Jonathan D. Sharp • Muayad H. M. Albehadili •
Frank J. Millero • Ryan J. Woosley
Received: 21 November 2014 /Accepted: 9 January 2015 Springer Science+Business Media Dordrecht2015
Abstract Measurements of density and compressibility of naturally occurring hypersaline brines (Red Sea, Dead Sea, Orca Basin, and Mono Lake) have been analyzed using Pitzer’s ionic interaction model. Pitzer’s volume and compressibility equations for the major components of brines have been used to est imate the densities and compressibilities as a function of temperature and salinity. The estimates at 25 C were in reasonable agreement with the measured values (0.008 ± 0.127 9 10-3 g cm-3). At higher and low er temperatures (0–40 C), estimates are less reliable (0.229 ± 0.246 9 10-3 g cm-3). This is largely due to the lack of Pitzer parameters for all the salts at high concentration as a function of temperature. The compressibility estimates at 25 C are in reasonable agreement with measured values (0.184 ± 0.261 9 10-6 bar-1), but the estimates from 15 to 35 C are less reliable (0.204 ± 0.726 9 10-6 9 bar-1), especially at high salinities. This is largely due to the limited compressibility data as a function of temperature for the major components of brines. These results demonstrate the utility of the Pitzer ionic interaction model to obtain reasonable estimates of density and compressibility of natural brines of known composition
Keywords Density Compressibility Natural brines Pitzer equations Molal volume Molal adiabatic compressibility
1 Introduction
The chemical compositions of natural brine solutions (Millero 1983b, 2009) in various ocations across the globe have been well documented. These brines include the deep J. D. Sharp F. J. Millero (&) R. J. Woosley Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker
Causeway, Miami, FL 33149, USA e-mail: fmillero@rsmas.miami.edu M. H. M. Albehadili Department of Marine Environmental Chemistry, Marine Science Centre, Basra University, Basra, Iraq waters of the Red Sea (Brewer et al. 1965; Millero et al. 1982), the Gulf of Mexico’s Orca Basin (Shokes et al. 1977; Millero et al. 1979), the Dead Sea (Krumgalz and Millero 1982a, 1982b, 1983, 1989), and Mono Lake (Jellison and Melack 1993; Jellison et al. 1999). Some direct measurements of density and sound speed on both natural and artificial samples of these brines are available (Millero et al. 1979, 1982; Krumgalz and Millero
1982b; Jellison et al. 1999). These measurements can be used to examine the reliability of ionic interaction models to estimate volumetric properties of multi-electrolyte solutions like natural brines. The Pitzer ionic interaction model (Pitzer 1991) has been used successfully in the past to estimate various geochemical properties of natural brines from their chemical compositions such as evaporation (Harvie et al. 1980; Hardie 1990; Charykova et al. 1995a, 1995b; Krumgalz 2001), mineral precipitation (Krumgalz and Millero 1983, 1989; Krumgalz et al. 1990, Krumgalz 2001), mineral solubility (Felmy and Weare 1986), and
density (Monnin 1989; Krumgalz et al. 1995, 2000). Three previous studies provide comparisons between density measurements and estimates made from the Pitzer model: Monnin (1989) on artificial Red Sea and Dead Sea measurements at 25 C with an accuracy of 0.239 ± 0.171 9 10-3 g cm-3 , Krumgalz et al. (1995) on artificial Dead Sea measurements at 25 C with an accuracy of 0.0 62 ± 0.030 9 10-3 g cm-3
, and Krumgalz et al. (2000) on artificial Dead Sea measurements from 20 to 40 C with an accuracy
of 0.143 ± 0.171 9 10-3 g cm-3 . Only Krumgalz et al. (1995) considered the need to use higher-order mixing parameters in the estimates. More recently, Pitzer’s model has been used successfully to estimate volumetric properties (density and compressibility) of seawater from 0 to 90 C and salinities from 0
to 45 g kg-1 (Rodriguez and Millero 2013). In Rodriguez and Millero’s work, the seawater density esti mates from 0 to 80 C and salinities from 0 to 45 g kg-1 agree with measured values to ±0.012 9 10-3 g cm-3 . Seawater adiabatic compressibility estimates from 0 to 70 C and salinities from 0 to 45 g kg-1 agree with measured values to ±0.04 9 10-6 bar-1 . In this paper, we have used the Pitzer equations to improve and expand upon the earlier density estimates of Monnin (1989) and Krumgalz et al. (1995, 2000). We have used updated single electrolyte molal volume coefficients for Pitzer’s model and higher-order mixing parameters to estimate density of four naturally occurring brines across a range of
