On elemental and isotopic fractionation of noble gases in geological fluids by molecular diffusion

Abstract

Noble gases are ideal natural tracers to characterize the storage, migration and origin of fluids in geological environments. They are chemically and biologically inert and therefore are only partially separated by physical processes including the one related to the molecular diffusion phenomenon, so called kinetic fractionation. However, its precise quantification is difficult to achieve and its modeling is still open for debates. Thus, in this work, we have investigated the capability of simple and predictive models to estimate elemental and isotopic fractionation of noble gases in various geological fluids. To do so, molecular dynamics simulations on noble gases in water, gas and oil under sub-surface conditions were performed. These numerical results were found to be consistent with previous ones including experiments and molecular simulations when available, i.e. in water. Interestingly, it appeared that the widely used square-root law is able to provide a good prediction for elemental fractionation between noble gases in all solvents, except for helium. Such unexpected result from the theoretical point of view is explained by a peculiar relationship between the molecular mass and the molecular size of noble gas elements. Regarding the noble gas isotopic fractionation, the square-root law is shown to be unable to provide reasonable results, confirming recent experimental and numerical works. As expected, it has been noticed that the kinetic theory relation provides a reasonable estimate of the isotopic fractionation in gas whereas it deteriorates in water and in oil. Finally, using the previous findings, we propose a simple and predictive scheme for the isotopic fractionation of noble gases in all studied geo-fluids which is noticeably better than both the square-root and the kinetic theory relations.

Introduction

Noble gases have been widely used as natural tracers to characterize the storage, migration and origin of fluids in geological environments (Ozima and Podosek, 2002, Ballentine et al., 2002, Burnard, 2013). Interestingly, they are chemically and biologically inert and therefore are only fractionated, i.e. partially separated, by physical processes (Ozima and Podosek, 2002). Among the existing physical processes, molecular diffusion is expected to significantly induce noble gases kinetic fractionation in geo-fluids (Marty, 1984, Prinzhofer et al., 2000, Ballentine et al., 2002). Such a kinetic fractionation, simply called fractionation in the following, emerges from the relative differences between molecular diffusion of noble gases when migrating into a fluid. However, its precise quantification and its modeling are still open for debates (Bourg and Sposito, 2008, Tyroller et al., 2014, Tyroller et al., 2018, Seltzer et al., 2019), wider than the noble gas community (Watkins et al., 2017, Wanner and Hunkeler, 2019). The purpose of this article is to provide new insights on the quantification of noble gases fractionation by molecular diffusion in various geo-fluids, in particular in oil and gas.

One of the main reasons for the debate to still be ongoing is the difficulty to experimentally quantify the elemental and even more the isotopic fractionation of noble gases due to molecular diffusion in geo-fluids (Jähne et al., 1987, Tempest and Emerson, 2013, Tyroller et al., 2014, Tyroller et al., 2018, Seltzer et al., 2019). Furthermore, these experiments are mostly limited to what occurs in water at standard conditions. As an alternative to experiments, molecular dynamics (MD) simulations (Allen and Tildesley, 2017, Frenkel and Smit, 2001) proved to be an effective tool for diffusion coefficients estimation in fluids. In particular, this numerical tool was already used to successfully estimate the elemental and isotopic fractionation of noble gases by molecular diffusion in water (Bourg and Sposito, 2008). With progresses in molecular modeling, MD simulations are now able to provide accurate results for the equilibrium and transport properties of various geo-fluids under subsurface conditions, including noble gases, natural gases and oil (Martin and Siepmann, 1998, Leach, 2001, Siu et al., 2012, Marrink and Tieleman, 2013, Hoang et al., 2017, Hoang et al., 2019).

A significant number of theoretical and empirical models are already proposed in the literature to quantify mass diffusion coefficients in various environments (Chapman and Cowling, 1970, Poling et al., 2001, Cussler, 2009). However, quite surprisingly, the most common approach to quantify the fractionation by molecular diffusion, whether isotopic or elementary, is simply based on the evaluation of the inverse of the square root of the mass ratios of the two species considered whatever the geo-fluids and the pressure and temperature conditions (Ballentine et al., 2002, Watkins et al., 2017, Wanner and Hunkeler, 2019). This simple relationship (called in the following the square root law) although theoretically correct for isotopic fractionation under low-density gas condition or in the limit of ultra-tight porous medium (Marty, 1984, Ballentine et al., 2002) only, consistently describes noble gases elemental fractionation in aqueous fluids under standard conditions (Jähne et al., 1987). Nevertheless, recent experimental studies and numerical simulations showed that the square root law tends to strongly overestimate noble gas isotopes fractionation in aqueous fluids (Bourg and Sposito, 2008, Tempest and Emerson, 2013, Tyroller et al., 2014, Tyroller et al., 2018, Seltzer et al., 2019). Similar findings have been noticed for other solute elements such as alkali and alkali earth metals, halides and CO₂, in both liquid water and silicate melts (Richter et al., 2006, Bourg et al., 2010, Zeebe, 2011, Watkins et al., 2017, Wanner and Hunkeler, 2019).

Thus, to rationalize all the results on noble gases, we propose in this work to systematically study the limits and capabilities of the various fractionation models applied to them in various geo-fluids, including not only water as already looked after in the seminal work of Bourg and Sposito (2008), but also gas (methane) and oil (n-hexane), using molecular simulations data. As it will be shown, this approach allowed us to explain why the square root law holds well for elemental fractionation and led us to propose a generic semi-empirical model able to provide a good estimate of noble gas isotopic fractionation by molecular diffusion whatever the geo-fluids and the thermodynamic conditions considered.

The article is organized as follows: in Section 2, we provide details on existing fractionation models and on numerical details of molecular simulations. The results obtained from molecular simulations and theoretical models are presented and discussed in 3 Results, 4 Discussion, respectively. Finally, the main results of this study are summarized in Section 5, which is the conclusion.