Energetics of water in the Solar System

Water is vital for space exploration, from drinking to fuel reformation, and is naturally 5 abundant in the Solar System 1–16 . While in-situ resource utilization (ISRU) requires vastly 6 less energy than transporting resources, the energetics has scarcely been explored besides 7 on Earth and limited analysis on Mars’ vapor. Here, we develop a thermodynamic 8 framework to quantify the energy requirements for resource extraction from 18 water 9 sources on 11 planetary bodies. We find that desalinating saline liquid brines, where 10 available, could be the most energetically favorable option and the energy required to 11 access water vapor can be four to ten times higher than accessing ice deposits. While 12 desalination energetics are highly sensitive to salt concentration, we show that desalination 13 energetics only vary by a factor of 2 with respect to the type of salt present. Additionally, 14 unlike chemical mixtures, the minimum energetics are insensitive to composition in 15 physical mixtures (e.g., ice-regolith and inert vapor mixtures). Additionally, by deriving 16 and computing the equation-of-state for pure water, we extend the least work estimates of 17 atmospheric water harvesting by 94°C lower than previous studies that depend on 18 predetermined databases. The presented approach and data may inform decisions 19 regarding water harvesting, habitation, and resource reformation.

Stable sources of water in the Solar System can generally exist as saline liquid water brines, water 24 vapor in the ambient air, or as water-ice. In many cases, liquid water sources solely exist deep 25 underground and are combined with a variety of complex salts 12 . Water vapor can be found in 26 many atmospheres, but generally occurs in sparse quantities 4,8,9 . Water-ice, on the other hand, is 27 the most common form. It can be found in ice caps, craters, clouds, or small bodies in space. Space 28 exploration and research has derived estimates of water temperature, pressure, and mixture 29 composition on various bodies in the Solar System 1-16 . 30 Prior literature has examined the water vapor properties including enthalpy, but this is limited in 31 creating an understanding of the minimum energy requirements for extraction 17 . On Earth, we 32 have a robust understanding of the minimum energy requirements, but it is limited to air mixtures 33 at Earth-standard temperatures and pressures 18 . Understanding the properties of water in extreme 34 environments, where it exists as highly saline mixtures, in high pressure environments (>100 35 MPa), and at high (> 1000K) and low (< 50K) temperatures, is still a primary research objective 36 in astrophysics and physical chemistry 19,20 . Overall, water in the Solar System is commonplace, 37 yet thermodynamically complex, and the analysis of pure water extraction consequently varies 38 significantly. 39 The least work framework is derived from the combination of the first and second laws of 40 thermodynamics. It quantifies the exergy, or thermodynamic minimum energy, required to do a 41 process and is computed using the properties of the water source that is used. Exergy-based 42 analyses have been used in desalination and atmospheric water harvesting to compare the 43 efficiencies of dissimilar processes but have not been used to evaluate the energetics of different 44 water sources 18,21,22 . 45 In Eq. 1, "#$%& represents the minimum energy requirement, or least work, needed to obtain water 46 from a given water source. is the Gibbs free energy, or embodied thermophysical energy, of 47 water in a given environment or mixture. The Gibbs free energy is a function of the temperature, 48 pressure, and chemical activity. The isothermal separation step is defined by the feed (input), 49 permeate (pure water), and brine (reject). Subscript f refers to the feed (f) -or naturally occurring 50 -water-mixture. p refers to the permeate, or pure water. b refers to the brine (b) -or reject -water-51 mixture after pure water is removed. The subscript Earth denotes the desired final state of liquid 52 water at: Earth standard temperature (300K) and pressure (1 bar). signifies the fractional recovery 53 of pure water from the bulk, feed mixture. *"$+#& and ℎ respectively signify the acceleration due 54 to gravity and relative height between the source and the surface of a given planetary body. The 55 three grouped terms represent isothermal separation, heating of homogenous composition, and a 56 change in gravitational potential.