temperatures and salinities. Additionally, in light of Rodriguez and Millero’s recent work (2013), we have tested the effectiveness of Pitzer’s model for estimating adiabatic compressibility of natural brines. We have used newly available single electrolyte molal adiabatic compressibility coefficients for Pitzer’s model to estimate compressibility of the same four brines across a similar range of temperatures and salinities (Millero and Sharp 2013). Our estimates of the two volumetric properties are compared to direct meas urements on both natural and artificial samples of the brines
2 Literature Data for Brines
The compositions of the four natural brines considered in this paper (Red Sea brines, Orc Basin brines, Dead Sea brines, and Mono Lake brines) along with seawater (Millero et al. 2008) are given in Table 1 by weight and molality. Measurements of density and sound speed were taken from the results of previous studies and are described in detail below. Density measurements of artificial Red Sea brines were taken from Millero et al. (1982). The measurements were made at 25 C and salinities from &26 to 257 g kg-1
. Density
| Seawater | Red Sea | Orca Basin | Dead Seaa | Mono Lake | ||||||||||
| % | m | % | m | % | m | % | m | % | m | |||||
| Na+ | 30.6598 | 0.4861 | 36.1715 | 5.4350 | 37.8648 | 5.5316 | 11.9941 | 1.8410 | 36.1781 | 1.4325 | ||||
| Mg2+ | 3.6506 | 0.0547 | 0.3159 | 0.0449 | 0.4176 | 0.0577 | 12.6734 | 1.8400 | 0.0347 | 0.0013 | ||||
| Ca2+ | 1.1719 | 0.0107 | 1.8339 | 0.1581 | 0.4336 | 0.0363 | 5.2245 | 0.4600 | 0.0066 | 0.0002 | ||||
| K+ | 1.1350 | 0.0106 | 0.8393 | 0.0742 | 0.2504 | 0.0215 | 2.2603 | 0.2040 | 1.7696 | 0.0412 | ||||
| Sr+ | 0.0226 | 0.0001 | 0.0170 | 0.0007 | ||||||||||
| Cl– | 55.0348 | 0.5658 | 60.4882 | 5.8936 | 59.4638 | 5.6332 | 66.1087 | 6.5800 | 20.9221 | 0.5372 | ||||
| SO42- | 7.7133 | 0.0293 | 0.2898 | 0.0104 | 1.4557 | 0.0509 | 0.1470 | 0.0054 | 11.9881 | 0.1136 | ||||
| HCO3– | 0.2978 | 0.0018 | 0.1141 | 0.0063 | 0.0069 | 0.0004 | 3.5995 | 0.0537 | ||||||
| Br– | 0.1912 | 0.0009 | 0.0444 | 0.0019 | 1.5851 | 0.0700 | ||||||||
and sound speed measurements of natural Orca Basin waters were taken from Millero et al. (1979). The measurements were made at 15, 25, and 35 C and at salinities of&251 g kg-1. Density measurements of artificial Dead Sea brines were taken from Krumgalz and Millero (1982b). Because Dead Sea brines differ slightly in composition at different times and in different locations (Neev and Emery 1966, 1967; Nissen baum 1970; Marcus 1977; Beyth 1980), a number of artificial solutions were prepared with somewhat different ionic compositions. The compositions were determined from the data of Marcus (1977), Neev and Emery (1967), and Levy (1979; personal communication), and are available in the appendix (Table 2). The density measurements were made from 20 to 40 C and salinities from &247 to 271 g kg-1. Density measurements of natural Mono Lake waters were taken from Jellison et al. (1999). The measurements were made from 5 to 25 C and salinity from &35 to 83 g kg-
3 Density and Compressibility Measurements
Additional measurements of density and compressibility were made on artificial solutions prepared according to the compositions in Table 1 (Dead Sea solution was prepared according to the average of the compositions in appendix Table 2) and diluted to lower salinities with deionized water. The densities of the brines were measured with an Anton Paar DMA 5000 vibrating tube densimeter (Anton Paar, Graz, Austria) at fixed temperatures determined by two platinum resistance thermometers embedded in the system. The densimeter was calibrated with deionized water (Millipore Super Q) and dry air. The densities were measured to a precision of ±0.003 kg m-3 The sound speeds were measured at 2 MHz with a Nus onic sing-around sound velocimeter (Nusonic, Inc.) in a 300-cm3 cell controlled to ±0.005 C with a Thermo Scientific bath and measured with a Guideline digital platinum resistance thermometer. The details of the sing-around sound velocimeter are described elsewhere (Millero and Kubinski 1975). The system was calibrated with deionized water (Millipore Super Q) using the equations of Del Grosso and Mader (1972) to a precision of ±0.03 m s-1 The adiabatic compressibility was calculated from sound speed measurements (U) according to bS ¼ 100= qU2 ð1Þ The typical relationship between density and adiabatic compressibility demonstrated by our measurements on artificial Mono Lake brines is shown in Fig. 1.
