Prediction of Nitrogen Solubility in Pure Water and Aqueous NaCl Solutions up to High Temperature, Pressure, and Ionic Strength

Transcription

1 Journal of Solution Chemistry, Vol. 30, No. 6, 2001 Prediction of Nitrogen Solubility in Pure Water and Aqueous NaCl Solutions up to High Temperature, Pressure, and Ionic Strength Rui Sun, 1 Wenxuan Hu, 2 and Zhenhao Duan 3 * Received November 13, 2000; revised March 12, 2001 A thermodynamic model for the solubility of nitrogen in pure water ( K, bar) and in aqueous NaCl solutions (0 4m, K, bar) is presented. The model is based on a specific interaction model for the liquid phase and a highly accurate equation of state for the vapor phase. Comparison of the model predictions with experimental data indicates that the model predictions are within or close to experimental uncertainty. Most experimental data sets are consistent within errors of about 7%. Although the parameters were evaluated from data for binary and ternary systems, the model can be used to predict nitrogen solubility in much more complicated systems like seawater. KEY WORDS: Nitrogen solubility; nitrogen thermodynamics; specific interaction modeling; aqueous nitrogen solution. 1. INTRODUCTION Nitrogen-bearing fluids have been reported in many geological settings. It has been found that occurs in fluid inclusions representative of diagenetic, hydrothermal, (1) magmatic, (2) and metamorphic (3 5) fluids. Due to the influence of partitioning on ph, and anion chemistry in aqueous solution, accurate predictions of solubility over a wide range of temperatures, pressures, and ionic strength would be a valuable step in developing reliable chemical models for geological fluids, such as seawaters, geothermal waters, hydrothermal ore-forming solutions, and oil-field brines. (6) It is also important for chemical 1 China University of Geosciences, Wuhan, , P.R. China. 2 The National Laboratory of Mineral Deposit Research, Department of Earth Sciences, Nanjing University, , P.R. China. 3 Department of Chemistry, University of California, San Diego, La Jolla, California /01/ $19.50/0 C 2001 Plenum Publishing Corporation

2 562 Sun, Hu, and Duan and nuclear engineering. (7,8) Because of its significance, there have been many experimental studies of the solubility of in pure water and in brines. The solubility varies with temperature, pressure, and brine composition. However, controversy over the reliability of data and the lack of an equation of state for the gas phase has prevented the development of quantitatively reliable models. For many temperature pressure composition conditions, nitrogen solubilities are still unknown. A few nitrogen solubility models (7,9 11) have been proposed. Among those, the models by Battino et al. (9) and of Li and Nghiem (10) are the most competitive. The empirical model of nitrogen solubility in pure water published by Battino et al. was intended for temperatures of 350 to 600 K at high pressures. However, in the absence of a theoretical basis, no reliable result can be obtained by extrapolation. Even within the above range, the model sometimes fails to reproduce experimental data at high temperatures [such as the data sets of Alvarez et al. (8,12) ]. Li and Nghiem (10) presented a model to calculate phase equilibria of oil, gas, and water/brine mixtures. In this treatment, the oil and gas are modeled by a cubic equation of state, the solubility of gas in the aqueous phase is estimated from Henry s law, and the presence of salt is treated by a scaled-particle theory. The model of Li and Nghiem (10) is intended to predict the solubility of in pure water up to 473 K and in aqueous NaCl solution up to 4m. However, it is, in general, not sufficiently accurate. For example, the deviation of their model calculations from the experimental solubility data in pure water and aqueous NaCl solution in 398 K is as large as 10 30% well above experimental uncertainty. In this article we introduce a model for this system covering a large T -P-m range with high accuracy. The chemical potential of nitrogen in the vapor phase is calculated using the accurate equation of state recently proposed by Duan et al., (13) assuming ideal mixing of and H 2 O in the vapor phase. This assumption may cause errors for the chemical potential of nitrogen, but the resulting error in the nitrogen solubility is approximately canceled in the fitting equation. The chemical potential of in the liquid phase is described by the specific interaction model established from solubility data. This will be discussed in the next section. Duan et al. (14) adopted the above principle to deal with the solubility of methane and achieved very accurate model for the methane water salt system. Considering that nitrogen has similar dissolution behavior to methane, our model, based on the above principle, is expected to predict the solubility of accurately. In order to disentangle the controversy over the experimental measurements, the available data are reviewed in Section 3. We find that most of the major data sets are consistent. Parameters are evaluated from experimental data. Comparison with experimental data in Section 4 indicates that the resulting model can predict nitrogen solubility in pure water from 273 to 623 K and from 0 to 600 bar, and in aqueous NaCl solution to

