Correlations between TDS and electrical conductivity for high-salinity formation brines characteristic of South Atlantic pre-salt basins

COPYRIGHT © The Author(s) Published under a Creative Commons Attribution 4.0 International Licence (CC BY 4.0) Total dissolved solids (TDS) is an important property in the characterization of natural waters for diversified applications, such as in geochemistry and the petroleum industry. Under appropriate circumstances, the determination of this parameter through correlations with the electrical conductivity (EC) of aqueous systems yields considerable advantages over the gravimetric method. However, the development of empirical equations correlating TDS and EC is still required due to the physical-chemical complexity of charge transport in multicomponent natural waters. Most existing correlations were built considering systems in the lower or medium salinity range. In this context, this research aims to provide experimental correlations between TDS and EC in a broad concentration range for high salinity formation brines characteristic of the pre-salt reservoirs. It contributes to filling a gap in the literature for geochemical systems of this nature. Moreover, correlations were also obtained for a concentrated desulphated seawater and an aqueous sodium chloride solution in the same salinity range. For all aqueous solutions, the polynomial fittings of degree greater than one fit the experimental data better compared to both linear and exponential equations. In addition, the solutions with higher concentration of divalent ions had lower EC than the solutions dominated by monovalent ions with the same ionic strength. This evidences the effect of ion pairing on the EC, particularly in solutions of high ionic strength. Therefore, the use of a general correlation to represent solutions with dramatic variations in chemical composition carries substantial error, particularly in the high salinity range. Thus, a specific correlation must be developed to represent brines with similar composition. Correlations between TDS and electrical conductivity for high-salinity formation brines characteristic of South Atlantic pre-salt basins


INTRODUCTION
Total dissolved solids (TDS) is an important property in the characterization of natural waters. It is defined as the total concentration of inorganic and organic matter in aqueous solution, which can be in ionic form or not (Hubert and Wolkersdorfer, 2015;McNeil and Cox, 2000). The inorganic components of TDS are composed in their majority by the ions calcium, magnesium, sodium, bicarbonate, chloride and sulfate; whereas the organic components of TDS are estimated based on the biochemical oxygen demand (BOD) and the chemical oxygen demand (COD) (Balasubramanian et al., 1999).
The acquisition of TDS of natural waters encounters diversified applications in geochemistry (Jonker et al., 2013), desalination industry (Walton, 1989), hydrology (Leske and Buckley, 2004), soil and groundwater science (Douglas, 2001;Verwey and Vermeulen, 2011), and the petroleum industry (Sun et al., 2015;Lord and LeBas, 2013;Brown and Sheedy, 2002). In geochemistry, TDS is particularly relevant for interpreting electrical well logs, correlating stratigraphic units and investigating the movement of subsurface waters (Collins, 1975). In the petroleum industry, TDS is essential to evaluate the possibility of formation of inorganic scales throughout the entire oil production system (Gudmundsson, 2018). Furthermore, in the field of enhanced oil recovery (EOR), TDS is also critical to ensuring the chemical stability of the fluids injected into petroleum reservoirs with the aim of increasing the recovered volume of hydrocarbons (Sheng, 2010).
TDS characterization is also relevant for environmental reasons. Global concern has been raised regarding the effect of effluent TDS on the biotic integrity of the streams (Helms et al., 2009;Weber-Scannell and Duffy, 2007). Several studies discuss the importance of evaluating physicochemical alteration of aqueous environments considerably affected by human interventions (Moncayo-Estrada et al., 2014;Moreyra and Padovesi-Fonseca, 2015;Deksissa et al., 2003). Clear effects of water salinity alteration to the biotic integrity in different systems have been reported elsewhere (Daniels et al., 2016;Ivanova and Kazantseva, 2006;Timpano et al., 2015).
The gravimetric method is the standard procedure to determine TDS. It consists of weighing the dry residue resulting from evaporating a measured volume of a filtered water sample (Hubert and Wolkersdorfer, 2015). However, a number of disadvantages have been attributed to this method (Hem, 1985;Raju, 2007;Gustafson and Behrman, 1939;Walton, 1989;Hubert and Wolkersdorfer, 2015). Incorrect quantification of bicarbonate ions occurs as half of them volatilize as carbon dioxide at temperatures around 100°C (Walton, 1989). During evaporation, the crystalline structure of precipitated salts can confine some water into them. In this case, the crystallization water will be weighed jointly with the precipitated salts (Hem, 1985). Additionally, the volatilization of acids, mainly at low pH values, causes the loss of some anionic content, such as chloride and nitrite ions.
