A comprehensive numerical model for the thermodynamic and transport properties of H₂O-NaCl fluids

Highlights

• The program is an open-source compilation of models, working in a wide range of PTx.

• Probrine is MS Excel extension, providing flexible input and output formats.

• The program provides a simple way to interpret large datasets.

Abstract

Saline fluids are common to a variety of geologic settings in Earth's crust and upper mantle. The binary system H₂O-NaCl is commonly used to interpret data obtained from fluid inclusions, and for geochemical modeling of mass and energy transport and fluid-rock interaction. Modeling of fluid properties in this binary system has generally relied on piecemeal compilations from available models specific to certain properties, whereas a standalone, comprehensive tool has been lacking. Here, we present a new computer package, entitled ProBrine (Properties of Brine) to evaluate the thermodynamic and transport properties of H₂O-NaCl fluids over the range of temperatures from 0 to 1000 °C, pressure from 1 to 5000 bar, and salinity from 0 to 100 wt% NaCl. ProBrine is designed to calculate a wide range of thermodynamic and transport properties, including (but not limited to): phase equilibria (liquid, vapor, and halite); molar volume, density, specific enthalpy, and viscosity. The program is also equipped to calculate derived properties such as: 1) the coefficient of isobaric thermal expansion; 2) the coefficient of isothermal compressibility; 3) the reduced susceptibility; 4) the isobaric specific heat capacity, and the fluxibility. In addition, the model will calculate solubility of the following six minerals: fluorapatite, calcite, corundum, fluorite, rutile, and quartz, as well as the respective temperature and pressure derivatives, which can be used to predict mineral dissolution and precipitation along a flow path. Moreover, the program is equipped to interpret fluid-inclusion data. The program is written in Visual Basic (VBA) in Microsoft Excel and is released open-source, allowing a user full scope to review, copy, modify and expand the program code.

Introduction

Geologic fluids in many settings are multicomponent solutions that include H₂O plus a variety of dissolved components (Roedder, 1972, Roedder, 1984; Kesler, 2005). Saline aqueous geologic fluids are commonly represented by simplified and well-characterized binary or ternary systems in geochemical modeling. These binary and ternary systems include various electrolytes (KCl, CaCl₂, MgCl₂) combined with H₂O (Steele-MacInnis et al., 2016). For example, widely used model chemical systems include H₂O-NaCl-CaCl₂ (Steele-MacInnis et al., 2011); H₂O-NaCl-FeCl₂ (Lecumberri-Sanchez et al., 2015); H₂O-NaCl-KCl (Lecumberri-Sanchez et al., 2020); and H₂O-NaCl-CO₂ (Steele-MacInnis, 2018; Li et al., 2020). For a detailed review of thermodynamic models available for other geologically relevant chemical systems, the reader is referred to Gottschalk (2007). Still, the most widely applicable and commonly used binary system used for representing hydrothermal fluids in geologic settings is H₂O-NaCl (Steele-MacInnis et al., 2012b; Klyukin et al., 2019).

The H₂O-NaCl system has been the subject of intensive characterization in terms of physical and chemical properties (Bodnar et al., 1985; Bischoff and Rosenbauer, 1988; Mao and Duan, 2009), and numerous numerical models (Anderko and Pitzer, 1993; Palliser and McKibbin, 1998a, Palliser and McKibbin, 1998b, Palliser and McKibbin, 1998c; Driesner, 2007; Driesner and Heinrich, 2007) and associated computer packages (Bowers and Helgeson, 1983; Driesner, 2007; Steele-MacInnis et al., 2012b; Bakker, 2018, Bakker, 2019) have been released to evaluate and interpret fluid properties in this system. Application of these models has revealed a variety of key consequences of considering the multicomponent nature of geologic fluids, compared to simpler models based exclusively on the single component H₂O: 1) for interpretation of data from fluid inclusions, salinity strongly affects estimation of density and isochore (Driesner, 2007), and the H₂O system is categorically insufficient to explain, for example, inclusions that homogenize at temperatures greater than the critical point of H₂O (Klyukin et al., 2016); 2) in theoretical modeling of hydrothermal systems, such as those at mid-ocean ridges, incorporation of salinity has key consequences that explain, for example, the maximum observed temperatures achieved in these systems (Jupp and Schultz, 2004; Coumou et al., 2008); 3) for hydrodynamic modeling of, for example, magmatic-hydrothermal systems, salinity has key consequences for fluid flow patterns and fluid phase equilibria (Weis et al., 2014; Weis, 2015); 4) for modeling fluid-rock reactions, salinity has key consequences for activities, chemical reactivity, and obvious effects on reactions such as alkali exchange (Miron et al., 2016; Frank et al., 2003); and 5) for reactive transport modeling, salinity has key consequences for where and how minerals are precipitated or dissolved (Steele-MacInnis et al., 2012a; Monecke et al., 2018). Thus, numerical models that can be used to quantify these phenomena are valuable to characterizing and interpreting a wide variety of geologic processes.

At present, several models are available to calculate various subsets of thermodynamic and transport properties of H₂O-NaCl fluids, but no single available computer package explicitly links these properties in one program that can be used to run simulations and/or interpret large datasets. Currently, existing programs are based on formulations (equations of state, EoS) for phase equilibria and transport or physical properties of H₂O-NaCl. Most notable of those is the fundamental EoS of Anderko and Pitzer (1993), and empirical EoS of Bowers and Helgeson (1983), Palliser and McKibbin, 1998a, Palliser and McKibbin, 1998b, Palliser and McKibbin, 1998c, Driesner (2007), and Driesner and Heinrich (2007). To date, the most accurate reproduction of the experimental data is achieved by the model of Driesner and Heinrich (2007) for phase equilibria of H₂O-NaCl and Driesner (2007) for density, enthalpy, and isobaric heat capacity. The fundamental EoS formulation of Anderko and Pitzer (1993) provides a wide range of thermodynamic properties, but in its current status is limited to temperatures above 300 °C, and it reproduces experimental data with less accuracy than those of Driesner (2007) and Driesner and Heinrich (2007).

Numerous existing programs have been designed to interpret fluid inclusions measurements, phase equilibria and/or fluid properties of H₂O-NaCl composition, including but not limited to: MacFlinCor (Brown and Hagemann, 1995), the model and EoS developed by Duan et al. (1995), SoWat, (Driesner, 2007; Driesner and Heinrich, 2007), HokieFlincs (Steele-MacInnis et al., 2012b) and AqSo_NaCl (Bakker, 2018, Bakker, 2019). MacFlinCor and the model by Duan et al. (1995) are currently unsupported. SoWat provides little functionality to interpret data from fluid inclusions and to evaluate fluid phase equilibria, density, and isobaric heat capacity. HokieFlincs is focused solely on interpretation of data from fluid inclusions. AqSo_NaCl is capable of evaluating fluid properties at specific PTx conditions or fluid inclusion properties.

In the present study, we describe a new computer package, entitled ProBrine (Properties of Brine), that incorporates a comprehensive and internally consistent set of numerical models, in order to comprehensively describe the properties of H₂O-NaCl from 0 to 1000 °C, 1 to 5000 bar, and 0 to 100 wt% NaCl. The model has been designed to be deliberately generic, allowing the user complete flexibility to decide the input and output parameters and ranges of physical conditions to explore. Below, we first briefly describe the phase equilibria and fluid properties of the H₂O-NaCl system, then describe their incorporation into the program ProBrine.