Solubility of Barite up to 250 Â°C and 1500 bar in up to 6 m NaCl

Article pubs.acs.org/IECR

Solubility of Barite up to 250 °C and 1500 bar in up to 6 m NaCl Solution Wei Shi,* Amy T. Kan, Chunfang Fan, and Mason B. Tomson Department of Civil and Environmental Engineering, Rice University, MS 519, 6100 Main Street, Houston, Texas 77005, United States ABSTRACT: The ultrahigh temperature (150−200 °C), pressure (1000−1500 bar), and TDS (over 300 000 mg/L) encountered in oil and gas production from deepwater pose significant challenges to scaling prediction and control. An apparatus has been built to test scale formation at temperature up to 250 °C and pressure to 1700 bar (24 000 psi). The study expands the current knowledge of Barite (BaSO4) solubility to the condition of high temperature, pressure, and ionic strength. By fitting Pitzer’s model to experimental solubility data, this study also provides a feasible approach to assess the temperature and pressure dependence of virial coefficients in the Pitzer’s equations of ion activity coefficients through measurement of mineral solubility. The prediction of Barite solubility made by the Brine Chemistry Consortium software ScaleSoftPitzer (SSP) that has incorporated the newly developed coefficients is consistent with experimental measurement.

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INTRODUCTION The increasing demand for oil and gas over the last few decades has brought a steady growth in production from deep or ultradeep water. According to the Minerals Management Service,1 there has been a growing contribution from deepwater to the overall production in the Gulf of Mexico in the last couple of decades. This trend is projected to continue into the 2020s. In 2002, Dyer and Graham2 reported that many oil and gas reservoirs in the North Sea were characterized by high pressure (800−1000 bar, 12 000−15 000 psi), high temperature (over 175 °C), and very high salinity (total dissolved solids (TDS) ∼ 300 000 mg/L). More recently, Payne3 pointed out that the industry is continuously making firm strides in developing equipment and drilling systems toward the objectives of handling downhole temperature of up to 300 °C and pressure of over 1400 bar (20 000 psi). Oilfield produced water is characterized by high salinity resulting from single or multiple electrolytes. Prediction and control of scales in deepwater development relies on a thorough and accurate understanding of the thermodynamics and kinetics of the dissolution and precipitation processes of common scaling minerals at the ranges of temperature, pressure and TDS routinely encountered in such processes. For instance, prediction of solubility of various minerals requires precise values of both equilibrium constants (including solubility product of the minerals (Ksp) and other association constants for complexes, if applicable) and activity coefficients. Of these two categories of parameters, equilibrium constants are usually considered only functions of temperature and pressure and are independent of solution composition, whereas activity coefficients are related to all three variables. Current models and literature provide both theoretical and experimental approaches to estimate equilibrium constants for mineral dissolution at high temperature and pressure. The solubility of Barite (BaSO4) has been examined by several authors.4−7 Blount4 systematically studied Barite solubility at temperatures from 25 to 300 °C and pressures from 1 to 1400 bar in DI water. The solubility product was calculated based on measured solubility and activity coefficients of Ba2+ and SO42− estimated by the extended Debye−Huckel equation. Blount © 2012 American Chemical Society

also measured Barite solubility in 0.1 and 4 m NaCl solutions, but the highest pressure applied was only 500 bar. Helgeson8 presented theoretical approaches to model the thermodynamic properties from estimates of entropy, enthalpy, heat capacity, and partial molar volume, enabling the calculation of equilibrium constants for a large number of hydrothermal reactions at high temperature and pressure. Monnin9 studied the solubilities of Barite and celestite in the Na−K−Ca−Mg− Ba−Sr−Cl−SO4−H2O system at up to 200 °C and 1000 bar and provided a model for calculating the Ksp’s at different temperatures and pressures based on the standard entropy, enthalpy, heat capacity, and standard molar volumes. The Ksp’s of a variety of minerals, including Barite, have been reported in various sources for temperature up to 350 °C and pressure up to 2000 bar, and the values from different sources are usually consistent with each other.10−12 Activity coefficients of ions in solution can be estimated by a variety of approaches, such as the Davis, Debye−Huckel, Truesdell, and Jones (TJ) equations, Pitzer’s specific ion interaction theory, and a more recent UNIQUAC model,13,14 of which the latter two are considered to most accurately model complicated solutions encountered in oil and gas production. Pitzer’s equations are used in this study to calculate the activity coefficients of various species. Pitzer’s theory describes the behavior of solutes in aqueous solvent by combining a modified Debye− Huckel term and a virial series for the effects of short-range forces that uses various virial coefficients to characterize the binary and ternary interactions among ions and solvents. The virial coefficients for interactions between specific ions are considered functions of both temperature and pressure and are usually determined empirically based on experimental data. While the temperature dependence of many ion interactions has been studied, the pressure dependence of many specific coefficients is typically unavailable due to lack of experimental data at pressure higher than atmosphere or water vapor Received: Revised: Accepted: Published: 3119

September 8, 2011 January 5, 2012 January 12, 2012 January 12, 2012 dx.doi.org/10.1021/ie2020558 | Ind. Eng.Chem. Res. 2012, 51, 3119−3128

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematic of the apparatus for testing Barite solubility at high temperature and pressure.