4 Partial Molal Volume and Compressibility Data for Brine Salts
To make estimates of the density and compressibility of brines requires reliable partial molal volume and compressibility parameters for the major components as a function of concentration and temperature. Partial molal volume parameters for a variety of salts at 25 C have been determined by a number of workers (Monnin 1987, 1989, 1990; Krumgalz et al. 1994, 1995, 1996, 2000; Pierrot and Millero 2000). Parameters for the major brine salts (NaCl, Na2SO4, MgCl2, MgSO4, KCl, and K2SO4) are available from 5 to 95 C (Connaugton et al. 1986; Dedick et al. 1990; Krumgalz et al. 2000), while parameters for minor brine salts are available from 0 to 50 C (Krumgalz et al. 2000). Partial molal
Fig. 1 Relationship between density and adiabatic compressibility observed fromdirect measurements of artificial Mono Lake brine at 15, 25, and 35 C adiabatic compressibility parameters for a variety of salts at 25 C have been determined by a number of workers (Millero et al. 1977; Millero 1983a; Millero and Sharp 2013). Parameters for major brine salts (NaCl, Na2SO4, MgCl2, and MgSO4) are available from 5 to 95 C (Millero et al. 1987; Millero and Sharp 2013), while parameters for minor brine salts (NaHCO3, Na2CO3, HCl, and NaOH) are available from 0 to 50 C (Hershey et al. 1983, 1984; Millero and Sharp 2013). This study uses the partial molal volume parameters reported in the work of Krumgalz et al. (2000), and the partial molal adiabatic compressibility parameters reported in the work of Millero and Sharp (2013). In Millero and Sharp’s work, temperature-dependent adiabatic compressibility parameters are only available for six brine salts (NaCl, MgCl2, Na2SO4, MgSO4, NaHCO3, and Na2CO3) leaving certain species (such as Ca?2 , K?, andBr-) unaccounted for. To remedy this, we have used the temperature coefficients for
similar salts to estimate changes in salt parameters for which temperature-dependent data are not available. Namely temperature coefficients for NaCl parameters are used to estimate changes in NaBr, NaF, KCl, KBr, and KF parameters; MgCl2 coefficients are used for CaCl2 and SrCl2 parameters; Na2SO4 coefficients are used for K2SO4 parameters; NaHCO3 coefficients are used for KHCO3 parameters; and Na2CO3 coefficients are used for K2CO3 parameters. All of these parameters and coefficients can be found in Millero and Sharp(2013)
5 Estimation of Density The density (q) of any multi-electrolyte solution can be estimated using (Krumgalz et al. 1995
i i i EX q = 1; M . 1;000v0 + X m V0 000 + X m + V
where mi0i and Mi are the molality and molar mass of each ionic component i, V is the partial molal volume at infinite dilution of each ionic component i, v0 is the specific volume of pure water (v0 = 1/q0), and VEX is the excess volume of the solution. The density of pure water (q0) is determined from the equations of Millero and Huang (2009). The equation to calculate the VEX term is adapted from Krumgalz et al. (1995
