pygcc.water_eos

Created on Wed Mar 17 16:02:22 2021

@author: adedapo.awolayo and Ben Tutolo, University of Calgary

Copyright (c) 2020 - 2021, Adedapo Awolayo and Ben Tutolo, University of Calgary

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>.

Functions implemented here include water equation of state and dielectric properties

Module Contents

Classes

Dummy

Class of functions to evaluate the IAPWS95 equation of state for calculating thermodynamic

iapws95

Implementation of IAPWS Formulation 1995 for ordinary water substance, revised release of 2016

ZhangDuan

Implementation of Zhang & Duan model Formulation for water at higher Temperature and Pressure conditions, i.e, Deep Earth Water - DEW

water_dielec

Class Implementation of Water dielectric constants, the Debye-Huckel "A" and "B" parameters and their derivatives at ambient to deep-earth Temperature and Pressure conditions with three different formulations

Functions

convert_temperature(T[, Out_Unit])

This function converts temperatures from Celsius to Kelvin and vice-versa

derivative(f, a[, method, h])

Compute the derivative of f, f'(a) with step size h.

readIAPWS95data()

returns all constants and coefficients needed for the IAPWS95 formulation, packed into a dictionary

Attributes

eps

J_to_cal

IAPWS95_COEFFS

pygcc.water_eos.eps = 2.220446049250313e-16
pygcc.water_eos.J_to_cal = 4.184
pygcc.water_eos.convert_temperature(T, Out_Unit='C')[source]

This function converts temperatures from Celsius to Kelvin and vice-versa

Parameters:

  • T (float, vector) – Temperature in °C or K

  • Out_Unit (string) – Expected temperature unit (C or K)

Returns:

T – Temperature in °C or K

Return type:

float, vector

Examples

>>> TC = 100; convert_temperature( TC, Out_Unit = 'K' )
    373.15
>>> TK = 520; convert_temperature( TK, Out_Unit = 'C' )
    246.85
pygcc.water_eos.derivative(f, a, method='central', h=0.001)[source]

Compute the derivative of f, f’(a) with step size h. :param f: Vectorized function of one variable :type f: function :param a: Compute derivative at x = a :type a: number :param method: Difference formula: ‘forward’, ‘backward’ or ‘central’ :type method: string :param h: Step size in difference formula :type h: number

Returns:

Difference formula:

central: f(a + h) - f(a - h))/2h forward: f(a + h) - f(a))/h backward: f(a) - f(a-h))/h

Return type:

float

pygcc.water_eos.readIAPWS95data()[source]

returns all constants and coefficients needed for the IAPWS95 formulation, packed into a dictionary

pygcc.water_eos.IAPWS95_COEFFS
class pygcc.water_eos.Dummy[source]

Bases: object

Class of functions to evaluate the IAPWS95 equation of state for calculating thermodynamic properties of water.

EOSIAPWS95(TK, rho, FullEOSppt=False)[source]

This function evaluates the IAPWS basic equation of state to calculate thermodynamic properties of water, which is written as a function of temperature and density.

Parameters:

  • TK (temperature [K]) –

  • rho (density [kg/m3]) –

  • FullEOSppt (Option to output all or essential water properties [False or True]) –

Returns:

  • px (pressure [bar])

  • ax (Helmholtz energy [kJ/kg-K])

  • sx (Entropy [kJ/kg/K])

  • hx (Enthalpy [kJ/kg])

  • gx (Gibbs energy [kJ/kg])

  • vx (Volume [m3/kg])

  • pdx (Derivative of pressure with respect to delta in bar)

  • adx (Helmholtz energy derivative with respect to delta)

  • ztx (zeta value (needed to calculate viscosity))

  • ptx (Derivative of pressure with respect to tau in bar)

  • ktx (Compressibility [/bar])

  • avx (Thermal expansion coefficient (thermal expansivity))

  • ux (Internal energy [kJ/kg] if FullEOSppt is True)

  • gdx (Gibbs energy derivative in kJ/kg if FullEOSppt is True)

  • bsx (Isentropic temperature-pressure coefficient [K-m3/kJ] if FullEOSppt is True)

  • dtx (Isothermal throttling coefficient [kJ/kg/bar] if FullEOSppt is True)

  • mux (Joule-Thomsen coefficient [K-m3/kJ] if FullEOSppt is True)

  • cpx (Isobaric heat capacity [kJ/kg/K] if FullEOSppt is True)

  • cvx (Isochoric heat capacity [kJ/kg/K] if FullEOSppt is True)

  • wx (Speed of sound [m/s] if FullEOSppt is True)

Usage

[px, ax, ux, sx, hx, gx, vx, pdx, adx, gdx, ztx, ptx, ktx, avx, bsx, dtx, mux, cpx, cvx, wx] = EOSIAPW95( TK, rho)

auxMeltingPressure(TK, P)[source]

This function calculates the melting pressure of ice as a function of temperature.