pressure. Relevant Pitzer’s coefficients for the H2O−CO2− NaCl−CaCO3 system were studied by Harvie et al.,15 Christov and Møller,16 Greenberg and Møller17, and Duan and Li18 for temperature up to 250 °C but were assumed only a function of temperature. He19,20 developed a computer model “EQPITZER” that summarized and incorporated the temperature dependence of various coefficients for the Pitzer’s equation. Monnin9 reported the dependence of Pitzer’s coefficients on temperature up to 200 °C and 1000 bar. The effect of pressure was examined but not explicitly modeled. One exception was a study published by Pitzer et al21 in which the dependence of binary and ternary coefficients on both temperature and pressure was thoroughly investigated for pure NaCl solutions, although interactions with other common scaling ions were not mentioned. The effect of pressure might be insignificant at relatively low values but may become dramatic as pressure rises. For instance, the β(0)NaCl coefficient, according to Pitzer et al,21 increases from 0.1002 to 0.1058 (by 5.6%) as pressure rises from 1 to 700 bar, and further to 0.1331 at 1400 bar (by 32.8%). The increase in the partial derivative of β(0)NaCl with respect to pressure suggests that the contribution of the Na−Cl binary interaction to the apparent molar volume is greater at higher pressures. At a molecular level this may be related to the rather “open” cluster structure of water.22 Prediction of scale solubility for deepwater development is currently limited by inadequate knowledge about the thermodynamics, or more specifically, the pressure dependence of activity coefficients associated with common minerals at high temperature, high pressure, and high concentrations of mixed electrolytes. In this study, Barite solubility was measured at various temperatures, pressures, and ionic strengths in the NaCl−H2O system, up to 250 °C and 1500 bar (22 000 psi) and 6 m NaCl. On the basis of these results, relevant coefficients for Pitzer’s equations of activity coefficients were evaluated. Empirical equations that describe the temperature and pressure dependence of Pitzer’s coefficients were constructed and validated using both experimental data and values reported in the literature.

column (SS316, OD 1.43 cm, ID 0.48 cm, High Pressure Equipment Company) with a length of 10.2 cm and a pore volume of approximately 1 mL (corresponding to a porosity of 50%). High purity NaCl (99.999% trace metals basis, SigmaAldrich) was used as background electrolyte in the Barite solubility measurement. EDTA solution (0.2 M) at pH 10 was made by dissolving EDTA disodium salt (ACS reagent grade, Fisher Chemical) in DI water, followed by adjusting the pH to 10. High purity Na2SO4 (99.99% trace metals basis, SigmaAldrich) and BaCl2 (99.998% trace metals basis, Sigma-Aldrich) were used to prepare feed solutions with elevated concentrations of SO42− and Ba2+, respectively. Barite Solubility Measurement at High Temperature and High Pressure (HTHP). The schematic of the apparatus for Barite solubility measurement at high temperature (up to 250 °C) and pressure (up to 1700 bar, 24 000 psi) is shown in Figure 1. The Barite-packed column was placed in an oven for temperature control. Also enclosed in the oven was a preheating coil that connected the pump to the column to heat the feed solution to the desired temperature prior to its contact with the Barite particles. A NaCl solution was pumped into the column by a high pressure syringe pump (ISCO Teledyne 65 HP, up to 1700 bar, 24 000 psi) at a steady flow rate. An EDTA solution (0.2 m) was injected via a tee into the end of the column using a second syringe pump (ISCO Teledyne 65 HP) to prevent precipitation of BaSO4 as the solution cooled and the pressure dropped. The effluent from the column was cooled to room temperature via a cooling coil in a water bath before it reached a back pressure regulator (TESCOM 54-2100 series) that maintained the upstream pressure (at which dissolution took place) at the desired level. The effluent from the back pressure regulator was collected at room temperature and 1 atm for ion concentration analysis. All tubings and connections were manufactured by High Pressure Equipment Company with pressure ratings of at least 2100 bar (30 000 psi) and were made of 316 stainless steel except for the parts enclosed in the oven, which were made of Hastelloy C alloy to prevent corrosion at high temperature. Ba2+ and SO42− concentrations in the effluent were measured, taking into account the slight dilution by the stream of EDTA. All measurements were based

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MATERIALS AND METHODS Chemicals. High purity Barite particles (99.998% trace metals basis, Sigma-Aldrich) were packed in a stainless steel 3120

dx.doi.org/10.1021/ie2020558 | Ind. Eng.Chem. Res. 2012, 51, 3119−3128


Article

working equations can be found in a variety of sources,23,24 including his textbook on thermodynamics.24 When applied to a NaCl solution with comparatively negligible concentrations of Ba2+ and SO42−, the above equations can be reduced to the following forms for the activity coefficients of Ba2+ and SO42−, respectively.

upon sample mass, and concentrations were expressed in molality units. Barite dissolution tests were conducted at temperatures of 25, 100, 200, and 250 °C, pressures of 34.5 (about 41 for tests at 250 °C), 483, 1103, and 1517 bar (500, 7000, 16 000, and 22 000 psi), and background NaCl concentrations of 0.1, 1, 2, 4, and 6 mol/kg-H2O (m). The effect of retention time (RT) on dissolution equilibrium was examined by varying the flow rate of the feed solution. Similar effluent concentrations were observed at RT ranging from 0.5 to 10 min, suggesting equilibrium was achieved in less than 0.5 min. A feed flow rate of 0.5 mL/min was therefore chosen for the convenience of sample collection, corresponding to a RT of 2 min in the column. The EDTA solution was pumped at 0.005 mL/min, corresponding to 1% of the mainstream rate. Concentrations of Ba and S in the effluents were measured using inductively coupled plasma optical emission spectrometry (ICP-OES, Perkin-Elmer 4300DV). Total sulfate was calculated from total S concentration assuming sulfate is the only S species in the solution. Solubility of BaSO4 was calculated as the geometric mean of the Ba2+ and SO42− concentrations in the column effluent. The difference between concentrations of Ba2+ and SO42− was within 5% for most tests. Pitzer’s Model and Parametrization. Pitzer’s equations for activity coefficients of cations and anions in mixed electrolyte solution are shown in eqs 1 and 2, respectively.23,24

ln γBa = zBa 2F + mCl (2BBaCl + ZCBaCl) + mNa (2Φ NaBa + mCl ΨBaNaCl) + |zBa|mNa mCl CNaCl ln γSO4 = zSO4 2F + mNa (2B NaSO4 + ZCNaSO4) + mCl (2ΦClSO4 + mNa ΨSO4C lNa) + |zSO4|mNa mCl CNaCl where the F function can be calculated by eq 5. ⎛ ⎞ I 2 F = − AΦ⎜ + ln(1 + b I )⎟ + mNa mCl B NaCl ′ ⎝1 + b I ⎠ b