accord where I is the total ionic strength of the solution, m is the molality of each cation (subscript c) or anion (subscript a), and zc is the charge of each cation. Av is the Debye-Hu¨ckel limiting slope derived by Pierrot and Millero (2000). BV is calculated ing to
ca ca ca BV = b(0)V + b(1)Vgÿy1 + b(2)Vgÿy2 (4)
The coefficients b(0)V, b(1)V, b(2)V and CV as a function of temperature are given for each
ca ca ca ca in Krumgalz et al. (2000). The value of g(yx) is given by
where y1 = a1I0.5 and y2 = a2I0.5, a1 = 2.0 and a2 = 0 for 1–2, 2–1, 3–1, and 1–2 elec- trolytes while a1 = 1.4 and a2 = 12.0 for 2–2 electrolytes (Pitzer 1991). The equation to define VEX’is adapted from Krumgalz et al. (1995)
c,c ,a VEX‘ = RT X X mcmc‘ “[2HV ‘ + X maWV ‘ #
c’ a a,a a,a ,c + RT X X mama‘ “2HV ‘ + X mcWV ‘
c,c ,a where HV ‘ , WV ‘ ,HV ‘ , and WV ‘denote higher-order mixing parameters due to inter- a,a a,a ,c actions between ions of like sign. These mixing parameters are used to improve our density estimates at 25 °C for the few systems where they are available (Connaughton et al. 1989; Krumgalz et al. 1995). The specific mixing parameters used differed between brines. Na,K Na,K,Cl The mixing parameters HV = 1.52 × 10—5 and WV = —6.72 × 10—6 have been shown in previous work to considerably improve Dead Sea density estimates at 25 °C (Krumgalz et al. 1995). They were used in this paper for density estimates of both Red Sea and Dead Sea brines at 25 °C due to the high potassium concentration of both brines.
Na,Mg
Cl,SO4 The mixing parameters HV = 1.8517 × 10—6 and HV = 2.7084 × 10—6 at
25 °C were taken from Connaughton et al. (1989). They were used for our density esti- mates of Orca Basin brines at 25 °C because of its high sulfate concentration.
No higher-order mixing parameters were shown to improve the density estimates of Mono Lake brines. This could be due to Mono Lake’s extremely high concentration of carbonate and bicarbonate, and the lack of available higher-order mixing parameters for those species
Estimation of Compressibility
The adiabatic compressibility (bs, hereafter referred to as b) of any brine solution can be estimated using (Rodriguez and Millero 2013
i bs = 1,000b0v0 + X mij0 + jEX . 1,000 + X miMi (7s where j0 is the partial molal adiabatic compressibility at infinite dilution of each ionic component i, and b0 is the adiabatic compressibility of pure water determined from the equations of Millero and Huang (2011). The jEX term is defined by Pierrot and Millero (2000)
C = ÿ—Aj,SI/1.2 lnÿ1 + 1.2I0.5 + 2RT X X mcma Bj + X mcZc jEX = —(oVEX/oP)
(8) a c according to slope derived by Pierrot and Mille Aj,S is the Debye-Hu¨ckel limiting ro (2000). Bj i
ca ca ca Bj = b(0)j + b(1)jgÿy1 + b(2)jgÿy2 (9)
No higher-order mixing parameters were used in our estimation of compressibility. The data that are available in this area are extremely sparse (Millero and Lampreia 1985), have not been fit to the Pitzer formalism, and are of unknown reliability.