This model is described in IAPWS R14-08(2011), Revised Release on the Pressure along the Melting and Sublimation Curves of Ordinary Water Substance, as may be found at: http://www.iapws.org/relguide/MeltSub.html

Five ice phases are covered here. The melting pressure is not a single-valued function of temperature as there is some overlap in the temperature ranges of the individual phases. There is no overlap in the temperature ranges of Ices III, V, VI, and VII, which together span the range 251.165 - 715K. The melting pressure is continuous and monotonically increasing over this range, albeit with discontinuities in slope at the triple points where two ice phases and liquid are in equilibrium. The problem comes in with Ice Ih, whose temperature range completely overlaps that of Ice III and partially overlaps that of Ice V. For a temperature in the range for Ice Ih, there are two possible melting pressures.

The possible ambiguity here in the meaning of melting pressure is not present if the temperature is greater than or equal to the triple point temperature of 273.16K, or if the pressure is greater than or equal to 2085.66 bar (the triple point pressure for Ice Ih-Ice III-liquid). If neither of these conditions are satisfied, then the Ice Ih-liquid curve will be used. To deal with the pressure condition noted above, this function assumes that an actual pressure is specified.

Parameters:

  • P (pressure [bar]) –

  • TK (temperature [K]) –

Returns:

Pmelt

Return type:

melting pressure [bar]

Usage

[Pmelt] = auxMeltingPressure( TK, P)

auxMeltingTemp(P)[source]

This function calculates the melting temperature of ice as a function of pressure.

This inverts the model for the melting pressure as a function of temperature. That model is described in IAPWS R14-08(2011), Revised Release on the Pressure along the Melting and Sublimation Curves of Ordinary Water Substance as may be found at: http://www.iapws.org/relguide/MeltSub.html

Inversion of the model for the melting pressure is done here using the secant method. This is chosen instead of the Newton-Raphson method to avoid potential problems with slope discontinuites at boundaries between the ice phases for pressures above 208.566 MPa, which is the equilibrium pressure for Ice Ih-Ice III-liquid. The corresponding equlibrium temperature is 251.165K. Putative melting temperatures should not be less than this for pressures above 208.566 Mpa, nor more than this for pressures less than this. :param P: :type P: pressure [bar]

Returns:

Tmelt

Return type:

temperature [K]

Usage

[Tmelt] = auxMeltingTemp( P)

waterviscosity(TC, P, rho)[source]

This function calculates the viscosity of water using Ref:

  1. “IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance” (IAPWS R12-08).

  2. Huber M.L., Perkins R.A., Laesecke A., Friend D.G., Sengers J.V., Assael M.J., Metaxa I.N., Vogel E., Mares R., and Miyagawa K. (2009) New International Formulation for the Viscosity of H2O. J. Phys. Chem. Ref. Data 38, 101-125.

Parameters:

  • [°C] (TC temperature) –

  • [bar] (P pressure) –

  • [kg/m3] (rho density) –

Return type:

visc viscosity [Pa.s]

Usage

[visc] = waterviscosity( TC, P, rho)

apxsatpropT(TK)[source]

This function evaluates the approximate pressure (psat) as a function of temperature along the vapor-liquid equilibrium curve, using equation 2.5 of Wagner and Pruss (2002). It also calculates the derivative of saturation pressure wrt temperature as well as the densities of the liquid and vapor phases using equations 2.6 and 2.7 from the same source.

Parameters:

TK temperature [K] (saturation temperature)

Returns:

Psat saturation pressure [bar]

Psat_t Derivative of saturation pressure with respect to temperature

rhosl density of liquid [kg/m3]

rhosv density of vapor [kg/m3]

Usage:

[Psat, Psat_t, rhosl, rhosv] = apxsatpropT( TK)

apxsatpropP(P)[source]

This function evaluates the approximate temperature (tsat) as a function of pressure along the vapor-liquid equilibrium curve, using equation 2.5 of Wagner and Pruss (2002). This is similar to apxsatpropT(TK), but evaluates the inverse problem (Tsat as a function of pressure instead of psat as a function of temperature). Newton-Raphson iteration is used.

