Calliope.solubility

`solubility`

`Solubility(composition)`

Solubility base class.

Pressures are in bar; subclasses return dissolved concentration in ppmw (parts-per-million by weight in the silicate melt).

Source code in src/calliope/solubility.py

def __init__(self, composition):
    self.callmodel = getattr(self, composition)

`SolubilityCH4(composition='basalt_ardia')`

Bases: Solubility

CH4 solubility models

Source code in src/calliope/solubility.py

def __init__(self, composition='basalt_ardia'):
    super().__init__(composition)

`basalt_ardia(p, p_total)`

Ardia 2013

Source code in src/calliope/solubility.py

def basalt_ardia(self, p, p_total):
    """Ardia 2013"""
    p_total *= 1e-4  # Convert to GPa
    p *= 1e-4  # Convert to GPa
    ppmw = p * np.exp(4.93 - (1.93 * p_total))
    return ppmw

`SolubilityCO(composition='mafic_armstrong')`

Bases: Solubility

CO solubility models

Source code in src/calliope/solubility.py

def __init__(self, composition='mafic_armstrong'):
    super().__init__(composition)

`mafic_armstrong(p, p_total)`

Armstrong 2015

Source code in src/calliope/solubility.py

def mafic_armstrong(self, p, p_total):
    """Armstrong 2015"""
    ppmw = 10 ** (-0.738 + 0.876 * np.log10(p) - 5.44e-5 * p_total)
    return ppmw

`SolubilityCO2(composition='basalt_dixon')`

Bases: Solubility

CO2 solubility models

Source code in src/calliope/solubility.py

def __init__(self, composition='basalt_dixon'):
    super().__init__(composition)

`basalt_dixon(p, temp)`

Dixon et al. (1995)

Source code in src/calliope/solubility.py

def basalt_dixon(self, p, temp):
    """Dixon et al. (1995)"""
    ppmw = (3.8e-7) * p * np.exp(-23 * (p - 1) / (83.15 * temp))
    ppmw = 1.0e4 * (4400 * ppmw) / (36.6 - 44 * ppmw)
    return ppmw

`SolubilityH2O(composition='peridotite')`

Bases: Solubility

H2O solubility models

Source code in src/calliope/solubility.py

def __init__(self, composition='peridotite'):
    super().__init__(composition)

`anorthite_diopside(p)`

Newcombe et al. (2017)

Source code in src/calliope/solubility.py

def anorthite_diopside(self, p):
    """Newcombe et al. (2017)"""
    return self.power_law(p, 727, 0.5)

`basalt_dixon(p)`

Dixon et al. (1995) refit by Paolo Sossi

Source code in src/calliope/solubility.py

def basalt_dixon(self, p):
    """Dixon et al. (1995) refit by Paolo Sossi"""
    return self.power_law(p, 965, 0.5)

`basalt_wilson(p)`

Hamilton (1964) and Wilson and Head (1981)

Source code in src/calliope/solubility.py

def basalt_wilson(self, p):
    """Hamilton (1964) and Wilson and Head (1981)"""
    return self.power_law(p, 215, 0.7)

`lunar_glass(p)`

Newcombe et al. (2017)

Source code in src/calliope/solubility.py

def lunar_glass(self, p):
    """Newcombe et al. (2017)"""
    return self.power_law(p, 683, 0.5)

`peridotite(p)`

Sossi et al. (2023)

Source code in src/calliope/solubility.py

def peridotite(self, p):
    """Sossi et al. (2023)"""
    return self.power_law(p, 524, 0.5)

`SolubilityN2(composition='libourel', x_SiO2=0.56, x_Al2O3=0.11, x_TiO2=0.01)`

Bases: Solubility

N2 solubility models.

Parameters:

Name	Type	Description	Default
`composition`	`str`	Solubility-law name. 'libourel' selects the linear Henry's-law form of Libourel et al. (2003); 'dasgupta' selects the physical-state-dependent form of Dasgupta et al. (2022).	`'libourel'`
`x_SiO2`	`float`	Melt mole fractions used by the Dasgupta et al. (2022) law to compute the molecular-N2 prefactor `dasfac_2`. Defaults (0.56, 0.11, 0.01) match the Earth-mantle reference adopted in prior CALLIOPE releases; override for non-Earth compositions. These kwargs have no effect when `composition='libourel'`.	`0.56`
`x_Al2O3`	`float`	Melt mole fractions used by the Dasgupta et al. (2022) law to compute the molecular-N2 prefactor `dasfac_2`. Defaults (0.56, 0.11, 0.01) match the Earth-mantle reference adopted in prior CALLIOPE releases; override for non-Earth compositions. These kwargs have no effect when `composition='libourel'`.	`0.56`
`x_TiO2`	`float`	Melt mole fractions used by the Dasgupta et al. (2022) law to compute the molecular-N2 prefactor `dasfac_2`. Defaults (0.56, 0.11, 0.01) match the Earth-mantle reference adopted in prior CALLIOPE releases; override for non-Earth compositions. These kwargs have no effect when `composition='libourel'`.	`0.56`

Source code in src/calliope/solubility.py

def __init__(self, composition='libourel', x_SiO2=0.56, x_Al2O3=0.11, x_TiO2=0.01):
    super().__init__(composition)

    # Stored on the instance so callers can introspect them; defaults
    # match the Earth-mantle reference used by Dasgupta et al. (2022).
    self.x_SiO2 = x_SiO2
    self.x_Al2O3 = x_Al2O3
    self.x_TiO2 = x_TiO2
    # dasfac_2 is only consumed by the dasgupta() path, so skip the
    # exp(...) precompute when libourel is selected. This avoids a
    # spurious RuntimeWarning at construction time when a libourel
    # caller passes extreme composition values that would overflow
    # the exponent (the dasgupta path is the only one that cares).
    if composition == 'dasgupta':
        self.dasfac_2 = np.exp(4.67 + 7.11 * x_SiO2 - 13.06 * x_Al2O3 - 120.67 * x_TiO2)
    else:
        self.dasfac_2 = None