3/2 1/2 1 ⎛ 2πN0ρw ⎞ ⎛ e 2 ⎞ ⎟ A = ⎜ ⎟ ⎜ 3 ⎝ 1000 ⎠ ⎝ DkT ⎠

∑ ma(2BMa + ZCma)

+

+

Na a=1 Na

∑

∑

a = 1 a ′= a + 1 Nn

+

Nc Na

mama ′ΨMa ′ a + |zM| ∑

∑ mcmaCca

c=1 a=1 Nn

ac

∑ mn(2λ nM) + ∑ ∑ mnmaξnMa

(1)

n=1 a=1

n=1

Nc

ln γX = zX 2F +

∑ mc(2BcX

+ ZCcX )

c=1 Na

+

+

Na

∑ ma(2ΦaX + ∑ mc ΨcaX ) a=1 Nc − 1

Nc

c = 1 c ′= c + 1 Nn

+

Nc Na

mc mc ′Ψcc ′ X + |zX | ∑

(1) (2) B NaSO4 = β(0) NaSO4 + β NaSO4g (αNaSO4 I ) + β NaSO4g (12 I )

(8)

CBaCl =

Nn Nc n=1 c=1

(7)

∑ mcmaCca

c=1 a=1

∑ mn(2λnX) + ∑ ∑ mnmc ζncX n=1

(1) (2) BBaCl = β(0) BaCl + βBaClg (αBaCl I ) + βBaClg (12 I )

where αBaCl = 2.0, αNaSO4 = 2.0, 2[1 − (1 + x)e−x]/x2.

a=1

∑ ∑

(6)

where N0 is the Avogadro’s number, ρw the density of water, e the charge of the electron, D the dielectric constant of water, k the Boltzman’s constant, and T the temperature in K. ρw and D are calculated from equations in Kell and Bradley et al.25,26 At 200 °C and 1103 bar, for instance, the values are 928.099 kg/m3 and 38.4453, respectively. The various binary and ternary virial coefficients in the Pitzer’s equations can be calculated using the following equations.

∑ mc(2ΦMc + ∑ maΨMca) c=1 Na − 1

(5)

Φ

a=1 Nc

(4)

I is the ionic strength. BNaCl′ is the first derivative of BNaCl with respect to I. AΦ is the Debye−Huckel limiting law slope as defined in eq 6.

Na

ln γM = zM 2F +

(3)

2 |zBazCl|

CNaSO4 =

CNaCl =

= 0,

(2) βNaSO4

= 0, and g(x) =

Φ CBaCl

(2)

where, γM and γX are the activity coefficients of cations (M) and anions (X), respectively, and m is the concentration in molality. B and C are coefficients that denote the interactions between two oppositely charged ions. Φ stands for the interaction between two like-charged ions. λ denotes the binary interaction between neutral species and ions. Ψ represents the ternary interactions among three ions, while ξ and ζ are for those among one neutral species, one cation, and one anion. Z is the total molality of charges in the system, and z denotes the charge of an individual species. The summation index, c, a, or n, denotes the sum over all cations, anions, or neutral species in the system. The double summation index, c < c′ or a < a′, represents the sum over all distinguishable pairs of dissimilar cations or anions, respectively. Details of Pitzer’s theory and

(2) βBaCl

(9)

Φ CNaSO4

2 |zNazSO4|

(10)

Φ CNaCl

2 |zNazCl|

(11)

ΦBaNa = θBaNa + E θBaNa(I )

(12)

ΦClSO4 = θClSO4 + E θClSO4(I ) (13) The mean ion activity coefficient γ±,BaSO4, as defined in eq 14,27,28 can then be calculated by combining eqs 3 and 4.

γ±,BaSO4 = (γBaγSO4)1/2 3121

(14)



Article

1 ln γ±,BaSO4 = ln(γBaγSO4)1/2 = (ln γBa + ln γSO4) 2

Table 1. Comparison of β(1) Values between He and Monnin at Various Temperatures

(15)

(1) βNaSO4

Pitzer’s Coefficients at Different Temperatures and Pressures. The solubility product of Barite is defined by eq 16.

K sp,BaSO4 = mBa γBa ·mSO4 γSO4

temperature (°C)

He

Monnin

He

Monnin

25 100 150 200 250

1.10 1.33 1.38 1.45 1.86

1.10 1.33 1.38 1.44 1.59

1.22 1.76 2.27 2.81 3.34

1.22 1.76 2.27 2.81 3.34

(16)

The value of Ksp,BaSO4 can be calculated as a function of temperature and pressure by following the approach in Kharaka (eqs 17−20).10 Δ log10 K500 and Δl og10 K1000 are constants at a specific temperature to express the incremental increases in the logarithm of Ksp from 1 bar to 500 and 500 to 1000 bar, respectively. 6

Δ log10 K500 = A1 + A2(T − 273.15) + A3(T − 273.15)

(17)

Δ log10 K1000 = A4 + A5(T − 273.15) + A 6(T − 273.15)6

(18)

fitting approach and those calculated using eq 22. z PZ(T , P) = z1 + 2 + z3T + z4 ln T + z5T 2 T z ⎛ ⎞ + ⎜z6 + 7 + z8T + z 9 ln T + z10T 2⎟P ⎝ ⎠ T z ⎛ ⎞ + ⎜z11 + 12 + z13T + z14 ln T + z15T 2⎟P 2 ⎝ ⎠ T z17 ⎛ ⎞ + ⎜z16 + + z18T + z19 ln T + z 20T 2⎟P 3 ⎝ ⎠ T

At pressure below 500 bar, log10 K sp,BaSO4 = A7 + A8 /T + A 9 log10 T +

P Δ log10 K500 500

(19)

(22)

(0) (0) Φ Φ where PZ(T,P) stands for βBaCl , βNaSO4 , CBaCl , or CNaSO4 . T is temperature in K, and P is pressure in bar.

