Ion association in concentrated NaCl brines from ambient to supercritical conditions: results from classical molecular dynamics simulations
© The Royal Society of Chemistry and the Division of Geochemistry of the American Chemical Society 2002
Received: 05 September 2002
Accepted: 18 November 2002
Published: 28 November 2002
Highly concentrated NaCl brines are important geothermal fluids; chloride complexation of metals in such brines increases the solubility of minerals and plays a fundamental role in the genesis of hydrothermal ore deposits. There is experimental evidence that the molecular nature of the NaCl–water system changes over the pressure–temperature range of the Earth's crust. A transition of concentrated NaCl–H2O brines to a "hydrous molten salt" at high P and T has been argued to stabilize an aqueous fluid phase in the deep crust.
In this work, we have done molecular dynamic simulations using classical potentials to determine the nature of concentrated (0.5–16 m) NaCl–water mixtures under ambient (25°C, 1 bar), hydrothermal (325°C, 1 kbar) and deep crustal (625°C, 15 kbar) conditions. We used the well-established SPCE model for water together with the Smith and Dang Lennard-Jones potentials for the ions (J. Chem. Phys., 1994, 100, 3757). With increasing temperature at 1 kbar, the dielectric constant of water decreases to give extensive ion-association and the formation of polyatomic (Na n Cl m ) n-m clusters in addition to simple NaCl ion pairs. Large polyatomic (Na n Cl m ) n-m clusters resemble what would be expected in a hydrous NaCl melt in which water and NaCl were completely miscible. Although ion association decreases with pressure, temperatures of 625°C are not enough to overcome pressures of 15 kbar; consequently, there is still enhanced Na–Cl association in brines under deep crustal conditions.
The compositions of fluid inclusions indicate that extremely concentrated NaCl brines can be involved in the transport of metals and the formation of hydrothermal ore deposits. There is a variety of evidence that Na and Cl ions become highly associated into NaCl ion pairs in high-temperature aqueous solutions at pressures below 2 kbar. Under such conditions, water and NaCl appear to behave like ideal mixtures[2, 3] so that the activity of water, equals its mole fraction ( ). Above 4 kbar, however, there is evidence that NaCl ion pairs become dissociated in NaCl–water mixtures. For example, Quist and Marshall find an increase in the electrical conductance of NaCl–H2Q mixtures between 2 and 4 kbar at 800°C. More recently, Aranovich and Newton measured the activity of water in concentrated NaCl solutions at 600–900°C and 2–15 kbar using the brucite-periclase equilibrium. At high pressure, the activity of water is well approximated by . This is the athermal activity expected if the NaCl–water system behaved as a hydrous salt melt consisting of water and completely dissociated NaCl. The much smaller activity of water under these conditions means that a free solution phase could coexist with an H2O-saturated granitic melt in the deep crust. Such a chloride-rich solution phase must play a fundamental role in scavenging metals prior to the formation of hydrothermal ore deposits.
Atomistic simulations of the NaCl–water system could confirm the interpretation of the experimental data and explore PT regimes that are not easily accessible in the laboratory. The simplest atomistic approach is the "restricted primitive model" where the solvent is replaced by a dielectric continuum and the ions are approximated as hard spheres with equal radii. Restricted primitive model simulations done by Pitzer and Schrieber and Gillan were used by Oelkers and Helgeson[8, 9] to derive association constants of polynuclear clusters in 1 : 1 electrolytes in supercritical aqueous solutions up to 4 kbar. These calculations predicted considerable ion pairing and clustering of Na–Cl in supercritical aqueous fluids. However, the use of a simple constant dielectric to model the solvent means we cannot understand any of the short-range physical interactions. It would be better to use an explicit molecular representation of the solvent. Koneshan and Rasaiah have shown that the degree of ion association in 1 m NaCl (at 683 K with a solvent density of 0.175 g cm-3) is signficantly different for continuum and molecular models simulations of the solvent.