On the other hand, extra mass can be considered due to oxidation or transformation into hydroxides during the heating process (Hubert and Wolkersdorfer, 2015).
Although the gravimetric method is laborious and time consuming, the accuracy of its results is not always acceptable as it mainly depends on selecting a drying temperature which allows the release of all crystallization water without provoking any chemical decomposition (Gustafson and Behrman, 1939). Another proposed method to estimate TDS relies on the conductivity of an electrolyte solution, which is its capability to conduct an electric current when a potential is applied between the electrodes immersed in it (Coury, 1999;Hem, 1985). In this context, the conductivity of a portion of an electrolyte solution, κ (in S/m or Ω -1 /m), with length l (in m) and area A (in m 2 ) is defined by Eq. 1 (Crow, 1994): where ρ is the reciprocal of κ, known as resistivity (in Ω•m), R is the resistance of the solution (in Ω) and G is the reciprocal of R, known as the conductance of the solution (in S or Ω -1 ). In this work, the term electrical conductivity (EC) is used to refer to the conductivity measured at 25°C, which is also defined as specific conductance in other publications (Miller et al., 1988). The parameter l/A is called the cell constant and is utilized to convert the measured conductance of an aqueous solution to its conductivity using Eq. 1. This parameter is determined by calibrating the cell by measuring the conductance of a reference solution with known conductivity (Cazes, 2004;Hubert and Wolkersdorfer, 2015;Crow, 1994;Walton, 1989).
The relationship between TDS and conductivity is often described in the literature by the following correlation (Eq. 2) (Pawlowicz, 2008;Visconti et al., 2010;Visconti Reluy et al., 2004;Hem, 1985): where f is a conversion factor and κ T is the conductivity at a specified temperature T (usually 25°C). This conversion factor ranges between 0.5 and 0.9 for most water types (Walton, 1989). In particular, in South African mine waters this factor was found to vary from 0.25 to 1.34 (Hubert and Wolkersdorfer, 2015), and it can be as elevated as 1.4 in meromictic saline lakes (Pawlowicz, 2008). In particular, sulphate ions were shown to affect the relationship between EC and concentration due to incomplete dissociation (Tanji, 1969). As natural waters are complex aqueous systems with diversified ratios of ionic and undissociated species, in many cases a non-linear relationship between TDS and EC arises (Hubert and Wolkersdorfer, 2015). The reason for this is that the EC of an aqueous solution depends on the activity of each specific Under appropriate circumstances, the use of correlations with EC to determine the TDS of natural waters provides considerable advantages over the gravimetric method and the chemical analysis due to the simplicity, speed, low cost and accuracy of EC measurements (Hayashi, 2004;Raju, 2007). Conductivity of aqueous solutions increases with temperature. Usually, conductivity measurements are carried out at different temperatures in the field and adjusted to conductivity at a reference temperature (i.e. 25°C) using a temperature coefficient. Since the type and concentration of electrolytes alter this coefficient, it should be measured for each specific system (Smith, 1962).
Accurate EC data can be collected in the field for a broad range of geochemical applications (Shirokova et al., 2000;Marandi et al., 2013). As a result, correlations between TDS (or ion concentrations) and EC were reported in studies related to the quality of natural waters ( (Bromley, 1972;Meissner and Kusik, 1978;Pitzer et al., 1978;Helgeson et al., 1981). Nevertheless, the accuracy of these tools for complex high salinity brines has yet to be assessed.
Charge transport in multicomponent aqueous systems is not yet entirely understood from the physical-chemical perspective. Hence, the development of empirical equations is still necessary to predict TDS from EC measurements (Visconti Reluy et al., 2004). To the best of our knowledge, published works in the literature mostly consider natural waters with a low salinity range, which does not exceed 40 000 mg/L (Rusydi, 2018;Marandi et al., 2013;McNeil and Cox, 2000;Raju, 2007;Alhumoud et al., 2010;Sylus and Ramesh, 2015). Hayashi (2004)  In this regard, the aim of this research is to develop experimental correlations between TDS and EC in a broad concentration range for two highly concentrated formation brines characteristic of the pre-salt environment, to fill the existing gap in literature. Furthermore, two additional aqueous solutions were included in this study to evaluate the effect of the chemical composition. The data were fitted using polynomial and exponential regressions to produce a set of correlations with different fitting errors. In addition, the EC was calculated using OLI Studio Stream Analyzer for all brines. The results were compared with the experimental data to validate the use of both methods in high salinity environments. The equations generated in this work can be used to estimate TDS from EC measurements for similar aqueous systems under a wide range of concentrations when there is uncertainty in the concentration of any of the species obtained by standard methods (McCartney et al., 2005). They can also be used as an alternative calculation method for complex high salinity brines; this application is still undergoing validation for currently available software.