3 Prediction of Nitrogen Solubility 563 high ionic strength (0 4m) with accuracy close to experiment. Our model not only covers a larger range than previous models, but also is more accurate. Applying this model to seawater illustrates its accuracy in complex systems and its capability for extrapolation. 2. PHENOMENOLOGICAL DESCRIPTION OF GAS SOLUBILITY AS A FUNCTION OF COMPOSITION, PRESSURE, AND TEMPERATURE Nitrogen solubility in aqueous solutions is determined from the equality of its chemical potential in the liquid phase, µ aq and in the gas phase, µ v. The potentialy can be written in terms of fugacity in the vapor phase and activity in the liquid phase as µ v (T, P, y) = µ v(0) (T ) + RT ln f N2 (T, P, y) = µ v(0) (T ) + RT ln y N2 P + RT ln φ N2 (T, P, y) (1) µ l (T, P, m) = µ l(0) (T, P) + RT ln a N2 (T, P, m) = µ l(0) (T, P) + RT ln m N2 + RT ln γ N2 (T, P, m) (2) At equilibrium, µ l = µ v, and we obtain, ln y P = µ l(0) (T, P) µ v(0) (T ) ln φ N2 (T, P, y) + ln γ N2 (T, P, m) (3) m N2 RT The standard chemical potential of in the liquid phase, µ l(0) is the chemical potential in the hypothetical ideal solution of unit molality. (15) The vapor phase standard chemical potential, µ v(0), is the hypothetically ideal gas chemical potential when the pressure is equal to 1 bar. In the following, µ v(0) is set equal to zero, since solubility is a function of the difference between µ l(0) and µ v(0) in the first term of Eq. (3). According to the equation of state of Duan et al., (13) the fugacity coefficient of in the vapor phase of H 2 O mixtures differs very little from that in pure between 273 and 623 K. Therefore, ln φ N2 can be calculated from the EOS for pure. (13) Since there are no vapor composition measurements for the H 2 O NaCl system, at high pressure, we assume that water vapor pressure is not affected by the total pressure of solutions NaCl and. Consequently, y N2 can be calculated approximately from y N2 = (P P H2 O)/P (4) where P H2 O is the pressure of pure water, which can be taken from steam tables. (16) This assumption may lead to errors (up to about 5%) for µ l(0) i /RT and ln γ l.

4 564 Sun, Hu, and Duan However, the errors cancel approximately in our parameterization and the effect on the calculation of solubility is negligible. A virial expansion of excess Gibbs Energy (17) is used to obtain ln γ N2 ln γ N2 = 2λ N2 cm c + 2λ N2 am a + ζ N2 a cm c m a (5) c a c a where λ and ζ are second-order and third-order interaction parameters, respectively. Substituting Eq. (5) in Eq. (3), we have ln γ P = µ l(0) m N2 RT ln φ + 2λ N2 cm c + 2λ N2 am a c a + ζ N2 c am c m a (6) c a In the above equation, λ s, ζ s, and the dimensionless standard chemical potential, µ l(0) /RT depend on temperature and total pressure. Following Pitzer et al., (18) we use the following equation for the parameters Par(T, P) = c 1 + c 2 T + c 3 / T + c 4 T 2 + c 5 /(680 T ) + c 6 P + c 7 P ln T + c 8 P/T + c 9 P/(680 T ) + c 10 P 2 /T (7) Equations (6) and (7) form the basis of our parameterization for the model. 3. REVIEW OF SOLUBILITY DATA OF The solubility of nitrogen in water has been measured for a wide range of temperatures and pressures (Table I). The most extensive studies are those of Wiebe et al., (19,20) Krase and co-workers, (21,22) and Smith et al. (23,24) As Young (25) concluded in 1981, the data of Smith and co-workers and the data of Wiebe et al. are accurate for the temperature range from 298 to 398 K; the data of Saddington and Krase (22) are the most reliable from 398 to 513 K. These data sets are consistent within errors of about 7%. However, the data of Goodman and Krase (21) deviate from other data sets by more than 10%. More recently, Kennan and Pollack (26) and Alvarez et al. (8,12) published new data. The data sets of Kennan and Pollack are consistent with Wiebe et al. (19,20) and the data sets of Alvarez et al. (8,12) extend to 640 K. There are also many solubility data at 1 atm, some of which (27 30) are listed in Table I. The data for solubility in aqueous NaCl solution at pressures above 1 atm are limited. Smith et al. (23) presented data at 303 K and at different pressures and salt concentrations. O Sullivan and Smith (24) presented another data set covering the T -P range from 324 to 398 K and from 100 to 610 bar. Smith et al. (23) also published solubility data in aqueous CaCl 2,Na 2 SO 4, and MgSO 4 solutions.