A molecular treatment of the solvent and ion interactions is practical for large systems if we can express the interatomic interactions in terms of two-body potential functions. We can use molecular dynamics (MD) or Monte Carlo methods to sample the statistical mechanics of the system and determine not only thermodynamic quantities but also structural information and ionic speciation.
The SPC/E (Extended Simple Point Charge) water model of Berendsen et al. gives a very simple parameterization for the effective charges and short-range potential for water. In the SPC/E model we represent water molecules by three point charges in a rigid geometry with an HOH bond angle slightly different (109.5°) from that in the gas-phase H2O molecule (104.5°). Although the model does not allow any polarization or dissociation of the water molecules, it accurately reproduces the thermodynamic and dielectric properties of water, at least along the liquid–vapor coexistence curve. In particular, the SPC/E model predicts the critical point of water to be at 362–374°C with a density of 0.29–0.326 gcm-3. For real water, the critical point is at 374°C with a density of 0.322 g cm-3. The SPC/E model also gives a good prediction of the dielectric constant of water and its temperature dependence: the predicted values of ε(SPCE) = 81.0 at 25°C and ε(SPCE) = 6. at T(c) vs. 78.0 and 5.3, respectively, in real water. It is important that the dielectric properties are reproduced as accurately as possible if we wish to predict ion clustering NaCl electrolytes.
Lennard-Jones parameters from Smith and Dang, 199414
Formal ionic charges q i of +1 and -1 are used for Na+ and Cl-. The parameters were used in molecular dynamical simulations of a NaCl ion pair in 216 water molecules. This was a fairly small simulation but it gave very accurate predictions of experimental hydration energies and complex geometries. Smith and Dang predict that at 25°C, Na+ cations will be surrounded by 5.8 water molecules with a Na-O bond length of 2.33 Å. The Cl- anions are solvated by 6.9 waters with a Cl-H distance of 2.22 Å. These are in good agreement with those observed experimentally.
We are assuming that the interatomic potentials we are using can describe the NaCl–water system at the densities of interest at high pressure and temperature. Physically this means that we are assuming that the bonding and charge distributions in the water molecules at 15 kbar, 625°C(p = 1–1.3 g cm-3) are reasonably similar to those at ambient conditions. More sophisticated calculations based on quantum mechanical (ah initio) molecular dynamics are needed to explore this problem. At present, however, such calculations are limited to very small systems for very short run times and cannot address the problem of NaCl ion association as done here. Classical calculations for the equation of state of water at high P and T give good predictions of the water equations of state. This suggests that the potentials used here should be reasonably valid at density conditions of deep crustal fluids.
The formation of ion-pairs and clusters in NaCl solutions has been studied by atomistic MD simulations of dilute to 1 molar NaCl solutions[10, 19–22] Few simulations, however, have addressed the nature of concentrated NaCl solutions at elevated pressure and temperature. Brodholt obtained pair distribution functions and compared the densities of the simulated solutions to those obtained from the equations of state of Archer and of Anderko and Pitzer and found very good agreement. This was done for solutions up to 5.22 m in concentration and between temperatures of 300 to 2573 K, and under pressures of 1 bar up to 5 kbar. Although Brodholt noted the existence of polynuclear clusters, their existence was not directly tested in his study. The objective of the work presented here is to understand the nature of extremely concentrated (up to 16 m) NaCl solutions at conditions from ambient to those of the lower continental crust (625°C, 15 kbar).