MATERIALS AND METHODS
Four high-salinity aqueous solutions were synthesized based on their natural compositions: two formation brines from Brazilian pre-salt fields, a concentrated desulphated seawater (DSW) used for injection at offshore operations and an aqueous sodium chloride solution. The typical TDS of the DSW injected in oil field operations is 39 548 mg/L; however, it was concentrated to 230 000 mg/L maintaining the ratio among the concentrations of all ions in order to compare the EC data from all of these aqueous solutions over a similar concentration range.
All brines were synthesized in the laboratory by weighting the corresponding masses of each inorganic salt on an analytical scale and dissolving them in deionized water (EC less than 1 µS/cm at 25°C, Gehaka OS10LXE reverse osmosis system), following their chemical compositions (Table 1). The salts used in this work, including their supplier and purity, are given in Table 2. After dissolution, brines were stirred for an hour before being connected to a vacuum pump for air removal. For each water type, triplicates were prepared to minimize experimental errors and to ensure the repeatability of the technique. Thereby, the presented results only consider the mean value of the triplicates of the EC measurements. The corresponding error bars on the plots indicate the standard error of the mean for each group of triplicates.
For all aqueous solutions, EC was measured using a Mettler Toledo InLab 731-ISM graphite, four-pole conductivity probe attached to a Mettler Toledo SevenExcellence S470 conductivity benchtop meter. This instrument has a 0.57 cm -1 cell constant and is able to measure EC values in the range of 0.01 to 1 000 mS/cm with a resolution of 0.01 µS/cm and an accuracy of ±0.5%. Using a fourpole conductivity cell makes the EC measurements more reliable by eliminating polarization effects, which become more relevant when measuring highly concentrated samples (Jespersen, 2006). Moreover, all measurements were carried out at 25°C using a thermostatic bath with temperature indication. Calculated data were obtained using OLI Studio Stream Analyzer 9.6.3.

Validation of the procedures employed in this work
In order to validate the procedures employed in this work, the EC data obtained from this study, both experimental and calculated, were compared to those found in the literature (Robinson and Stokes, 2002) for aqueous sodium chloride solutions (Fig. 1).
Both experimental and calculated EC data presented relative errors lower than 5% when compared to the EC data provided by Robinson and Stokes (2002) for all the concentrations considered. This result shows that the EC data produced through the experimental measurements and the calculations with OLI Studio in this study are in agreement with Robinson and Stokes (2002), which supports their validity.

Development of correlations
As can be seen, both experimental and calculated data for all water types (Figs 2 to 5) generate curves with a decreasing slope, particularly at the higher concentration range. This behaviour agrees with well-known effects that retard the movement of ions in systems subject to an electrical field (Wright, 2007). First, the relaxation effect is caused by the attractive force exerted by oppositely charged ions in the surrounding atmosphere, which reduce the activity coefficient (Atkins and De Paula, 2006;Glueckauf, 1949). In addition, the electrophoretic effect is the consequence of ion interactions with the solvation molecules around the other ions (Simón and García, 1999). As concentration increases, ion-ion and ion-solvent interactions become more substantial. As a result, the EC of the aqueous solutions rises at progressively lower rates with increasing TDS (Hem, 1985;McNeil and Cox, 2000;Walton, 1989). This explains the nonlinearity observed in EC with increasing TDS (Walton, 1989).
Moreover, Figs 2 to 5 illustrate good agreement between experimental and calculated data. For concentrations below 100 000 mg/L in all aqueous solutions, the maximum relative difference between calculated and experimental EC values was 3.14%. Furthermore, the maximum difference for the higher TDS range in all aqueous solutions was 9.29%.
The previously discussed phenomena are linked to ion concentration. In contrast, ion pairing is related to both concentration and type of ions in solution (Smedley, 1980). Divalent ions (such as Ca 2+ , Mg 2+ and SO 4 2-) are more likely to form ion pairs than monovalent ions like Na + , K + and Cl - (Alzubaidi and Webster, 1983). These pairs may have reduced (or even neutral) charge, having lower contribution to the conductivity. As a result, ion pairing decreases the EC of the solution (Chang et al., 1983;Simon et al., 1994;Simón and García, 1999). To evaluate the effect of the concentration of divalent ions, Fig. 6 shows the EC as a function of the ionic strength using data calculated with OLI Studio, whose model considers ion-ion interactions (Wang et al., 2002). As can be seen, both solutions with the lowest concentration of divalent cations (sodium chloride solution and Field D brine) have higher EC values at the same ionic strengths. In addition, Field B brine, which contains the greatest concentration of divalent ions, has the lowest EC. Furthermore, the difference in EC between the solutions dominated by monovalent ions (sodium chloride solution and Field D brine) and the brines with greater concentration of divalent ions (Field B brine and concentrated DSW) broadens as the ionic strength increases. This is in agreement with previous investigations studying ion-pairing in solutions with lower ionic strengths than those considered in this work (Timpson and Richardson, 1986;Marion and Babcock, 1976;Simón and García, 1999).
