubility of magnesite at temperatureEnergies 2019, 12 ranging, x FOR PEER between REVIEW 0 and 200 ◦C, and pressure ranging between 1 and 1000 bar. Magnesite10 of 16 solubility decreases with temperature and increases with pressure. Figure6b shows the magnesite solubility1 and 1000 with bar. CO Magnesite2 mole fraction solubility at various decreases temperatures with temperature and 100 and bar. increases From the with results, pressure. the presence Figure of 6b shows the magnesite solubility with CO2 mole fraction at various temperatures and 100 bar. From CO2 in gas phase significantly enhances magnesite solubility in water. Figure6c shows the magnesite solubilitythe results, varying the presence with NaCl of molalitiesCO2 in gasat phase 100 barsignificantly and various enhances temperatures magnesite under solubility conditions in water. of gas Figure 6c shows the magnesite solubility varying with NaCl molalities at 100 bar and various free or 100% CO2. The NaCl molality can enhance the dissolution of magnesite. With same temperature, temperatures under conditions of gas free or 100% CO2. The NaCl molality can enhance the pressure, and NaCl molality, when the solution is in equilibrium with CO2, the magnesite solubility dissolution of magnesite. With same temperature, pressure, and NaCl molality, when the solution is increase is significant. in equilibrium with CO2, the magnesite solubility increase is significant. Similar behavior of nesquehonite and lansfordite solubilities are observed from Figure6d–i Similar behavior of nesquehonite and lansfordite solubilities are observed from Figure 6d–i at at various conditions except temperature effects. Nesquehonite solubility in water decreases with various conditions except temperature effects. Nesquehonite solubility in water decreases with temperature at lower temperature range (about 0–120 C) and increases with temperature at higher temperature at lower temperature range (about 0–120 °C)◦ and increases with temperature at higher temperaturetemperature range range (about (about more more than than 120 120◦ °C,C, FigureFigure6 6d).d). LansforditeLansfordite solubility in in water water increases increases with with temperaturetemperature with with the the entire entire range range from from 0–200 0–200◦ °CC (Figure(Figure6 6g).g).

0.0008 0.0007 P=1bar 0.0006 P=500 bar 0.0005 P=1000 bar 0.0004 (molality) 0.0003

Magnesite solubility 0.0002 0.0001 0 270 320 370 420 470 Temperature (K) (a) 0.04 1 0.035 100 bar 0.03 0.1 373.15 K 0.025 Total pressure: 100 bar 0.02 323.15K 0.01 0.015 373.15K 0% CO₂ in gas 423.15K 0.01 0.001 0.005 Magnesite solubility (molality) Magnesite solubility Magnesite solubility (molality) Magnesite solubility 0 0.0001 0 0.2 0.4 0.6 0.8 1 0246 CO mole fraction in gas phase NaCl molality 2 (b) (c)

Figure 6. Cont.

Energies 2019, 12, 4533 11 of 16 Energies 2019, 12, x FOR PEER REVIEW 11 of 16

0.09 0.6 0.08 323.15K 0.5 0.07 373.15K 1 bar 0.06 0.4 500 bar 0.05 1000 bar 0.3 Total pressure: 100 bar 0.04 (molality) (molality) 0.03 0.2 0.02 0.1 Nesquehonite solubility Nesquehonite solubility 0.01 0 0 0 0.2 0.4 0.6 0.8 1 270 320 370 420 470 CO2 mole fraction in gas phase Temperature (K) (d) (e) 1 0.45 0.4 0.35 0.1 100 bar 0.3 373.15 K 0.25 1 bar 0.2 500 bar

(molality) 1000 bar 0.01 0.15 0% CO₂ mole fraction in gas 0.1 Nesquehonite solubility 100% CO₂ mole fraction in gas 0.05

0.001 Lansfordite solubility (molality) 0 0246 270 320 370 420 470 NaCl molality in aqueous phase Temperature (K) (f) (g) 1.4 1.2 1.2 Total pressure: 100 bar 1 1 0.8 100 bar 0.8 373.15 K 0.6 0.6 0% CO₂ mole fraction in gas (molality) 0.4 323.15 K 0.4 100% CO₂ mole fraction in gas 373.15 K 0.2 Lansfordite solubilty 0.2 423.15 K 0

Lansfordite solubility (molality) 0 0 0.2 0.4 0.6 0.8 1 0246

CO2 mole fraction in gas phase NaCl molality in aqueous phase

(h) (i)