At pressure over 500 bar

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log10 K sp,BaSO4 = A7 + A8 /T + A 9 log10 T + Δ log10 K500 +

(1) βBaCl

P − 500 (log10 K1000 − Δ log10 K500) 500

RESULTS AND DISCUSSION Barite Solubility at Different Temperatures, Pressures, and Ionic Strengths. Solubilities of Barite at different temperatures, pressures, and ionic strengths are plotted in Figure 2. At a specified temperature and ionic strength, Barite becomes more soluble as pressure increases. At a specified pressure and ionic strength, Barite is also more soluble at higher temperature, with the exception at 0.1 m NaCl, at which condition the solubility increases and then decreases with temperature. For instance, at NaCl concentration of 0.1 m and pressure of 483 bar, the solubility increases from 0.046 mmol/ kg-H2O (mm) at 25 °C to 0.090 mm at 100 °C but decreases to 0.075 mm at 200 °C and further to 0.068 mm at 250 °C, a trend that is also observed at other pressures. Higher ionic strength results in, generally, higher solubility with the exception at relatively low temperature (25 °C, for instance) and high ionic strength (above 2 m), where the solubility appears less sensitive to ionic strength; the value either increases less rapidly (483 bar), remains stable (1103 bar), or slightly decreases (1517 bar) with increasing ionic strength. A similar trend is also observed at 100 °C. The maximum in solubility, or minimum in mean activity coefficient, is often explained as a balance between decreasing ion−ion interactions with ionic strength and increasing activity coefficients due to less free water in solution.29 The activity coefficients of barium and sulfate, as well as the mean activity coefficients, are plotted in Figure 3 against NaCl concentration for two conditions, 25 °C and 1517 psi and 250 °C and 1517 psi. The solubility product Ksp is a constant at a specified temperature and pressure, leaving the solubility only a function of (inversely related to) the mean activity coefficients. At 250 °C, both γBa and γSO4 decrease as NaCl concentration increases, and so does the mean activity coefficient, resulting in greater solubility at higher NaCl concentration. At 25 °C, however, although γSO4 continuously decreases with salt concentration, γBa decreases to a minimal value at about 1.5 m NaCl and then begins increasing as salt concentration further increases. The net result is that the mean activity coefficient becomes insensitive to background salt concentration at over

(20)

where T is temperature in K and P is pressure in bar. A1 to A12 are as follows. A1 = 0.394, A2 = −1.119 × 10−4, A3 = 1.5305 × 10−15, A4 = 0.674, A5 = 1.229 × 10−4, A6 = 1.9202 × 10−15, A7 = 136.035, A8 = −7680.41, and A9 = −48.595. The experimentally determined mean ion activity coefficient, γ±,BaSO4, can be calculated by 1/2

γ±,BaSO4 = (γBaγSO4)

⎛ K sp,BaSO4 ⎞1/2 =⎜ ⎟ ⎝ mBa mSO4 ⎠

(21)

where mBa and mSO4 are measured concentrations of Ba2+ and SO42− at equilibrium, respectively. For a specific temperature and pressure, the mean ion activity coefficient is only a function of the ionic strength (the NaCl concentration) and can be fitted to the experimentally determined activity coefficient by adjusting various binary and ternary coefficients in Pitzer’s equations. Pitzer et al.21 suggested in their investigation of the NaCl system that β(0) and CΦ were functions of both temperature and pressure, whereas β(1) was affected only by temperature. In this (0) (0) Φ Φ study, βBaCl , βNaSO4 , CBaCl , and CNaSO4 at each specific temperature and pressure were acquired using the above approach of fitting Φ eq 15 to experimental data calculated by eq 21. CNaCl was 21 obtained from Pitzer et al. as a function of both temperature and pressure, and other virial coefficients (including β(1)) were from He,20 who employed a similar format to Pitzer’s to describe the temperature dependence of various coefficients.19 The β(1) values calculated by He’s EQPITZER are compared with those reported by Monnin9 in Table 1. The two data sets agree well with each other, in spite of the slight difference at high temperature for the Na−SO4 interaction. An empirical expression that is similar to those proposed by Pitzer et al.21 and He19 is employed to describe the dependence of these four Pitzer coefficients on temperature and pressure (eq 22). Each Pitzer’s coefficient, z1 to z20, are adjustable parameters to achieve the best fit between values obtained from the above 3122



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Figure 3. Activity coefficients of Ba and SO4 and the mean activity coefficient at (a) 25 °C and 1517 bar and (b) 250 °C and 1517 bar.

lack of solubility data for minerals (including Barite), especially at high pressure. One of the very few sources was the study by Blount,4 who examined Barite dissolution at up to 300 °C and 1400 bar, but only in DI water. In his tests of up to 6 m NaCl solution, nonetheless, the highest pressure applied was only 500 bar. As one of the few attempts in recent years toward experimentally determining mineral solubility at high temperature, high pressure, and high ionic strength, not only do the results presented in this paper contribute to the extremely limited database, but the study also provides a reliable approach for acquiring data at these extreme conditions, whose testing capability can be expanded to accommodate more complicated solution conditions and other minerals. Model Construction for Solubility Prediction. Prediction of the Barite solubility at high temperature, pressure, and ionic strength requires precise values of two parameters, the solubility products (Ksp,BaSO4) and activity coefficients (γBa and γSO4). The solubility products used in this study are obtained by regression of high temperature−high pressure data reported by Helgeson and others (1978) as those used in SOLMINEQ.88 (Kharaka10), a computer code designed to model water-rock systems at high temperatures and pressures with much of the theoretic basis developed by Helgeson and his coworkers.8,30−32 The values are compared with those obtained from tests of Barite dissolution in DI water by Blount4 in Figure 4. The Ksp’s calculated by another software package that uses Helgeson’s theory to model standard molal thermodynamic properties of minerals, SUPCRT92,11 are also included in the comparison. Ksp,BaSO4 used in this study is consistent with those from the other two sources at temperatures below 200 °C and most pressures. At 250 °C, the values in this study agree well with Blount’s, in spite of the slightly greater

Figure 2. Solubility of Barite (in mmol/kg-H2O) at different background NaCl concentrations, pressures, and temperatures of (a) 25, (b) 100, (c) 200, and (d) 250 °C.