To provide accurate correlations for TDS as a function of EC measurements, several curve fittings were executed on the experimental data of each aqueous solution. The curve fittings consisted of 1-to-4-degree polynomial fittings and exponential fittings. The resulting correlations of the polynomial fittings can be expressed in the form of the following general equation: where TDS is total dissolved solids in mg/L, κ is EC in µS/cm and a, b, c, d and e are coefficients whose values are presented in Table 3 for each type of polynomial fitting and aqueous solution. Table 3 also gives the coefficients of determination (R 2 ) obtained for all polynomial fittings.
For the exponential fittings, a generic equation was used to obtain the correlations (Eq. 4), where TDS is total dissolved solids in mg/L and κ is EC in µS/cm. The values of coefficients a and b for each aqueous solution along with the coefficients of determination (R 2 ) of all of the exponential fittings are presented in Table 4. Considering the R 2 values (Tables 3 and 4), the exponential correlations did not result in a better fit than the polynomial ones. For only the sodium chloride solution did the exponential fitting presented a higher R 2 than the linear one. Moreover, the polynomial correlations of second and higher degrees fit the experimental data better than both linear and exponential correlations. The fact that the experimental data are better described by polynomial correlations of higher degrees is in agreement with the nonlinear relationship between TDS and EC, especially at a higher concentration range. For instance, if the linear equation were used to calculate the TDS of a sodium chloride solution from a measured EC of 238 819 µS/cm (last experimental point in Fig. 5), the relative error compared to the experimental value would be 12.15%. On the other hand, if the quadratic equation were used for the same purpose, the relative error would be 1.45%. However, increasing the degree of the polynomial correlations above the second degree did not yield a substantial increase in R 2 in any of the aqueous solutions. In the aforementioned example, if the fourth-degree correlation were used to calculate the TDS of the same sodium chloride solution, the relative error would be 1.40%, only 0.05% lower than the one obtained from the second-degree correlation.
As this study shows, the determination of the TDS based on the EC needs brine-specific correlations. The relevance of the chemical composition of aqueous systems for their EC has been reported elsewhere (Marandi et al., 2013;Siosemarde et al., 2010;Walton, 1989). The equations generated in this work (Tables 3 and 4) also support this relevance. For instance, if the quadratic equation obtained for Field D brine was used to calculate the TDS of the sodium chloride solution of the example in the previous paragraph, the relative error would be 20.98%, as opposed to the 1.45% obtained when the correct second-degree correlation was used. This corroborates the relevance of developing specific correlations for complex brines containing high concentrations of divalent cations (Van Niekerk et al., 2014). The use of correlations generated with model brines regardless of proper chemical composition characterization is not recommended as it may result in erroneous TDS determinations (Pawlowicz, 2008;Raju, 2007;Hubert and Wolkersdorfer, 2015).

CONCLUSIONS
The determination of total dissolved solids (TDS) has application in a variety of fields, such as geochemistry, hydrology and environmental science. The characterization of waters in the petroleum industry requires estimating the TDS in high salinity brines, for which ion-ion and ion-solvent interactions have a substantial effect. This study presents experimental correlations of the TDS as a function of electrical conductivity (EC) for brines typical of pre-salt formations, with salinities between 20 000 and 292 200 mg/L.
For all brines, the higher degree polynomials presented a better fitting of the experimental data, showing that there is no linear correlation between TDS and EC for higher brine concentrations. In contrast, the use of exponential correlations did not improve the R 2 of the fitting.
Chemical composition is of remarkable relevance for the calculation of TDS. The correlations between TDS and EC depend on the type of ions and their concentrations in the aqueous solution. Therefore, a specific correlation should be generated for each type of brine. The use of equations developed for model brines may carry substantial error, particularly when analysing high salinity brines.
This study may serve as reference for the EC of high-salinity presalt brines. Moreover, the correlations generated in this work can be used to estimate the TDS from EC measurements when the chemical composition is analogous to the pre-salt waters used by our group. As previously discussed, given the tendency of divalent cations to form ion pairs, having a similar concentration and type of divalent cations is particularly important when using these correlations in analogous solutions.