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

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

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

Class Implementation of Water dielectric constants, the DebyeHuckel "A" and "B" parameters and their derivatives at ambient to deepearth Temperature and Pressure conditions with three different formulations 
Functions

This function converts temperatures from Celsius to Kelvin and viceversa 

Compute the derivative of f, f'(a) with step size h. 
returns all constants and coefficients needed for the IAPWS95 formulation, packed into a dictionary 
Attributes
 pygcc.water_eos.eps = 2.220446049250313e16
 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 viceversa
 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(ah))/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/kgK])
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 temperaturepressure coefficient [Km3/kJ] if FullEOSppt is True)
dtx (Isothermal throttling coefficient [kJ/kg/bar] if FullEOSppt is True)
mux (JouleThomsen coefficient [Km3/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 R1408(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 singlevalued 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 IhIce IIIliquid). If neither of these conditions are satisfied, then the Ice Ihliquid 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 R1408(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 NewtonRaphson 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 IhIce IIIliquid. 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:
“IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance” (IAPWS R1208).
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, 101125.
 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 vaporliquid 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 vaporliquid 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). NewtonRaphson 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 NewtonRaphson 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 IAPWS95 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 NewtonRaphson 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 viceversa.
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/kgK] 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 [Pas] if FullEOSppt is True
bsx (float, vector) – Isentropic temperaturepressure coefficient [Km3/kJ] if FullEOSppt is True
dtx (float, vector) – Isothermal throttling coefficient [kJ/kg/bar] if FullEOSppt is True
mux (float, vector) – JouleThomsen coefficient [Km3/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:
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
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
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
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
For water saturation properties at any saturation Temperature :
water = iapws95(T = T),
where T is temperature in celsius
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, 4.96478e03, 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, 1.0035e03, 3.883, 10079.17 >>> water.adx, water.ztx, water.ptx, water.ktx, water.avx, water.mu, water.gdx 93.120, 2.189e03, 7.348e+03, 3.205e05, 6.809e04, 1.914e04, 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
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
 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:
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
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, 2.3283e05, 0.0004889
>>> deepearth = ZhangDuan(T = 200, rho = 1100) >>> deepearth.P, deepearth.G, deepearth.drhodP_T, deepearth.drhodT_P 7167.2231, 57319.0980, 2.3282e05, 0.0005122
References
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.
Zhang, C. and Duan, Z., 2009. “A model for COH 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.
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
 class pygcc.water_eos.water_dielec(**kwargs)[source]
Class Implementation of Water dielectric constants, the DebyeHuckel “A” and “B” parameters and their derivatives at ambient to deepearth 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) – DebyeHuckel “A” parameters [kg^1/2 mol^1/2]
Bh (float, vector) – DebyeHuckel “B” parameters [kg^1/2 mol^1/2 Angstrom^1]
bdot (float, vector) – bdot at any given temperature T
Adhh (float, vector) – DebyeHuckel “A” parameters associated with apparent molar enthalpy
Adhv (float, vector) – DebyeHuckel “A” parameters associated with apparent molar volume
Bdhh (float, vector) – DebyeHuckel “B” parameters associated with apparent molar enthalpy
Bdhv (float, vector) – DebyeHuckel “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:
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
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
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
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 R897, 1997).
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 DebyeHückel Coefficients. J. Phys. Chem. Ref. Data 26, 11251166.
Helgeson H. C. and Kirkham D. H. (1974) Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolytes at High Pressures and Temperatures: II. DebyeHuckel Parameters for Activity Coefficients and Relative Partial Molal Properties. Am. J. Sci. 274, 11991251.
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 291:541648
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
 dielec_FGL97(TC, rho)[source]
This function employs the FGL91 formulation to calculate the dielectric constant of water (E), the DebyeHuckel “A” parameters and DebyeHuckel “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 (DebyeHuckel “A” parameters [kg^1/2 mol^1/2])
Bh (DebyeHuckel “B” parameters [kg^1/2 mol^1/2 Angstrom^1])
bdot (bdot at any given temperature T)
Adhh (DebyeHuckel “A” parameters associated with apparent molar enthalpy)
Adhv (DebyeHuckel “A” parameters associated with apparent molar volume)
Bdhh (DebyeHuckel “B” parameters associated with apparent molar enthalpy)
Bdhv (DebyeHuckel “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
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 R897, 1997).
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 DebyeHückel Coefficients. J. Phys. Chem. Ref. Data 26, 11251166.
Helgeson H. C. and Kirkham D. H. (1974) Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolytes at High Pressures and Temperatures: II. DebyeHuckel Parameters for Activity Coefficients and Relative Partial Molal Properties. Am. J. Sci. 274, 11991251.
 dielec_JN91(TC, rho)[source]
This dielec_JN91 implementation employs the JN91 formulation to calculate the dielectric properties of water and steam, the DebyeHuckel “A” parameters and DebyeHuckel “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 : DebyeHuckel “A” parameters [kg^1/2 mol^1/2]
Bh : DebyeHuckel “B” parameters [kg^1/2 mol^1/2 Angstrom^1]
bdot : bdot at any given temperature T
Adhh : DebyeHuckel “A” parameters associated with apparent molar enthalpy
Adhv : DebyeHuckel “A” parameters associated with apparent molar volume
Bdhh : DebyeHuckel “B” parameters associated with apparent molar enthalpy
Bdhv : DebyeHuckel “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
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 291:541648
Helgeson H. C. and Kirkham D. H. (1974) Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolytes at High Pressures and Temperatures: II. DebyeHuckel Parameters for Activity Coefficients and Relative Partial Molal Properties. Am. J. Sci. 274, 11991251.
 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 DebyeHuckel “A” parameters and DebyeHuckel “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 : DebyeHuckel “A” parameters [kg^1/2 mol^1/2]
Bh : DebyeHuckel “B” parameters [kg^1/2 mol^1/2 Angstrom^1]
bdot : bdot at any given temperature T
Adhh : DebyeHuckel “A” parameters associated with apparent molar enthalpy
Adhv : DebyeHuckel “A” parameters associated with apparent molar volume
Bdhh : DebyeHuckel “B” parameters associated with apparent molar enthalpy
Bdhv : DebyeHuckel “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
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
Helgeson H. C. and Kirkham D. H. (1974) Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolytes at High Pressures and Temperatures: II. DebyeHuckel Parameters for Activity Coefficients and Relative Partial Molal Properties. Am. J. Sci. 274, 11991251.