2 m NaCl, with the minimum value at approximately 3 m NaCl, corresponding to the maximum solubility at that point. The solubility measured in this study agrees well with those provided by other authors. For instance, Uchameysvili et al.5 reported Barite solubilities of about 0.24 and 0.5 mm at 1 and 2 m ionic strengths, respectively, at 250 °C and vapor pressure (41 bar), compared to 0.26 and 0.52 mm found in this study for these conditions, respectively. A similar comparison was with the study by Blount,4 who reported 0.23 mm and 0.34 mm at 100 and 200 °C, respectively, for 1 m ionic strength and 500 bar, whereas the values we found were 0.24 mm and 0.37 mm at the same conditions. In general, however, there has been a 3123



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Figure 4. Comparison of Ksp,BaSO4 values among Kharaka, SUPCRT92, and Blount at various temperatures and pressures.

Table 2. Fitting Coefficients for Pitzer’s Equations at Different Temperatures and Pressures T (°C)

P (bar)

(0) βBaCl

(1) a βBaCl

φ CBaCl

θBaNaa

ΨBaNaCla

(0) βNaSO4

a (1) βNaSO4

φ CNaSO4

θClSO4a

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

34.5 483 1103 1517 34.5 483 1103 1517 34.5 483 1103 1517 41 483 1103 1517

0.32892 0.34737 0.35581 0.32926 0.37533 0.36729 0.38470 0.36751 0.28739 0.25909 0.25673 0.21990 0.40837 0.29602 0.25859 0.26076

1.2499 1.2499 1.2499 1.2499 1.7642 1.7642 1.7642 1.7642 2.8052 2.8052 2.8052 2.8052 3.3402 3.3402 3.3402 3.3402

−0.02709 −0.03918 −0.03734 −0.02116 −0.05846 −0.05075 −0.05259 −0.04306 −0.03611 −0.03086 −0.03568 −0.01698 −0.06495 −0.02747 −0.02064 −0.02415

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0.042656 0.061114 0.069548 0.042995 0.18029 0.17225 0.18966 0.17247 0.17198 0.14368 0.14132 0.10449 0.26276 0.15041 0.11298 0.11515

1.0974 1.0974 1.0974 1.0974 1.3312 1.3312 1.3312 1.3312 1.4438 1.4438 1.4438 1.4438 1.5895 1.5895 1.5895 1.5895

0.002435 −0.00966 −0.00773 0.008365 −0.04498 −0.03727 −0.03911 −0.02958 −0.02533 −0.02009 −0.0249 −0.0062 −0.05757 −0.02009 −0.01326 −0.01677

0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

a

ΨSO4ClNaa

correlation coefficient (R2)

standard deviation of log10(γ±,BaSO4)

0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014

0.9966 0.9999 0.9991 0.9780 0.9924 0.9989 0.9966 0.9898 0.9796 0.9912 0.9955 0.9860 0.9999 0.9972 0.9978 0.9991

0.0144 0.0027 0.0060 0.0264 0.0250 0.0086 0.0126 0.0207 0.0663 0.0430 0.0300 0.0468 0.0043 0.0283 0.0245 0.0148

These coefficients are from He.20

250 °C among different sources could affect the accuracy of the calculations. The dependence of Pitzer’s coefficients on temperature and pressure is examined by following the approach presented in the Material and Methods section. Various coefficients for Pitzer’s equations of the Barite system (eqs 3 and 4) at each

discrepancy at higher pressure; the difference between Kharaka and Geological10 and SUPCRT92 appears more substantial, consistent with the observation by Kan and Tomson.33 In the following section, the solubility product from Kharaka10 is used in eq 21 to calculate the mean ion activity coefficient γ±BaSO4, although it is worthwhile to consider that the inconsistencies at 3124



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Table 3. Parameters z1 to z20 for eq 22 that Describe the Temperature and Pressure Dependence of Select Coefficients in Pitzer’s Equations z1 z2 z3 z4 z5 z6 z7 z8 z9 z10 z11 z12 z13 z14 z15 z16 z17 z18 z19 z20 a (1) βBaCl

(0) βBaCl

(1) a βBaCl

φ CBaCl

(0) βNaSO4

a (1) βNaSO4

φ CNaSO4

95.801749 −5.4608477 × 103 −4.8833520 × 10−2 −11.818390 5.3297770 × 10−5 1.1039358 × 10−1 6.3417923 × 10−1 1.4753289 × 10−4 −2.5932889 × 10−2 −9.8066716 × 10−8 9.4014442 × 10−3 −2.3046112 × 10−1 4.1372067 × 10−6 −1.7052096 × 10−3 −1.6464403 × 10−9 −6.2370652 × 10−6 1.5158183 × 10−4 −2.7826669 × 10−9 1.1335536 × 10−6 1.1220740 × 10−12

−104.22916 4.3740805 × 103 0.00322576 15.87491 −6.774397 × 10−6

−590.56823 1.5319574 × 104 −2.3638170 × 10−1 105.66257 8.5662630 × 10−5 7.29396 × 10−1 −1.9508071 × 101 2.7525616 × 10−4 −1.2950289 × 10−1 −9.2431384 × 10−8 −5.9503520 × 10−3 1.4543046 × 10−1 −2.6323817 × 10−6 1.0800715 × 10−3 1.0532704 × 10−9 3.6740758 × 10−6 −8.9164338 × 10−5 1.6430419 × 10−9 −6.6797724 × 10−7 −6.6394784 × 10−13