Parameters:

P pressure [bar]

Returns:

Tsat saturation temperature [K]

Usage:

[Tsat] = apxsatpropP( P)

calcsatpropT(TK)[source]

This function calculates the saturation properties as a function of specified temperature. This is achieved using Newton-Raphson iteration to refine values of pressure, vapor density, and liquid density, starting with results obtained using approximate equations included by Wagner and Pruss (2002) in their description of the IAPWS-95 model.

Parameters:

[K] (TK temperature) –

Returns:

  • Psat saturation pressure [bar]

  • rhosl density of liquid [kg/m3]

  • rhosv density of vapor [kg/m3]

Usage

[Psat, rhosl, rhosv] = calcsatpropT( TK)

calcsatpropP(P)[source]

This function calculates the saturation properties as a function of specified pressure. This is done by iterating using Newton method on pressure to obtain the desired temperature. This implementation calls calcsatpropT(TK) to calculate the saturation pressure, liquid and vapor densities.

Parameters:

[bar] (P pressure) –

Returns:

  • Tsat temperature [K]

  • rhosl liquid density [kg/m3]

  • rhosv vapor density [kg/m3]

Usage

[Tsat, rhosl, rhosv] = calcsatpropP( P)

fluidDescriptor(P, TK, *rho)[source]

This function calculates the appropriate description of the H2O fluid at any given temperature and pressure

A problem may occur if the pressure is equal or nearly equal to the saturation pressure. Here comparing the pressure with the saturation pressure pressure may lead to the wrong description, as vapor and liquid coexist at the saturation pressure. It then becomes neccesary to compare the fluid density with the saturated vapor and saturated liquid densities. If the density is known, it will be used. If it is not known, the results obtained here will determine the starting density estimate, thus in essence choosing “vapor” or “liquid” for pressures close to the saturation pressure.

Parameters:

P pressure [bar]

TK temperature [K]

rho density [kg/m3] (optional)

Returns:

phase fluid description

rhosl liquid density [kg/m3]

rhosv vapor density [kg/m3]

Usage:

[udescr, rhosl, rhosv] = fluidDescriptor( P, TK)

calcwaterppt(TC, P, *rho0, FullEOSppt=False)[source]

This function evaluates thermodynamic properties of water at given temperature and pressure. The problem reduces to finding the value of density that is consistent with the desired pressure. The Newton-Raphson method is employed. Small negative values of calculated pressure are okay. Zero or negative values for calculated “pdx” (pressure derivative with respect to delta) imply the unstable zone and must be avoided.

Parameters:

T : temperature [°C]

P : pressure [bar]

rho0 : starting estimate of density [kg/m3] (optional) FullEOSppt: Option to output all or essential water properties [False or True]

Returns:

rho : density [kg/m3]

gx : Gibbs energy [cal/mol]

hx : Enthalpy [cal/mol]

sx : Entropy [cal/mol/K]

vx : Volume [m3/mol]

Pout : pressure [bar]

Tout : temperature [°C]

ux : Internal energy [cal/mol] if FullEOSppt is True

ax : Helmholtz energy [cal/mol/K] if FullEOSppt is True

cpx : Isobaric heat capacity [cal/mol/K] if FullEOSppt is True

Usage:

[rho, gxcu, hxcu, sxcu, vxcu, uxcu, axcu, cpxcu, Pout, Tout] = calcwaterppt(T, P),

calcwaterppt_Prho(P, rho, FullEOSppt=False)[source]

This function evaluates thermodynamic properties of water at given density and pressure. The problem reduces to finding the value of temperature that is consistent with the desired pressure.

Parameters:

P : pressure [bar]

rho : density [kg/m3]

FullEOSppt: Option to output all or essential water properties [False or True]

Returns:

rho : density [kg/m3]

gx : Gibbs energy [cal/mol]

hx : Enthalpy [cal/mol]

sx : Entropy [cal/mol/K]

vx : Volume [m3/mol]

Pout : pressure [bar]

Tout : temperature [°C]

ux : Internal energy [cal/mol] if FullEOSppt is True

ax : Helmholtz energy [cal/mol/K] if FullEOSppt is True

cpx : Isobaric heat capacity [cal/mol/K] if FullEOSppt is True

Usage:

[rho, gxcu, hxcu, sxcu, vxcu, uxcu, axcu, cpxcu, Pout, Tout] = calcwaterppt_Prho(P, rho),

calcwaterstdppt(TK, hx, sx, vx, ux=None, cpx=None, Out_Unit='standard')[source]

This function converts thermodynamic properties of water from kilogram units to standard thermochemical scale (calorie units) and vice-versa.