Results and Discussion
The differences between measured and calculated densities (qmeas qcalc) of the four brine solutions across a range of temperatures and salinities are given in the appendix (Tables 3, 4, 5 and 6). The average differences between measured and calculated values along with the standard deviations are provided for each individual brine. Overall, the difference between measured and calculated density for the four brines varied between 0.000800 and 0.000246 g cm-3 at 25 °C. The deviations were larger at other temperatures. The average difference between measured and calculated density at 25 °C was 0.008 ± 0.127 9 10-3 g cm–
Density estimates at 25 °C were improved by higher-order mixing parameters. Spe- cifically, mixing parameters improved Red Sea estimates by 0.004 ± 0.00015 g cm-3, Dead Sea estimates by 0.000244 ± 0.000002 9 10-3 g cm-3, and Orca Basin estimates by 0.000071 ± 0.000000 g cm-3. No higher-order mixing parameters were used on Mono Lake estimates. Across the broader temperature range (0–40 °C), the larger differences between mea- sured and calculated density are likely due to both errors in the volumetric properties of individual electrolytes at high concentrations and the unavailability of reliable volumetric mixing parameters at temperatures other than 25 °C. Figure 2 demonstrates the effect that
Na,K Na,K,Cl higher-order mixing parameters (Hj = 1.52 × 10—5, wV = —6.72 × 10—6) have on
density estimates of artificial Dead Sea brines. Due to the unavailability of data at other temperatures, only the 25 °C comparisons consider higher-order mixing parameters and are far more accurate as a result. Our Red and Dead Sea density estimates at 25 °C show significant improvement over the results of Monnin (1989), whose accuracy of estimating Red Sea density and Dead Sea density was 0.000072 ± 0.00007 g cm-3 and 0.000387 ± 0.000040 g cm-3, respectively
Fig. 2 Comparison between the measured and calculated density of artificial Dead Sea brine as a function of salinity. Higher-order mixing parameters for the Na+– K+–Cl– system, which are currently only available at 25 °C (Krumgalz et al. 1995), are shown to greatly improve the accuracy of the estimates This can be compared to our estimated accuracy of 0.000009 ± 0.000028 g cm-3 and _0.000017 ± 0.000035 g cm-3. This improvement is not surprising as the Pitzer volu- metric interaction parameters have been improved since Monnin’s estimations. Also, Monnin chose not to use higher-order mixing parameters into consideration. We also compared our Dead Sea density estimates with the work of Krumgalz et al. (1995, 2000). Our estimates at 25 °C show slight improvement over the estimates of Krumgalz et al. (1995), who used higher-order mixing parameters and whose accuracy was 0.000062 ± 0.000030 g cm-3 compared to our accuracy of -0.000017 ± 0.000035 g cm-3. They are also fairly consistent with the estimates of Krumgalz et al. (2000), who achieved an accuracy of 0.000143 ± 0.000171 g cm-3 from 20 to 40 °C compared to our accuracy of 0.000244 ± 0.000124 9 10-3 g cm-3 over the same temperature range. Interestingly, our Dead Sea density estimates used the same Pitzer volumetric inter- action parameters and literature measurements as the estimates of Krumgalz et al. (1995, 2000). However, while our estimates are in fair agreement, they are not identical. A contributing factor to this discrepancy is that Krumgalz et al. (1995, 2000) used the Debye- Hu¨ckel slope (Av) of Rogers and Pitzer (1982) and the pure water density (q0) of Kell (1975), while we used Millero and Huang (2009). These changes can alter density estimates by a magnitude of about 10-6 g cm-3. Moreover, the density estimates presented by Krumgalz et al. (1995, 2000) from 20 to 40 °C, without the use of higher-order mixing parameters, are the lowest at 25 °C. This is unexpected as Pitzer volumetric interaction parameters are typically most accurate at 25 °C. This irregularity, seen in the density estimates of Krumgalz et al. (1995, 2000) suggests a possible error in their calculations; however, without access to these calculations, we were unable to ide ntify where that may have occurred. We can only present our own density estimates which show impr vement over those of Krumgalz et al. (1995) at 25 °C and are in reasonable agreement with those of Krumgalz et al. (2000) from 0 to 40 °C. The differences between measured and calculated adiabatic compressibilities— (bmeas bcalc) of the four brine solutions, across a range of temperatures and salin ities, are given in the appendix (Tables 7, 8, 9 and 10). The average differences between measured and calculated values along with the standard deviations are provided for each individual brine. Overall, the average difference between measured and calculated adiabatic com- pressibility for the four brines was 0.204 ± 0.726 9 10-6 bar-1. At 25 °C, the deviations the Debye-Hu¨ckel slope of Pierrot and Millero (2000) and the pure water density of