593.05428 −1.6896561 × 104 1.9730520 × 10−1 −103.591 −5.5665840 × 10−5 1.1057962 × 10−1 6.2973669 × 10−1 1.4761806 × 10−4 −2.596682 × 10−2 −9.810188 × 10−8 9.4011715 × 10−3 −2.3045459 × 10−1 4.1370820 × 10−6 −1.7051599 × 10−3 −1.6463887 × 10−9 −6.2369633 × 10−6 1.5157943 × 10−4 −2.7826208 × 10−9 1.1335353 × 10−6 1.1220547 × 10−12

−39.96416 −1.34296016 × 103 −0.07893828 11.28639004 5.3952418 × 10−5

−607.44173 1.5866776 × 104 −2.4075460 × 10−1 108.52396 8.6432240 × 10−5 7.3028907 × 10−1 −1.9531613 × 101 2.7561490 × 10−4 −1.2966257 × 10−1 −9.2565083 × 10−8 −5.9526195 × 10−3 1.4549027 × 10−1 −2.6332934 × 10−6 1.0804767 × 10−3 1.0536104 × 10−9 3.6751900 × 10−6 −8.9193715 × 10−5 1.6434898 × 10−9 −6.6817641 × 10−7 −6.6411462 × 10−13

(1) and βNaSO4 are from He.20

nonideality, which could potentially account for the deviation between modeled and measured data. While the validation and improvement of such a model may require collection of more experimental data from different sources, the model presented in this study, nevertheless, represents one of the first trials to examine the empirical dependence of Pitzer’s coefficients on temperature and pressure for the Barite system and also demonstrates a feasible working approach of investigating these relationships through measurement of mineral solubility. Application toward Mixed Electrolytes. Challenges associated with applying Pitzer’s model to concentrated solutions with mixed electrolytes at high temperature and pressure, which is commonly encountered in deep water production, result from the need to account for not only various interactions among different species but also possible formation of ion pairs between solutes exhibiting strong association. According to Monnin,9 the concentration of the barium sulfate ion pair BaSO4(0), which is negligible in Barite saturated pure water, accounts for 50% of the total barium in 0.01 m Na2SO4 solution when calculated using the ion pair stability constant reported by Felmy et al.34 Pitzer’s model employs a specific coefficient β(2) (as in eqs 7 and 8, the value of which is zero except for 2−2 ion pairs) to account for the association between divalent cations and anions (Ba2+ and SO42−, for instance), although it has been suggested by other authors that an explicit ion pair term has to be included in the model instead of using the β(2) correction.9,15 Pitzer24 shows that the term is related to the association constant of the ion pair Kassoc by

temperature and pressure are listed in Table 2. For each of these coefficients, fitting parameters z1 to z20 in eq 22 are listed in Table 3. These parameters are then used to model the activity coefficients of Ba2+ and SO42−, which, together with the Ksp values discussed above, are used to model the solubility of Barite as a function of temperature, pressure, and NaCl concentration. The modeled solubilities are plotted in Figure 5 as continuous or dashed lines. The discrete data points represent the values obtained from experimental measurement in this study, except for those labeled with open diamonds, which are from Blount, for comparison. It appears that the current model achieves a close fit to the experimental data from both this study and the one of the very few other data sources (Blount) under most conditions despite occasional discrepancies. For instance, the prediction at 200 °C and 4 m NaCl slightly overestimates the solubility at all pressures; the modeled value is about 13% higher than the measured at 1517 bar. The trend of incremental solubility at 6 m NaCl also appears inconsistent with other conditions at high pressure. The inclusion of pressure dependence of select coefficients in the Pitzer’s equations has significantly improved the model’s prediction, as exemplified by the comparison in Figure 6 for 200 °C, 6 m NaCl, and various pressures. At 1103 bar, for instance, the prediction without pressure dependence is 27% lower than the measured value, which has been reduced to less than 2% when the pressure dependence is included. The current approach of model construction has assumed that the binary and ternary Ba−Cl and Na−SO4 interactions are the predominant contributions to the nonideality of Ba2+ and SO42− ions in concentrated NaCl solution23,24 and therefore examined the temperature and pressure dependence of only the corresponding β and CΦ terms in the Pitzer equations; the other terms denoting the interactions between like-charged ions and among three ions were obtained from the literature as constants.20 It is possible that at certain points the variations of these coefficients with temperature and pressure become important enough to make significant contributions to the overall

β(2) = −

K assoc 2

(23)

Experiments using 1 m NaCl solutions with different Ba2+ and SO42− concentrations were conducted to test the applicability of the current model which incorporated the temperature and pressure dependence of Pitzer’s coefficients for Ba−Cl and Na−SO4 interactions derived in pure NaCl 3125



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Figure 6. Comparison between predictions with and without pressure dependence of Pitzer’s coefficient. (2) associated with Ba−SO4 interaction (including βBaSO4 ) are 35 obtained from Kaasa who assumes that this interaction is the same as that between Ca and SO42−, but not derived in this study. Table 4 lists the temperatures, pressures, and feed Ba2+ and SO42− concentrations of the series of experiments. Also presented in the table are the saturation indices (SI), defined as the logarithms of the ion activity product (aBa·aSO4) over the solubility product (Ksp,BaSO4), the values of which should be zero at dissolution equilibrium. The fact that the SI values are mostly within the range of plus or minus 0.1 for tests with Ba2+ concentration of 280 mg/kgH2O and SO42− concentration of 200 mg/kg-H2O suggests that the various coefficients currently used are sufficient to account for the Ba−SO4 interaction (including ion pair association), enabling the model to provide reliable predictions at this level of Ba2+ and SO42− concentrations. The greater deviations at SO42− concentration of 2800 mg/kg-H2O (up to 0.4 SI unit) could be mostly eliminated by adjusting only β(2) as a function of temperature (T in K) and pressure (P in bar) (eq 24).