Parameters:

TK : temperature [K]

hx : Enthalpy [kJ/kg] or [cal/mol]

sx : Entropy [kJ/kg/K] or [cal/mol/K]

vx : Volume [m3/kg] or [m3/mol]

ux : Internal energy [kJ/kg] or [cal/mol]

cpx : Isobaric heat capacity [kJ/kg/K] or [cal/mol/K]

Returns:

gx : Gibbs energy [kJ/kg] or [cal/mol]

hx : Enthalpy [kJ/kg] or [cal/mol]

sx : Entropy [kJ/kg/K] or[cal/mol/K]

vx : Volume [m3/kg] or[m3/mol]

ax : Helmholtz energy [kJ/kg/K] or[cal/mol/K]

ux : Internal energy [kJ/kg] or [cal/mol]

cpx : Isobaric heat capacity [kJ/kg/K] or[cal/mol/K]

Usage:

[gx, hx, sx, vx, ux, ax, cpx] = calcwaterstdppt(TK, hx, sx, vx, ux, cpx, Out_Unit = ‘kilogram’)

class pygcc.water_eos.iapws95(**kwargs)[source]

Implementation of IAPWS Formulation 1995 for ordinary water substance, revised release of 2016

Notes

Temperature and Pressure input limits

  • -22 ≤ TC ≤ 1000 and 0 ≤ P ≤ 100,000

Parameters:

  • T (float, vector) – Temperature [°C]

  • P (float, vector) – Pressure [bar]

  • rho (float, vector) – Density [kg/m³]

  • rho0 (float, vector) – Starting estimate of density [kg/m³]

  • rhom (float, vector) – Molar density [kg/m³]

  • delta (float, vector) – Reduced density, rho/rhoc

  • tau (float, vector) – Reduced temperature, Tc/T

  • v (float, vector) – Specific volume [m³/kg]

  • vm (float, vector) – Specific molar volume [m³/mol]

  • Out_Unit (string) – Expected units (‘standard’ or ‘kilogram’)

  • FullEOSppt (bool) – Option to output all or essential water properties [False or True]

Returns:

  • The calculated instance has the following potential properties

  • rho (float, vector) – Density [kg/m3]

  • G (float, vector) – Gibbs energy [cal/mol] or [kJ/kg]

  • H (float, vector) – Enthalpy [cal/mol] or [kJ/kg]

  • S (float, vector) – Entropy [cal/mol/K] or [kJ/kg/K]

  • V (float, vector) – Volume [m3/mol] or [m3/kg]

  • P (float, vector) – Pressure [bar]

  • TC (float, vector) – Temperature [°C]

  • TK (float, vector) – Temperature [K]

  • U (float, vector) – Internal energy [cal/mol] or [kJ/kg] if FullEOSppt is True

  • F (float, vector) – Helmholtz energy [cal/mol/K] or [kJ/kg-K] if FullEOSppt is True

  • Cp (float, vector) – Isobaric heat capacity [cal/mol/K]

  • rhosl (float, vector) – Density of liquid [kg/m3]

  • rhosv (float, vector) – Density of vapor [kg/m3]

  • pdx (float, vector) – Derivative of pressure with respect to delta in bar

  • adx (float, vector) – Helmholtz energy derivative with respect to delta

  • ztx (float, vector) – zeta value (needed to calculate viscosity)

  • ptx (float, vector) – Derivative of pressure with respect to tau in bar

  • gdx (float, vector) – Gibbs energy derivative [kJ/kg] if FullEOSppt is True

  • ktx (float, vector) – Compressibility [/bar]

  • avx (float, vector) – Thermal expansion coefficient (thermal expansivity)

  • mu (float, vector) – viscosity [Pa-s] if FullEOSppt is True

  • bsx (float, vector) – Isentropic temperature-pressure coefficient [K-m3/kJ] if FullEOSppt is True

  • dtx (float, vector) – Isothermal throttling coefficient [kJ/kg/bar] if FullEOSppt is True

  • mux (float, vector) – Joule-Thomsen coefficient [K-m3/kJ] if FullEOSppt is True

  • cvx (float, vector) – Isochoric heat capacity [kJ/kg/K] if FullEOSppt is True

  • wx (float, vector) – Speed of sound [m/s] if FullEOSppt is True

Usage:

The general usage of iapws95 is as follows:

  1. For water properties at any Temperature and Pressure not on steam saturation curve:

    water = iapws95(T = T, P = P),

    where T is temperature in celsius and P is pressure in bar

  2. For water properties at any Temperature and Pressure on steam saturation curve:

    water = iapws95(T = T, P = ‘T’),

    where T is temperature in celsius, followed with a quoted character ‘T’ to reflect steam saturation pressure

    water = iapws95(T = ‘P’, P = P),

    where P is pressure in bar, followed with a quoted character ‘P’ to reflect steam saturation temperature

  3. For water properties at any Temperature and density :

    water = iapws95(T = T, rho = rho),

    where T is temperature in celsius and rho is density in kg/m³

  4. For water properties at any Pressure and density :

    water = iapws95(P = P, rho = rho),

    where P is pressure in bar and rho is density in kg/m³

  5. For water saturation properties at any saturation Temperature :

    water = iapws95(T = T),

    where T is temperature in celsius

  6. For water saturation properties at any saturation Pressure :

    water = iapws95(P = P),

    where P is pressure in bar

Examples

>>> water = iapws95(T = 200., P = 50, FullEOSppt = True)
>>> water.rho, water.G, water.H, water.S, water.V, water.P, water.T, water.mu
    867.2595, -60368.41787, -65091.03895,  25.14869,  4.96478e-03,  50.00000,
    200.000, 0.00013546

>>> water = iapws95(T=200, rho=996.5560, Out_Unit='kilogram', FullEOSppt=True)
>>> water.P, water.F, water.S, water.H, water.G, water.V, water.Cp, water.pdx
    2872.063, -234.204, 2.051, 1024.747, 53.994, 1.0035e-03, 3.883, 10079.17
>>> water.adx, water.ztx, water.ptx, water.ktx, water.avx, water.mu, water.gdx
    93.120, 2.189e-03, -7.348e+03,  3.205e-05,  6.809e-04, 1.914e-04, 1011.40

>>> water = iapws95(T = 350)
>>> water.P, water.rhosl, water.rhosv
    165.2942 574.7065 113.6056

>>> water = iapws95(P = 150)
>>> water.TC, water.rhosl, water.rhosv
    342.1553, 603.5179, 96.7271

References

  1. Wagner, W., Pruß, A., 2002. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31, 387–535. https://doi.org/10.1063/1.1461829

kwargs
mwH2O = 18.015268
__checker__(**kwargs)[source]
__calc__(**kwargs)[source]
class pygcc.water_eos.ZhangDuan(**kwargs)[source]

Implementation of Zhang & Duan model Formulation for water at higher Temperature and Pressure conditions, i.e, Deep Earth Water - DEW

Notes

Temperature and Pressure input limits

  • 0 ≤ TC ≤ 1726.85 and 1000 ≤ P ≤ 300,000

Parameters:

  • T (float, vector) – Temperature [°C]

  • P (float, vector) – Pressure [bar]

  • rho (float, vector) – Density [kg/m³]

  • rho0 (float, vector) – Starting estimate of density [kg/m³]

  • densityEquation (string) – specify either ‘ZD05’ to use Zhang & Duan (2005) or ‘ZD09’ to use Zhang & Duan (2009)

Returns:

  • The calculated instance has the following potential properties

  • rho (float, vector) – Density [kg/m3]

  • rhohat (float, vector) – Density [g/cm³]

  • G (float, vector) – Gibbs energy [cal/mol]

  • drhodP_T (float, vector) – Partial derivative of density with respect to pressure at constant temperature

  • drhodT_P (float, vector) – Partial derivative of density with respect to temperature at constant pressure

Usage:

The general usage of ZhangDuan is as follows:

  1. For water properties at any Temperature and Pressure:

    deepearth = ZhangDuan(T = T, P = P),

    where T is temperature in celsius and P is pressure in bar

  2. For water properties at any Temperature and density :

    deepearth = ZhangDuan(T = T, rho = rho),

    where T is temperature in celsius and rho is density in kg/m³

Examples

>>> deepearth = ZhangDuan(T = 25, P = 5000)
>>> deepearth.rho, deepearth.G, deepearth.drhodP_T, deepearth.drhodT_P
    1145.3065, -54631.5351, 2.3283e-05, -0.0004889

>>> deepearth = ZhangDuan(T = 200, rho = 1100)
>>> deepearth.P, deepearth.G, deepearth.drhodP_T, deepearth.drhodT_P
    7167.2231, -57319.0980, 2.3282e-05, -0.0005122

References

  1. Zhang, Z., Duan, Z., 2005. Prediction of the PVT properties of water over wide range of temperatures and pressures from molecular dynamics simulation. Phys. Earth Planet. Inter. 149, 335–354. https://doi.org/10.1016/j.pepi.2004.11.003.