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In this work, we consider the least work of harvesting water from its existing state on a planetary 58 body to the desired state at the given surface with Earth-standard temperature and pressure, as 59 shown by Fig. 1. Extending this framework, we apply water mixture property models for extreme shown as a function of the ambient temperature. The desired temperature is assumed to be 300K (average temperature 72 on Earth). Each subfigure considers the case where the water source is on the surface of the planet (in this, the change 73 in gravitational potential is negligible).

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The material phase of the source (solid, liquid, vapor) is the dominant factor for the energy 75 requirements of pure water extraction, as described by Fig. 1. The energy requirement for 76 extracting pure water from concentrated liquid mixtures is generally one to two orders of 77 magnitude lower than extracting from water-ice or water vapor. The energy requirement for 78 extracting water from water vapor vastly ranges from near 0 (humid) to over 600 kJ/kg (arid).

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As the temperature of the ambient environment approaches the desired temperature (assumed to 80 be Earth standard 300K), the heating requirements decrease exponentially. Liquid source energy 81 requirements are not as sensitive to temperature as they are to composition. This is due to the fact 82 that water at Earth's average temperature (300K) naturally exists as a liquid, and therefore have 83 lower heating requirements (< 10 kJ/kg).

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The molar concentration of a liquid water mixture is the primary factor in determining the energy -are limited in what may be extracted, since water-ice is the primary form that is available.

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Furthermore, Venus is fundamentally the least favorable, as water vapor is the only water option.

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However, acquiring such water may still be desirable, as the least work of such intensive vapor 138 extraction is still significantly less than the energy required for deep space transport by rockets.

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A lower bound for the theoretical minimum energy to take an object into space is the kinetic energy cooling that has further complexities 32 .

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The least work framework, for the minimum energy to obtain pure water, helps prioritize water 165 sources by their macro properties. The parametric study of energetics (Fig. 1) and discrete case 166 studies (Fig. 2)   (2) The least work is divided into separation, heating, and gravitational components.  Where Z is the compressibility factor, which represents deviation from ideal gas behavior. is the 235 specific volume and R being the gas constant for water vapor. This equation is rearranged for 236 volume and the partial derivative with respect to temperature is taken, while holding pressure 237 constant.
The differential forms for changes in entropy and enthalpy are simplified with the compressibility 240 factor, below.
Combining these equations yields a differential form of Gibbs free energy, with respect to a dead 243 state 4 . In this section, lower case g represents the specific Gibbs free energy on a mass basis.
Where ′ is the virial coefficient as a function of temperature, expressed in Pa •• . This correlation 252 was used by Wexler (1977) to predict the compressibility factor within 0.01% over a wide range 253 of temperatures (173K -600K) 37 .

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The vapor pressure of ambient water is used as the dead state pressure. This is found via the Buck 255 correlations for saturated water vapor over liquid water or ice 38 .

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To model the free energy of water ice, the sample is assumed to be incompressible, which  Table S1. The ranges of conditions for each planet 268 are considered to be static and uniform, rather than either spatially or temporally weighted. water. To generalize to planets with unknown atmospheres, we assumed water is inert in the vapor 279 mixture and used partial properties to simplify property models. Validating this assumption, we 280 find that water vapor generally exists in low temperature or low humidity environments. At low 281 vapor pressures and temperatures, such as those considered in this work, water vapor behaves 282 nearly like an ideal gas. For real mixtures with highly volatile gases, the interspecies bonding 283 energy will lead likely to a slightly higher least work prediction in saturated and high temperature 284 environments. Fig. 1C is most accurate at lower temperature and humidity. The error may be near 285 5% at low concentrations (RH < 40%), as shown by a comparative study with real air mixtures 286 (Fig. S7). Additionally, to generalize property models in liquid brine mixtures, we considered form. This is a reasonable assumption in many cases, like the icy moons of Saturn and Jupiter. The 292 thermodynamic state is also limited in that it cannot capture the energetics of physically mixed 293 substances like regolith-water-ice. For liquid and ice sources that naturally exist in clathrates or 294 other physically absorbent structures, such as regolith, zeolites, or metal organic frameworks, the 295 structure-specific adsorption energy barrier is an additional consideration 39 .