β(2) BaSO4 = − 9451.078842 − 15073.43637/ T + 1401.983844 ln T + 0.076846245P

(24)

At this point, however, it is difficult to examine the correlation between β(2) and K(0) because of the lack of the latter data. The stability constant of BaSO4(0), for instance, is only reported at room temperature in DI water and 1 m NaClO4 solution.34,36 Determination of K(0) in high salinity systems is further complicated by insufficient knowledge about the activity coefficients of ion pairs. This study suggests a feasible approach to estimate stability constants by eq 23 through parametrization (2) of various Pitzer’s coefficients (including βBaSO4 ) using solubility measured in the entire range of pressures and temperatures as well as Ba2+ and SO42− concentrations. These tests are currently being conducted and will be reported as separate studies addressing adjustment of various coefficients for model applications toward more complicated solutions at high temperature and pressure.

Figure 5. Prediction of Barite solubility at various temperatures, pressures, and background NaCl concentrations using the temperature and pressure dependence parameters listed in Table 3. In each graph, continuous or dashed lines denote predictions for different background NaCl concentrations as labeled on the right. Discrete data points are values measured in this study, with the exception of those labeled with open diamonds, which are values reported by Blount included for comparison.

■

CONCLUSION Despite the difficulty in conducting scaling tests at high temperature and pressure, an apparatus was built to investigate scale formation and inhibition at ultrahigh temperature (up to 250 °C) and pressure (up to 1700 bar). The apparatus offers a reliable and efficient method for conducting studies on mineral dissolution under these extreme conditions. The experimental

solution to a condition possibly associated with substantial formation of the BaSO4(0) ion pair. Note that the coefficients 3126



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Table 4. Effluent Barite SI Values for Tests at Different Ba and SO4 Concentrations in the Feed Solution temperature (°C)

pressure (bar)

ionic strength (m)

feed Ba2+ (mg/kg-H2O)

feed SO42− (mg/kg-H2O)

25 150 250 25 150 250 250 25 150 250 250

35 500 1000 35 500 1000 1500 35 500 1000 1500

1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 280 280 280 280

200 200 200 2800 2800 2800 2800 0 0 0 0

*

(2) The original βBaSO4 values are from Kaasa.35

measurement of Barite solubility expands the currently limited database of mineral solubility to the area that combines high temperature, high pressure, and high ionic strength, with the flexibility to adapt to more complicated solution conditions, other types of minerals, and other modes of testing. This study also represents one of the first viable attempts to assess the dependence of Pitzer’s coefficients for the Barite system on both temperature and pressure through measurement of solubility. The Brine Chemistry Consortium software SSP that has incorporated the newly developed coefficients provides reliable prediction of Barite solubility that is consistent with experimentally measured values from both this study and the literature at most conditions. On the other hand, the extremely limited availability of thermodynamic data at high temperature, high pressure, and high ionic strength with mixed electrolytes has been one of the critical factors that confines the construction of models for accurate prediction of scale formation and dissolution at these conditions. While the solubility of Barite has been measured in a few studies at elevated temperature and pressure, collection of more extensive solubility data at different conditions, especially in the presence of mixed electrolytes, is highly desirable not only to validate the model presented in this study but also to address specific issues such as proper handling of ion pair formation for model applications toward actual oil field brines. The examination of the temperature and pressure dependence of various Pitzer’s coefficients would not only benefit solubility prediction in particular but could also be extended to investigating the thermodynamic properties of other systems where the specific interactions addressed here (for instance, Ba−Cl and Na−SO4) are important. Examples include freezing point depression, boiling point elevation, vapor pressure lowering, isopiestic and vapor equilibrium, enthalpy of mixing, heat capacity, diffusion measurements, and solubility of other minerals. Expansion of testing capacity is also needed in terms of the type of scale, modes of testing (e.g., precipitation or scale inhibition), and ranges of temperature, pressure, and brine composition to accommodate the continuing growth of deepwater production.

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original* (2) βBaSO4 −54.24 −118.74 −170.34 −54.24 −118.74 −170.34 −170.34 −54.24 −118.74 −170.34 −170.34

effluent SI

adjusted (2) βBaSO4

adjusted effluent SI

0.025 0.046 0.013 0.388 0.236 0.109 0.152 0.123 0.068 −0.003 0.016

−1511.05 −970.787 −626.811 −1511.05 −970.787 −626.811 −587.063 −1511.05 −970.787 −626.811 −587.063

−0.008 0.025 0.012 −0.057 −0.026 −0.028 0.020 0.093 0.049 −0.004 0.001

■

ACKNOWLEDGMENTS

■

REFERENCES

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

(1) Minerals Management Service. Deepwater Gulf of Mexico 2008: America’s Offshore Energy Future; 2008. (2) Dyer, S. J.; Graham, G. M. The effect of temperature and pressure on oilfield scale formation. J. Pet. Sci. Eng. 2002, 35 (1−2), 95−107. (3) Payne, M. HP/HT Challenges. J. Pet. Technol. 2011, 4, 86. (4) Blount, C. W. Barite solubilities and thermodynamic quantities up to 300 degrees C and 1400 bar. Am. Mineral. 1977, 62 (9−10), 942−957. (5) Uchameyshvili, N. Y.; Malinin, S. D.; Khitarov, N. L. Solubility of Barite in concentrated chloride solutions of some metals at elevated temperatures in relation to problems of the genesis of Barite deposits. Geochem. Int. 1966, 10, 951−963. (6) Templeton, C. C. Solubility of barium sulfate in sodium chloride solutions from 25 to 95 °C. J. Chem. Eng. Data 1960, 5 (4), 514−516. (7) Jiang, C. Solubility and solubility constant of barium sulfate in aqueous sodium sulfate solutions between 0 and 80°C. J. Solution Chem. 1996, 25 (1), 105−111. (8) Helgeson, H. C. Thermodynamics of hydrothermal systems at elevated temperatures and pressures. Am. J. Sci. 1969, 267 (7), 729− 804. (9) Monnin, C. A thermodynamic model for the solubility of Barite and celestite in electrolyte solutions and seawater to 200°C and to 1 kbar. Chem. Geol. 1999, 153 (1−4), 187−209. (10) Kharaka, Y. K. SOLMINEQ.88, a computer program for geochemical modeling of water-rock interactions; Dept. of the Interior, U.S. Geological Survey; U.S. Geological Survey, Books and Open-File Reports: Menlo Park, CA; Denver, CO, 1989. (11) Johnson, J. W.; Oelkers, E. H.; Helgeson, H. C. SUPCRT92: A software package for calculating the standard molal thermodynamic properties of minerals, gases, aqueous species, and reactions from 1 to 5000 bar and 0 to 1000°C. Comput. Geosci. 1992, 18 (7), 899−947. (12) Naumov, G. B.; Ryzhenko, B. N.; Khodakovskii, I. L.; Barnes, I.; Speltz, V. Handbook of thermodynamic data; U.S. Geological Survey, Water Resources Division: Menlo Park, CA; Springfield, VA, 1974. (13) Thomsen, K.; Rasmussen, P. Modeling of vapor-liquid-solid equilibrium in gas-aqueous electrolyte systems. Chem. Eng. Sci. 1999, 54 (12), 1787−1802.