  2. Zhang, C. and Duan, Z., 2009. “A model for C-O-H fluid in the Earth’s mantle”, Geochimica et Cosmochimica Acta, vol. 73, no. 7, pp. 2089–2102, doi:10.1016/j.gca.2009.01.021.

  3. Sverjensky, D.A., Harrison, B., Azzolini, D., 2014. Water in the deep Earth: The dielectric constant and the solubilities of quartz and corundum to 60kb and 1200°C. Geochim. Cosmochim. Acta 129, 125–145. https://doi.org/10.1016/j.gca.2013.12.019

kwargs
__calc__(**kwargs)[source]
ZD_Pressure_drhodP(TC, rhohat, method=None)[source]
ZD_Density(TC, P, method='ZD05', error=None)[source]
GibbsEnergy(TC, P, method='VolumeIntegral')[source]
class pygcc.water_eos.water_dielec(**kwargs)[source]

Class Implementation of Water dielectric constants, the Debye-Huckel “A” and “B” parameters and their derivatives at ambient to deep-earth Temperature and Pressure conditions with three different formulations

Parameters:

  • T (float, vector) – Temperature [°C]

  • P (float, vector) – Pressure [bar]

  • rho (float, vector) – Density [kg/m³]

  • Dielec_method (string) – specify either ‘FGL97’ or ‘JN91’ or ‘DEW’ as the method to calculate dielectric constant (optional), if not specified, default - ‘JN91’

  • Dielec_DEWoutrange (string) – specify either ‘FGL97’ or ‘JN91’ as the method to calculate dielectric constant for out of range for ‘DEW’ method if any

Returns:

  • The calculated instance has the following potential properties

  • E (float, vector) – dielectric constant of water

  • rhohat (float, vector) – density [g/cm³]

  • Ah (float, vector) – Debye-Huckel “A” parameters [kg^1/2 mol^-1/2]

  • Bh (float, vector) – Debye-Huckel “B” parameters [kg^1/2 mol^-1/2 Angstrom^-1]

  • bdot (float, vector) – bdot at any given temperature T

  • Adhh (float, vector) – Debye-Huckel “A” parameters associated with apparent molar enthalpy

  • Adhv (float, vector) – Debye-Huckel “A” parameters associated with apparent molar volume

  • Bdhh (float, vector) – Debye-Huckel “B” parameters associated with apparent molar enthalpy

  • Bdhv (float, vector) – Debye-Huckel “B” parameters associated with apparent molar volume

  • dEdP_T (float, vector) – Partial derivative of dielectric constant with respect to pressure at constant temperature

  • dEdT_P (float, vector) – Partial derivative of dielectric constant with respect to temperature at constant pressure

Notes

FGL97 Temperature and Pressure input limits:

  • -35 ≤ TC ≤ 600 and 0 ≤ P ≤ 12000

DEW Temperature and Pressure input limits:

  • 100 ≤ TC ≤ 1200 and 1000 ≤ P ≤ 60000

JN91 Temperature and Pressure input limits:

  • 0 ≤ TC ≤ 1000 and 0 ≤ P ≤ 5000

Usage

The general usage of water_dielec is as follows:

  1. For water dielectric properties at any Temperature and Pressure:

    dielect = water_dielec(T = T, P = P, Dielec_method = ‘JN91’),

    where T is temperature in celsius and P is pressure in bar

  2. For water dielectric properties at any Temperature and density :

    dielect = water_dielec(T = T, rho = rho, Dielec_method = ‘JN91’),

    where T is temperature in celsius and rho is density in kg/m³

  3. For water dielectric properties at any Temperature and Pressure on steam saturation curve:

    dielect = water_dielec(T = T, P = ‘T’, Dielec_method = ‘JN91’),

    where T is temperature in celsius and P is assigned a quoted character ‘T’ to reflect steam saturation pressure

    dielect = water_dielec(P = P, T = ‘P’, Dielec_method = ‘JN91’),

    where P is pressure in bar and T is assigned a quoted character ‘P’ to reflect steam saturation temperature