5 Prediction of Nitrogen Solubility 565 Table I. Measurements of Nitrogen Solubility Authors Solution T (K) P (bar) N a Goodman and Krase (Ref. 21) Water Weibe et al. (Ref. 19) Water Weibe et al. (Ref. 20) Water Saddington and Krase (Ref. 22) Water Smith et al. (Ref. 23) Water O Sullivan and Smith (Ref. 24) Water Kennan and Pollack (Ref. 26) Water Alvarez and Fernandez-Prini Water (Ref. 12) Alvarez and Fernandez-Prini Water (Ref. 8) Klots and Benson (Ref. 28) Water Morrison and Billet (Ref. 29) Water Fox (Ref. 27) Water Murray et al. (Ref 30) Water Smith et al. (Ref. 23) NaCl ( M) O Sullivan and Smith (Ref. 24) NaCl (1 4m) a Number of measurements. 4. PARAMETERIZATION AND COMPARISON WITH EXPERIMENTAL DATA In order to calculate the solubility of as a function of temperature, pressure, and salt concentration, we need to determine the λ and ζ parameters for Na + and Cl in liquid as well as the standard chemical potential µ l(0) in Eq. (6). Since measurements can be made only in electrically neutral solutions, one parameter must be assigned arbitrarily. (31) We set λ N2 Cl to zero and fit the remaining parameters. µ l(0) /RT was first evaluated using the solubility data in pure water. Parameters λ N2 Na and ζ N2 Na Cl were then evaluated simultaneously by leastsquares fitting of solubility data for aqueous NaCl solutions of Smith et al. (23) with an overall fitting variance of 7.5%. All these parameters vary with T and P. However, the variations of the λ and ζ with T, P are small, which means that we can extrapolate this model to higher temperatures and pressures. The temperatureand pressure-dependent coefficients are listed in Table II. By substituting the parameters into Eq. (6), the solubility in pure water ( K, bar) and aqueous NaCl solutions (0 4m, K, bar) can be calculated. Solubilities in pure water and in 4m NaCl so obtained are compiled in Tables III and IV, respectively. Figures 1, 2, and 3 show the agreement between the experimental data and our model. It can be seen from these figures that most experimental data can be represented adequately, within or close to experimental uncertainty (with an average deviation of about 7%). Figures 1, 2,

6 566 Sun, Hu, and Duan Table II. Interaction Parameters T -P coefficient µ l(0) /RT λ N2 Na ξ N2 Na Cl c c c c c c c c c c and 3 also suggest that our model not only covers a wider T-P-m range, but also is, in general, more accurate than that of Battino et al. (9) and that of Li and Nghiem. (10) For example, the solubility of nitrogen in water at K and 1013 bar predicted by Battino et al. (9) is 15% less than that measured by Wiebe et al. (20) The solubility in water at K with pressures higher than 300 bar predicted by Battino et al. is 30% less than that measured by Alvarez et al. (12) The solubility in aqueous NaCl solutions at K predicted by Li and Nghiem (10) is 10 30% greater than that measured by O Sullivan and Smith. (24) This discrepancy is larger than that given by the model of Battino et al. However, at 398 K there is a large discrepancy Table III. Calculated Nitrogen Solubility in Water a T (K) P(bar) a Units: mol/kg water.

7 Prediction of Nitrogen Solubility 567 Table IV. Calculated Nitrogen Solubility a in 4m Aqueous NaCl T (K) P(bar) a mol/kg water. (about 15%) between the experimental data of O Sullivan and Smith (24) and those of Saddington and Krase. (22) Our model predictions lie between them, while the model of Battino et al. does not reproduce the data of Saddington and Krase. Figure 4 indicates that the isobaric minimum solubility is at about 353 K. At lower temperatures (from room temperature to about 400 K), our model predicts the solubility in pure water up to 1000 bar, as indicated by Fig. 1. Nitrogen and methane exhibit similar dissolution behavior because both are nonpolar gases and have similar intermolecular potentials, (13) as can be illustrated by comparing the present model with the earlier study of Duan et al. (14) In the T-P-m range covered by our model, the solubility of increases with pressure and decreases with increasing ionic strength. Nitrogen is generally less soluble than methane. The partial molar volume of in aqueous solution can be derived from Eq. (2): V N2 (l) RT = ( µ l(0) /RT P ) T,m ( ) ln γn2 + P T,m ( µ l(0) ) /RT = + ( ) λn2 c 2m c + P T,m c P T,m a + ( ) λn2 c a m c m a c a P T,m ( ) λn2 a 2m a P T,m (8)