AUTHOR INFORMATION

Corresponding Author

*Tel.: 713-348-2149. E-mail: [email protected]. 3127



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(14) García, A. V.; Thomsen, K.; Stenby, E. H. Prediction of mineral scale formation in geothermal and oilfield operations using the Extended UNIQUAC model: Part II. Carbonate-scaling minerals. Geothermics 2006, 35 (3), 239−284. (15) Harvie, C. E.; Møller, N.; Weare, J. H. The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3CO3-CO2-H2O system to high ionic strengths at 25°C. Geochim. Cosmochim. Acta 1984, 48 (4), 723−751. (16) Christov, C.; Moller, N. A chemical equilibrium model of solution behavior and solubility in the H-Na-K-Ca-OH-Cl-HSO4-SO4H2O system to high concentration and temperature. Geochim. Cosmochim. Acta 2004, 68 (18), 3717−3739. (17) Greenberg, J. P.; Møller, N. The prediction of mineral solubilities in natural waters: A chemical equilibrium model for the Na-K-Ca-Cl-SO4-H2O system to high concentration from 0 to 250°C. Geochim. Cosmochim. Acta 1989, 53 (10), 2503−2518. (18) Duan, Z.; Li, D. Coupled phase and aqueous species equilibrium of the H2O-CO2-NaCl-CaCO3 system from 0 to 250 °C, 1 to 1000 bar with NaCl concentrations up to saturation of halite. Geochim. Cosmochim. Acta 2008, 72 (20), 5128−5145. (19) He, S.; Morse, J. W. The carbonic acid system and calcite solubility in aqueous Na-K-Ca-Mg-Cl-SO4 solutions from 0 to 90°C. Geochim. Cosmochim. Acta 1993, 57 (15), 3533−3554. (20) He, S. The carbonic acid system and solubility of calcium carbonate and sulfate in aqueous solutions over a wide range of solution composition, temperature and pressure. Texas A&M University: College Station, TX, 1992. (21) Pitzer, K. S.; Peiper, J. C.; Busey, R. H. Thermodynamic Properties of Aqueous Sodium Chloride Solutions. J. Phys. Chem. Ref. Data 1984, 13 (1), 1−102. (22) Bockris, J. O. M.; Reddy, A. K. N. Modern Electrochemistry 1; Plenum Press: New York, NY, 1998. (23) Pitzer, K. S. Thermodynamics of electrolytes. I. Theoretical basis and general equations. J. Phys. Chem. 1973, 77 (2), 268−277. (24) Pitzer, K. S. Thermodynamics; McGraw-Hill, Inc.: New York, 1995. (25) Kell, G. S. Density, thermal expansivity, and compressibility of liquid water from 0° to 150 °C: Correlations and tables for atmospheric pressure and saturation reviewed and expressed on 1968 temperature scale. J. Chem. Eng. Data 1975, 20 (1), 97−105. (26) Bradley, D. J.; Pitzer, K. S. Thermodynamics of electrolytes. 12. Dielectric properties of water and Debye-Hueckel parameters to 350.degree.C and 1 kbar. J. Phys. Chem. 1979, 83 (12), 1599−1603. (27) Langmuir, D. Aqueous environmental geochemistry; Prentice Hall: 1997. (28) Stumm, W.; Morgan, J. J. Aquatic Chemistry; Wiley-Interscience: New York, NY, 1996. (29) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworth: London, U.K., 1959. (30) Helgeson, H. C. Thermodynamics of complex dissociation in aqueous solution at elevated temperatures. J. Phys. Chem. 1967, 71 (10), 3121−3136. (31) Helgeson, H. C.; Kirkham, D. H.; Flowers, G. C. Theoretical prediction of the thermodynamic behavior of aqueous electrolytes by high pressures and temperatures; IV, Calculation of activity coefficients, osmotic coefficients, and apparent molal and standard and relative partial molal properties to 600 degrees C and 5kb. Am. J. Sci. 1981, 281 (10), 1249−1516. (32) Shock, E. L.; Helgeson, H. C. Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: Correlation algorithms for ionic species and equation of state predictions to 5 kb and 1000°C. Geochim. Cosmochim. Acta 1988, 52 (8), 2009−2036. (33) Kan, A. T.; Tomson, M. B. Scale Prediction for Oil and Gas Production. Presented at CPS/SPE International Oil & Gas Conference and Exhibition, Beijing, China, 2010. (34) Felmy, A. R.; Rai, D.; Amonette, J. E. The solubility of Barite and celestite in sodium sulfate: Evaluation of thermodynamic data. J. Solution Chem. 1990, 19 (2), 175−185.

(35) Kaasa, B. Prediction of pH, mineral precipitation and multiphase equilibria during oil recovery. Norges Teknisk-Naturvitenskapelige Universitet: 1998. (36) Sillén, L. G.; Martell, A. E.; Högfeldt, E.; Perrin, D. D. Stability constants of metal-ion complexes: supplement; Chemical Society: London, 1971; Vol. 21−22, p v.

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Solubility of Barite up to 250 Â°C and 1500 bar in up to 6 m NaCl

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