Examples

>>> dielect = water_dielec(T = 50, P = 500, Dielec_method = 'JN91')
>>> dielect.E, dielect.rhohat, dielect.Ah, dielect.Bh, dielect.bdot
    71.547359, 1.00868586, 0.52131899,   0.33218072,   0.04088528
>>> dielect.Adhh, dielect.Adhv, dielect.Bdhh, dielect.Bdhv
    0.64360153,   2.13119279,  15.6936832 , -14.52571678
>>> dielect.dEdP_T, dielect.dEdT_P
    0.03293026,   -0.32468033

>>> dielect = water_dielec(T = 200, rho = 1100, Dielec_method = 'FGL97')
>>> dielect.E, dielect.rhohat, dielect.Ah, dielect.Bh, dielect.bdot
    49.73131404,  1.1,  0.5302338, 0.34384714,  0.04452579
>>> dielect.Adhh, dielect.Adhv, dielect.Bdhh, dielect.Bdhv
    1.21317825,  2.21165281, 28.0047878, -34.21216547
>>> dielect.dEdP_T, dielect.dEdT_P
    0.01444368, -0.16864644

>>> dielect = water_dielec(T = 250, P = 5000, Dielec_method = 'DEW')
>>> dielect.E, dielect.rhohat, dielect.Ah, dielect.Bh, dielect.bdot, dielect.Adhh
    39.46273008,  1.0238784,  0.62248141,   0.35417088, 0.02878662, 0.80688122
>>> dielect.Adhv, dielect.Bdhh, dielect.Bdhv, dielect.dEdP_T, dielect.dEdT_P
     3.13101408, 39.76402294, -35.29670957, 0.0129006 , -0.08837842

References

  1. Release on the Static Dielectric Constant of Ordinary Water Substance for Temperatures from 238 K to 873 K and Pressures up to 1000 MPa” (IAPWS R8-97, 1997).

  2. Fernandez D. P., Goodwin A. R. H., Lemmon E. W., Levelt Sengers J. M. H., and Williams R. C. (1997) A Formulation for the Permittivity of Water and Steam at Temperatures from 238 K to 873 K at Pressures up to 1200 MPa, including Derivatives and Debye-Hückel Coefficients. J. Phys. Chem. Ref. Data 26, 1125-1166.

  3. Helgeson H. C. and Kirkham D. H. (1974) Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolytes at High Pressures and Temperatures: II. Debye-Huckel Parameters for Activity Coefficients and Relative Partial Molal Properties. Am. J. Sci. 274, 1199-1251.

  4. Johnson JW, Norton D (1991) Critical phenomena in hydrothermal systems: State, thermodynamic, electrostatic, and transport properties of H2O in the critical region. American Journal of Science 291:541-648

  5. D. A. Sverjensky, B. Harrison, and D. Azzolini, “Water in the deep Earth: the dielectric constant and the solubilities of quartz and corundum to 60 kb and 1200 °C,” Geochimica et Cosmochimica Acta, vol. 129, pp. 125–145, 2014

kwargs
__checker__(**kwargs)[source]
__calc__(**kwargs)[source]
dielec_FGL97(TC, rho)[source]

This function employs the FGL91 formulation to calculate the dielectric constant of water (E), the Debye-Huckel “A” parameters and Debye-Huckel “B” parameters (3) and their derivatives as a function of temperature and pressure

Notes

Temperature and Pressure input limits:

  • -35 ≤ TC ≤ 600 and 0 ≤ P ≤ 12000

Parameters:

  • TC (temperature [°C]) –

  • rho (density [kg/m3]) –

Returns:

  • E (dielectric constant of water)

  • rhohat (density [g/cm³])

  • Ah (Debye-Huckel “A” parameters [kg^1/2 mol^-1/2])

  • Bh (Debye-Huckel “B” parameters [kg^1/2 mol^-1/2 Angstrom^-1])

  • bdot (bdot at any given temperature T)

  • Adhh (Debye-Huckel “A” parameters associated with apparent molar enthalpy)

  • Adhv (Debye-Huckel “A” parameters associated with apparent molar volume)

  • Bdhh (Debye-Huckel “B” parameters associated with apparent molar enthalpy)

  • Bdhv (Debye-Huckel “B” parameters associated with apparent molar volume)

  • dEdP_T (Partial derivative of dielectric constant with respect to pressure at constant temperature)

  • dEdT_P (Partial derivative of dielectric constant with respect to temperature at constant pressure)

Usage

[E, rhohat, Ah, Bh, bdot, Adhh, Adhv, Bdhh, Bdhv, dEdP_T, dEdT_P] = dielec_FGL97( TC, rho)

References

  1. Release on the Static Dielectric Constant of Ordinary Water Substance for Temperatures from 238 K to 873 K and Pressures up to 1000 MPa” (IAPWS R8-97, 1997).