Figure 6. MgCO3 mineral solubility at various temperatures, pressures, NaCl molalitis, and CO2 mole Figure 6. MgCO3 mineral solubility at various temperatures, pressures, NaCl molalitis, and CO2 molefractions fractions in gas in gasphase. phase. (a) (Magna) Magnesiteesite solubility solubility in water in water varying varying with with temperature temperature at atvarious various pressures; (b) magnesite solubility in water varying with CO2 mole fraction in gas phase at various pressures; (b) magnesite solubility in water varying with CO2 mole fraction in gas phase at various temperaturetemperature and and 100 100 bar; bar; (c )( magnesitec) magnesite solubility solubility in in NaCl NaCl solutions solutions varying varying with with NaCl NaCl molality molality in casesin cases of 100% CO2 or 0% CO2 in gas phase; (d) nesquehonite solubility in water varying with of 100% CO2 or 0% CO2 in gas phase; (d) nesquehonite solubility in water varying with temperature at temperature at various pressures; (e) nesquehonite solubility in water varying with CO2 mole fraction various pressures; (e) nesquehonite solubility in water varying with CO2 mole fraction in gas phase. in gas phase. (f) nesquehonite solubility in NaCl solutions varying with NaCl molality; (g) lansfordite (f) nesquehonite solubility in NaCl solutions varying with NaCl molality; (g) lansfordite solubility in solubility in water varying with temperature at various pressures; (h) lansfordite solubility in water water varying with temperature at various pressures; (h) lansfordite solubility in water varying with

CO2 mole fraction in gas phase; (i) lansfordite solubility in NaCl solutions varying with NaCl molality.

Energies 2019, 12, x FOR PEER REVIEW 12 of 16

Energiesvarying2019, 12 with, 4533 CO2 mole fraction in gas phase; (i) lansfordite solubility in NaCl solutions varying with12 of 16 NaCl molality.

3.3.2. Solution Properties 3.3.2. Solution Properties

With the new thermodynamic model of CO2-H2O-NaCl-MgCO3 systems, the solution properties With the new thermodynamic model of CO2-H2O-NaCl-MgCO3 systems, the solution properties (such as pH, various species concentrations, distribution of carbonate species, etc.) can be calculated. (such as pH, various species concentrations, distribution of carbonate species, etc.) can be calculated. Figure7 shows the pH of solutions (saturated with CO 2) varying with pressure from 1 to 1000 bar at Figure 7 shows the pH of solutions (saturated with CO2) varying with pressure from 1 to 1000 bar at different temperatures under conditions of MgCO3 saturated or free. NaCl molality is 4 molal for all different temperatures under conditions of MgCO3 saturated or free. NaCl molality is 4 molal for all the scenarios. From Figure7, equilibrium with MgCO 3 minerals can significantly increase pH values the scenarios. From Figure 7, equilibrium with MgCO3 minerals can significantly increase pH values of the solutions. The MgCO3 minerals can be treated as “buffer minerals” for aqueous solutions. of the solutions. The MgCO3 minerals can be treated as “buffer minerals” for aqueous solutions.

4 pH 3

2 323.15K, saturated with MgCO3 mineral 343.15K, saturated with MgCO3 mineral 1 373.15K, saturated with MgCO3 mineral 323.15K 0 0 100 200 300 400 500 600 700 800 900 1000 Pressure (bar)

Figure 7. pH of solutions at various temperatures and pressures with or without MgCOMgCO33 saturated.

From the previous previous sections, sections, when when CO CO2 2oror carbonate carbonate minerals minerals dissolved dissolved in water, in water, it can it can be in be the in (aq) 2 (aq) theforms forms of ofCO CO2(aq)2, HC, HCOO3−, 3 C−O, CO32−, 3and−, and MgC MgCOO3(aq).3 Figure. Figure 8 8shows shows the the various various carbon carbon species species concentrations varyingvarying withwith pressure pressure at at 100 100◦C °C under under conditions conditions of MgCOof MgC3 mineralsO3 minerals saturated saturated or free. or (aq) Atfree. di ﬀAterent different conditions, conditions, most of most the carbonof the incarbon aqueous in aqueous solution issolution in the formis in ofthe CO form2 , of and CO HCO2(aq), 3and− is secondary.HCO3− is secondary. When the solutions When the are solutions in equilibrium are in with equilibrium the MgCO with3 minerals, the MgC higherO3 concentrationsminerals, higher of diconcentrationsﬀerent forms of different carbon can forms be observed. of carbon can be observed.

Energies 2019, 12, 4533 13 of 16 Energies 2019, 12, x FOR PEER REVIEW 13 of 16

1.0E+1 1.0E+0 1.0E-1 CO2(a) 1.0E-2 1.0E-3 CO₃²⁻ 1.0E-4 HCO₃⁻ 1.0E-5 CO2(a), MgCO3 1.0E-6 saturated

Species molality 1.0E-7 CO₃²⁻, MgCO3 saturated 1.0E-8 HCO₃⁻, MgCO3 1.0E-9 saturated 1.0E-10 1.0E-11 0 200 400 600 800 1000 Pressure (bar)

Figure 8. Carbonate concentrations varying with pressure under conditions of MgCOMgCO33 saturated or MgCOMgCO3 free.free. The The solid solid lines lines represent represent the the results with MgCOMgCO3 freefree and dashed lines represent the results with MgCOMgCO3 saturated.