Fig. 3 Comparison between the measured and calculated adiabatic compressibility of artificial Red Sea brine as a function of absolute salinity. Estimates at 15 and 35 °C are reasonable at low salinities but become increasingly unreliable as salinity increases again were much smaller. The average difference between measured and calculated adi- abatic compressibility at 25 °C was 0.184 ± 0.261 9 10-6 bar-1. The accuracy of our adiabatic compressibility estimates (0.204 ± 0.726 9 10-6 bar-1) was considerably worse than the accuracy of the estimates made by Rodriguez and Millero (2013) on seawater, which agreed with measured values to ±0.04 9 10-6 bar-1. The discrepancy is likely due to the high salinities of the brines, which magnify any errors present in the Pitzer interaction parameters. Figure 3 depicts differences between the measured and calculated densities of Red Sea brines to illustrate this problem. The estimates are quite good at low salinities, but diverge quickly as salinity increases, especially at 15 and 35 °C. The accuracy of our compressibility estimates improves to 0.134 ± 0.297 9 10-6 bar-1 for solutions less than 80 g kg-1 in absolute salinity. Besides the magnification of inherent errors in the Pitzer parameters, two additional factors likely contribute to the high salinity issue. Temperature-dependent adiabatic compr essibility parameters are only available for six brine salts (NaCl, MgCl2, Na2SO4, MgSO4, NaHCO3, and Na2CO3). To include other important parameters, we chose to estimate the temperature dependence of some brine salts based on similar salts for which temperature-dependent data are available. This has improved the accuracy of our com- pressibility estimates (0–40 °C) from 0.479 ± 1.033 9 10-6 bar-1 to 0.204 ± 0.726 9 10-6 bar-1. Still, our estimates of temperature dependence are not based on measured values and are sure to introduce some error. In addition, reliable higher-order mixing parameters for calculating compressibility changes in mixed electrolyte solutions are not available.
Conclusions
The results of this study are important as they expand and improve upon the density estimates of hypersaline brines reported in previous papers (Monnin 1989; Krumgalz et al. 1995, 2000). They also demonstrate the utility of the Pitzer ionic interaction model to predict the adiabatic compressibility of any complex hypersaline brine.Moreover, these results reveal the areas in which additional investigations are neces- sary. Further research on higher-order mixing parameters for calculating volume changesin mixed electrolyte solutions is necessary to improve density estimates. An increased database of temperature-dependent Pitzer parameters for calculating compressibility of single electrolyte solutions along with further research on higher-order mixing parameters for calculating compressibility changes in mixed electrolyte solutions is necessary to improve the estimates of adiabatic compressibility. Considerable work is left to be done to improve the effectiveness of Pitzer’s ionic interaction model. That being said, as new data continues to become available in this field, the utility of the Pitzer model to predict volumetric pro perties of natural hypersaline brines will surely improve. Acknowledgments The authors wish to ac knowledge the support of the oceanographic section of the National Science Foundation and the National Oceanic and Atmospheric Administration Office for sup- porting our Marine Physical Chemistry work.
Appendix
See Tables 2, 3, 4, 5, 6, 7, 8, 9 an 1d0.
Table 2 Salt composition of artificial Dead Sea water patterns used for the measurements of Krumgalz and Millero (1982b)
Measured values are from Krumgalz and Millero (1982b)
a Dqmeas = qmeas – q0
b Dqcalc = qcalc – q0
c Dq = qmeas – qcalc
Avg 9 (qmeas – qcalc) 9 103 0.30 SD 9 (qmeas – qcalc) 9 103 0.411
Measured values are from Jellison et al. (1999)
a Dqmeas = qmeas – q0
b Dqcalc = qcalc – q0
c Dq = qmeas – qcalc
Measured values are from this study
a Dbmeas = bmeas – b0
b Dbcalc = bcalc – b0
c Db = bmeas – bcalc
Measured values are from Millero et al. (1979)
a Dbmeas = bmeas – b0
b Dbcalc = bcalc – b0
c Db = bmeas – bcalc
Measured values are from this study
a Dbmeas = bmeas – b0
b Dbcalc = bcalc – b0
c Db = bmeas – bcalc
Measured values are from this study
a Dbmeas = bmeas – b0
b Dbcalc = bcalc – b0
c Db = bmeas – bcalc
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