  2. Fernandez D. P., Goodwin A. R. H., Lemmon E. W., Levelt Sengers J. M. H., and Williams R. C. (1997) A Formulation for the Permittivity of Water and Steam at Temperatures from 238 K to 873 K at Pressures up to 1200 MPa, including Derivatives and Debye-Hückel Coefficients. J. Phys. Chem. Ref. Data 26, 1125-1166.

  3. Helgeson H. C. and Kirkham D. H. (1974) Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolytes at High Pressures and Temperatures: II. Debye-Huckel Parameters for Activity Coefficients and Relative Partial Molal Properties. Am. J. Sci. 274, 1199-1251.

dielec_JN91(TC, rho)[source]

This dielec_JN91 implementation employs the JN91 formulation to calculate the dielectric properties of water and steam, the Debye-Huckel “A” parameters and Debye-Huckel “B” parameters and their derivatives

Notes

Temperature and Pressure input limits:

  • 0 ≤ TC ≤ 1000 and 0 ≤ P ≤ 5000

Parameters:

  • TC (temperature [°C]) –

  • rho –

rhohat : density [g/cm³]

Ah : Debye-Huckel “A” parameters [kg^1/2 mol^-1/2]

Bh : Debye-Huckel “B” parameters [kg^1/2 mol^-1/2 Angstrom^-1]

bdot : bdot at any given temperature T

Adhh : Debye-Huckel “A” parameters associated with apparent molar enthalpy

Adhv : Debye-Huckel “A” parameters associated with apparent molar volume

Bdhh : Debye-Huckel “B” parameters associated with apparent molar enthalpy

Bdhv : Debye-Huckel “B” parameters associated with apparent molar volume

dEdP_T : Partial derivative of dielectric constant with respect to pressure at constant temperature

dEdT_P : Partial derivative of dielectric constant with respect to temperature at constant pressure

Usage

References

  1. Johnson JW, Norton D (1991) Critical phenomena in hydrothermal systems: State, thermodynamic, electrostatic, and transport properties of H2O in the critical region. American Journal of Science 291:541-648

  2. Helgeson H. C. and Kirkham D. H. (1974) Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolytes at High Pressures and Temperatures: II. Debye-Huckel Parameters for Activity Coefficients and Relative Partial Molal Properties. Am. J. Sci. 274, 1199-1251.

dielec_DEW()[source]

This watercalc implementation employs the DEW formulation embedded in Sverjensky et al. (2014) to calculate the dielectric properties of water and steam, the Debye-Huckel “A” parameters and Debye-Huckel “B” parameters and their derivatives. This function has been set up to use either Johnson and Norton (1991) or Fernandez et al. (1997) formulation below 5000 bar and Sverjensky et al. (2014) formulation above 5000 bar.

Notes

Temperature and Pressure input limits:

  • 100 ≤ TC ≤ 1200 and 1000 ≤ P ≤ 60000

Parameters:

  • TC (temperature [°C]) –

  • P –

rhohat : density [g/cm³]

Ah : Debye-Huckel “A” parameters [kg^1/2 mol^-1/2]

Bh : Debye-Huckel “B” parameters [kg^1/2 mol^-1/2 Angstrom^-1]

bdot : bdot at any given temperature T

Adhh : Debye-Huckel “A” parameters associated with apparent molar enthalpy

Adhv : Debye-Huckel “A” parameters associated with apparent molar volume

Bdhh : Debye-Huckel “B” parameters associated with apparent molar enthalpy

Bdhv : Debye-Huckel “B” parameters associated with apparent molar volume

dEdP_T : Partial derivative of dielectric constant with respect to pressure at constant temperature

dEdT_P : Partial derivative of dielectric constant with respect to temperature at constant pressure

Usage

References

  1. D. A. Sverjensky, B. Harrison, and D. Azzolini, “Water in the deep Earth: the dielectric constant and the solubilities of quartz and corundum to 60 kb and 1200 °C,” Geochimica et Cosmochimica Acta, vol. 129, pp. 125–145, 2014

  2. Helgeson H. C. and Kirkham D. H. (1974) Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolytes at High Pressures and Temperatures: II. Debye-Huckel Parameters for Activity Coefficients and Relative Partial Molal Properties. Am. J. Sci. 274, 1199-1251.