2.0 Computational method and parameters
Molecular dynamics simulations were done on systems consisting of 975–1100 H2O molecules and 10–160 NaCl pairs. We believe our systems are large enough to describe the system insofar as simulations on much smaller systems (200–300 H2O, 5–20 NaCl pairs) gave essentially the same speciation and density. The simulations were conducted using the MOLDY molecular dynamics program. MOLDY implements periodic boundary conditions and the link-cell method, and uses quaternions to describe molecular orientations. It also uses the Ewald summation in the evaluation of coulombic interactions, and the link-cell algorithm for evaluation of the interactions. The real (rC) and k-space (kC) interaction cut-offs and Ewald parameter (α) were determined using eqn. (2)-(4), such that an accuracy of E = exp(-p) = 10-5 in the coulombic potential energy was achieved:
where N is the number of molecules, V is the volume of the cell and tR/tF has been empirically determined to be 5.5 for MOLDY. For a typical box length of 33 Å (e.g., in a simulation of 1100 H2O molecules and 80 NaCl pairs at 1 kbar), this gave rC = 12.5 Å. We used a time step of 0.25 fs as larger steps caused the system to be unstable. Each run was equilibrated for 25 ps (for temperature scaling, discussed below) and statistics were accumulated for 100–150 ps.
Statistics were collected on a constant NPT ensemble. The pressure was kept constant using the method of Parrinello and Rahman, and fixing all the off-diagonal components of the stress matrix to zero. During the equilibration phase, the temperature of the simulation was controlled by re-scaling the velocities every 20 time steps by the factor
where g is the number of degrees of freedom, kB is the Boltzmann constant, T the desired temperature, and <k> is the rolling average of the system kinetic energy over the previous 20 time steps. The scaling was carried out separately for translational and rotational components. The re-scaling was turned off once the temperature of the system has reached equilibrium about the desired value, in order to generate a realisation of the constant NPT ensemble. During the unsealed runs, temperatures were constant to within ~ 3%.
3.0 Results and discussion
3.2 Structure of water in NaCl brines
3.2 Na and Cl solvation and ion-association
The coordination numbers and bond lengths for dilute NaCl solutions at 25°C, 1 bar are in good agreement with those from previous calculations and experiment. For dilute NaCl, we predict a coordination number of 5.3 with only waters in the solvation sphere for Na+ at 25°C, I bar. With increasing NaCl molality, we find increased Cl complexation of Na. At 25°C and 1 bar the Na+ ions in an 8 m solution of NaCl have 4.3 waters and 1.0 Cl ligands in their first coordination shell. There is some evidence of solvent-separated Na–Cl ion pairs from the peak in the Na–Cl pair distribution function at 5 Å. However, this disappears with increasing temperature.
3.3 Dynamics of Na–Cl association
Since conductance measurements have been used to measure ion association in NaCl brines, it is of interest to determine the mobility of ions and clusters as a function of pressure, temperature and concentration. In the dilute limit, the limiting conductance (Λ0) of a monovalent electrolyte is
where e is the electronic charge, F is the Faraday constant, kB is Boltzmann's constant and D+,- are the diffusion constants for the individual ions. The self-diffusion constant (D) of a species can be determined from the Einstein relation
The simulations show that with increasing temperature there is increased association of Na+ and Cl- at the expense of solvation by water molecules. This is expected in terms of the decreased dielectric constant of water. The effect of pressure up to 15 kbar is not enough to overcome the effect of temperature to 625°C. Strong association between Na+ and Cl- ions persist to extreme (625°C, 15 kbar) conditions. There is little fundamental difference between the structures of the NaCl–water mixtures at 1 kbar, 325°C and 15 kbar, 625°C. The molecular picture of fully dissociated ions in high pressure NaCl–water mixtures that has been put forward by previous authors, therefore, is not correct. However, the large clusters have short lifetimes and the residence time of a Na or Cl ion in a polyatomic cluster is comparable to the time between atomic collisions. Because of this dynamic nature of the ion association, the transition from a conventional electrolyte to a hydrous molten salt is continuous with pressure and temperature.
MDC's studentship was supported by NERC and a CASE award from Rio Tinto Technology. Computer time on the T3E at CSAR Manchester was provided by NERC grant GR9/03550 (administered by John Brodholt and David Price, UCL). Computer time was also provided by the Laboratory for Advanced Computation in the Mathematical Sciences, University of Bristol.
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