4. Conclusions With regards to the importance of magnesium carbonate minerals to CO geological storage With regards to the importance of magnesium carbonate minerals to CO22 geological storage projects, we developed a thermodynamic model of CO -H O-NaCl-MgCO systems from 0–200 C, projects, we developed a thermodynamic model of CO22-H22O-NaCl-MgCO33 systems from 0–200 °C,◦ 1–10001–1000 bar bar,, and and halite halite up up to to high high concentration. concentration. The The model model can cancalculate calculate the phase the phase equilibria equilibria and and speciation including gas phase mole fractions, molality of aqueous species (such as CO 2 , speciation including gas phase mole fractions, molality of aqueous species (such as CO32−, HCO3 3−−, HCO , Mg2+, Mg(OH)+,H+, OH , CO (aq), and MgCO (aq)), pH, and dissolution and precipitation of Mg2+,3 −Mg(OH)+, H+, OH−, CO2(aq), −and MgC2 O3(aq)), pH, and3 dissolution and precipitation of MgCO3 MgCOminerals.3 minerals. To validate the model, model, we we compared compared the the model model results results with with the the current current existing existing data data in interms terms of of CO solubility in aqueous solutions, and MgCO mineral solubilities. From the comparison, CO CO2 solubility2 in aqueous solutions, and MgCO3 3mineral solubilities. From the comparison, CO22 solubility in in NaCl NaCl solutions solutions can can be be reproduced reproduced in ina wide a wide temperature, temperature, pressure pressure,, and andsalinity salinity range range with withsimilar similar accuracy accuracy as the previous as the previous work [31, work46]. The [31, 46experimental]. The experimental solubility of solubility nesquehonite, of nesquehonite, magnesite, magnesite, and lansfordite in aqueous solutions with various temperature and CO partial pressure can and lansfordite in aqueous solutions with various temperature and CO2 partial2 pressure can be bereproduced reproduced by bythis this model model.. The The AADAAD% %between between model model results results and and experimental experimental data data are are calculated. calculated. From the results, most of of the the experimental experimental data data can can be be reproduced reproduced with with AADAAD%% less less than than 10%. 10%. The model is used for the prediction of phase equilibria of CO -H O-NaCl-MgCO systems with The model is used for the prediction of phase equilibria of CO22-H22O-NaCl-MgCO33 systems with temperature fromfrom 0–2000–200◦ °C,C, pressure pressure from from 1–1000 1–1000 bar, bar and, and halite halite concentration concentration up up to 6to molal. 6 molal. From From the results,the results, the followingsthe followings can can be concluded. be concluded. (1) TemperatureTemperature usually decreases the mineral solubilities, and pressure usually increases the solubility.solubility. However, However, for for nesquehonite, nesquehonite, the the solubility solubility decreases decreases with temperature when the temperaturetemperature is is less less than than about about 100 100 °C◦C and and increases increases when when the the temperatu temperaturere is is higher higher than than 100 100 °C.◦C. ForFor lansfordite, lansfordite, the the solubility solubility increases with temperature from 0–2000–200 ◦°C.C. (2) TheThe presence presence of of CO C2Oin2 aqueousin aqueous solution solution or gases or phase gases will phase significantly will significantly enhance the enhance dissolution the dissolutionof MgCO3 minerals.of MgCO3 minerals. 2 3 (3) ForFor C COO 2 saturatedsaturated solutions, solutions, the the dissol dissolutionution of of MgC MgCOO 3 mineralsminerals will will increase increase the the pH of the 3 solutionssolutions at at different different temperature and pressure conditions. MgC MgCOO3 mineralsminerals can be treated as “buffer“buffer minerals”. (4) The influences of MgCO3 minerals on CO2 solubility are insignificant. However, the concentrations of carbon-bearing ions in the solutions are significantly increased by the dissolution of MgCO3 minerals.

Energies 2019, 12, 4533 14 of 16

(4) The influences of MgCO3 minerals on CO2 solubility are insignificant. However, the concentrations of carbon-bearing ions in the solutions are significantly increased by the dissolution of MgCO3 minerals.

Author Contributions: Conceptualization, methodology, validation, investigation, resources, data curation, and writing—original draft preparation, J.L.; writing—review and editing, X.L. and J.L. Funding: This research was funded by National Natural Science Foundation of China (Grant No. 41502246) and National Key R&D Program of China (Grant No. 2016YFE0102500). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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