8 568 Sun, Hu, and Duan Fig. 1. Nitrogen solubility in pure water, Comparison of our model with experimental data and other models. The derivatives in the above equation are obtained by differentiating Eq. (7) with respect to P at fixed T : ( ) Par(T, P) = c 6 + c 7 ln T + c 8 /T + c 9 /(680 T ) + 2c 10 P/T (9) P T,m Table V compares the experimental partial molar volume of nitrogen in pure water (24) with the results calculated from Eq. (8). It can be seen from Table V that our model accurately predicts the partial volume of nitrogen. 5. NITROGEN SOLUBILITY IN SEAWATER: EXTRAPOLATION OF THE MODEL The advantage of the specific interaction approach is that the model, although it was evaluated binary and ternary data, can be applied to more complex systems. (32) Natural waters often contain NaCl, KCl, MgCl 2, CaCl 2, and sulfate and carbonate salts, although NaCl is often the major component. Because of data limits, a direct fit to experimental measurements is possible only for the

9 Prediction of Nitrogen Solubility 569 Fig. 2. Nitrogen solubility in pure water, Comparison of our model with experimental data and other models. NaCl H 2 O system. In order to treat more complex systems, we include Ca 2+, K +,Mg 2+,SO 2 4,CO2 3, and HCO 3 in this model with an approximation used by Duan et al. (14) As Duan et al. (14) pointed out, the interaction parameters(λ s, ζ s) for ions of the same charge have roughly the same value, and the CH 4 bivalent cation interaction parameters are about twice as large as CH 4 monovalent interaction

10 570 Sun, Hu, and Duan Fig. 3. Nitrogen solubility in aqueous NaCl solution, Comparison of our model with experimental data and other models. parameters, within the accuracy of experiment, which is true at different temperatures and pressures. The CH 4 anion interaction parameters are relatively small and therefore contribute little to the calculations. Hence, Duan et al. (14) approximated all CH 4 monovalent cation and CH 4 bivalent cation interaction parameters as λ CH4 Na and 2λ CH4 Na, respectively, and neglected all ternary parameters, but ξ CH4 Na Cl. As stated above, nitrogen and methane exhibit similar dissolution Fig. 4. Isobaric minimum solubilities of.

11 Prediction of Nitrogen Solubility 571 Table V. Partial Molar Volume of Dissolved in Pure Water T (K) P(atm) V a V b a Experimental data by Smith et al. (1970). b The model of this study. behavior in pure water and aqueous NaCl. Hence, we assume that all monovalent cation and bivalent cation interaction are equal to λ N2 Na and 2λ N2 Na, respectively, and neglect all ternary parameters except ξ N2 Na Cl to deal with the solubility of nitrogen in seawater-type brines. The following equation is obtained: ln m N2 = ln y N2 φ N2 P µ l(0) /RT 2λ N2 Na(m Na + m K + 2m Ca + 2m Mg ) m Na m Cl (10) In order to test this approximation, we compared Eq. (10) with experimental data for nitrogen in seawater. (30,33) Figure 5 shows that the error from this approximate approach is less than 4%, which is a remarkable agreement between this model and the experiment. [The chemical composition of seawater is from Holland (34) ]. Fig. 5. Nitrogen solubility in seawater.

12 572 Sun, Hu, and Duan 6. CONCLUSIONS A nitrogen solubility model has been developed based on the equation of state by Duan et al. (13) and the theory of Pitzer (17). Comparison with experimental data demonstrates that this model gives results within or close to experimental uncertainty (about 7%) in the temperature range from 273 to 623 K, for pressure from 0 to 600 bar, and for ionic strength 0 4m. Following the approach adopted by Duan et al., (14) we extend this model to complex brines and find that it represents the solubility data in seawater satisfactorily. ACKNOWLEDGMENT This work is supported by Zhenhao Duan s Outstanding Young Scientist funds (No ) of the National Natural Science Foundation of China, and the visiting scholar foundation of the Education Ministry of China. We appreciate the valuable comments by Dr. Robert L. Kay and two reviewers. LIST OF SYMBOLS T Absolute temperature, kelvin P = P N2 + P H2 O Total pressure, bar y Mole fraction composition in vapor phase R Universal gas constant: bar-mol 1 -K. m Molality of or salt in the aqueous phase φ Fugacity coefficient γ Activity coefficient µ Chemical potential λ N2 ion Interaction parameter ζ N2 cation anion Interaction parameter Par Parameter Subscripts a c Anion Cation Superscripts v l (o) aq Vapor Liquid Standard state Aqueous phase

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