`dasgupta(p, ptot, temp, fO2_shift)`

Dasgupta et al. (2022)

Source code in src/calliope/solubility.py

def dasgupta(self, p, ptot, temp, fO2_shift):
    """Dasgupta et al. (2022)"""

    # convert bar to GPa
    pb_N2 = p * 1.0e-4
    pb_tot = ptot * 1.0e-4

    pb_tot = max(pb_tot, 1e-15)

    # calculate N2 concentration in melt
    ppmw = pb_N2**0.5 * np.exp(5908.0 * pb_tot**0.5 / temp - 1.6 * fO2_shift)
    ppmw += pb_N2 * self.dasfac_2

    return ppmw

`libourel(p)`

Libourel et al. (2003)

Source code in src/calliope/solubility.py

def libourel(self, p):
    """Libourel et al. (2003)"""
    ppmw = self.power_law(p, 0.0611, 1.0)
    return ppmw

`SolubilityNobleGas(gas)`

Bases: Solubility

Noble gas solubility by Henry's law, Jambon et al. (1986).

Each noble gas dissolves in silicate melt in proportion to its partial pressure, ppmw = const * p. What sets it apart from the reactive CHNOS volatiles is the absence of any chemistry: the law carries no melt-composition, temperature, or redox dependence, and the gas couples to no other species through a reaction.

Parameters:

Name	Type	Description	Default
`gas`	`str`	Noble gas symbol; one of `He`, `Ne`, `Ar`, `Kr`, `Xe`.	required

Notes

The calibration is tholeiitic basalt at 1 bar and 1250-1600 C. Applying it at the high surface pressures of a noble-gas-rich atmosphere is an extrapolation of a 1-bar, linear Henry law with no saturation term.

Source code in src/calliope/solubility.py

def __init__(self, gas: str):
    if gas not in noble_gases:
        raise ValueError(
            f"SolubilityNobleGas: '{gas}' is not a noble gas. "
            f'Expected one of {noble_gases}.'
        )
    self.gas = gas
    self.const = jambon86_ppmw_per_bar(gas)
    super().__init__('jambon86')

`jambon86(p)`

Jambon et al. (1986) linear Henry's law: ppmw = const * p.

Source code in src/calliope/solubility.py

def jambon86(self, p):
    """Jambon et al. (1986) linear Henry's law: `ppmw = const * p`."""
    return self.power_law(p, self.const, 1.0)

`SolubilityS2(composition='gaillard', x_FeO=10.0)`

Bases: Solubility

S2 solubility models.

Parameters:

Name	Type	Description	Default
`composition`	`str`	Solubility-law name (currently only 'gaillard' is implemented).	`'gaillard'`
`x_FeO`	`float`	Melt FeO content [wt%] used by the Gaillard et al. (2022) law. The default value matches the Earth-mantle reference adopted in prior CALLIOPE releases; override for non-Earth bulk compositions.	`10.0`

Source code in src/calliope/solubility.py

def __init__(self, composition='gaillard', x_FeO=10.0):
    self.fO2_model = OxygenFugacity()
    self.x_FeO = x_FeO
    super().__init__(composition)

`jambon86_ppmw_per_bar(gas)`

Henry's-law solubility constant for a noble gas [ppmw / bar].

Converts the Jambon et al. (1986) STP-volume Henry constant for gas into parts-per-million by weight of dissolved gas per bar of partial pressure, using the melt-independent chain

const [ppmw/bar] = (k_STP / V_STP) [mol/g/bar]
                   * M [g/mol]
                   * 1e6 [ppmw per mass fraction]

where k_STP is the tabulated constant in cm3 STP/g/bar, V_STP is the molar volume of an ideal gas at STP, and M is the molar mass. The result is the linear coefficient of the ppmw = const * p Henry law.

Parameters:

Name	Type	Description	Default
`gas`	`str`	Noble gas symbol; one of `He`, `Ne`, `Ar`, `Kr`, `Xe`.	required

Returns:

Type	Description
`float`	Solubility constant in ppmw per bar.

Raises:

Type	Description
`KeyError`	If `gas` is not a Jambon et al. (1986) noble gas.

Source code in src/calliope/solubility.py

def jambon86_ppmw_per_bar(gas: str) -> float:
    """Henry's-law solubility constant for a noble gas [ppmw / bar].

    Converts the Jambon et al. (1986) STP-volume Henry constant for `gas`
    into parts-per-million by weight of dissolved gas per bar of partial
    pressure, using the melt-independent chain

        const [ppmw/bar] = (k_STP / V_STP) [mol/g/bar]
                           * M [g/mol]
                           * 1e6 [ppmw per mass fraction]

    where `k_STP` is the tabulated constant in cm3 STP/g/bar, `V_STP` is the
    molar volume of an ideal gas at STP, and `M` is the molar mass. The
    result is the linear coefficient of the `ppmw = const * p` Henry law.

    Parameters
    ----------
    gas : str
        Noble gas symbol; one of `He`, `Ne`, `Ar`, `Kr`, `Xe`.

    Returns
    -------
    float
        Solubility constant in ppmw per bar.

    Raises
    ------
    KeyError
        If `gas` is not a Jambon et al. (1986) noble gas.
    """
    k_stp = JAMBON86_STP_HENRY[gas]
    molar_mass_g = molar_mass[gas] * 1.0e3  # kg/mol -> g/mol
    return (k_stp / STP_MOLAR_VOLUME_CM3) * molar_mass_g * 1.0e6