SeaFreeze 0.9.1.post2

thermodynamic properties of the phases of H₂O

SeaFreeze

V0.9.1

The SeaFreeze package allows computation of the thermodynamic and elastic properties of water and ice polymorphs Ih, III, V and VI in the 0-2300 MPa and 220-500 K range. It is based on the evaluation of Local Basis Functions for each phase. The formalism is described in more details in Brown (2018), Journaux et al. (2019), and in the liquid water Gibbs parametrization by Bollengier, Brown, and Shaw (2019).

Installation

This package will install uw-highP-geophysics-tools and its dependencies.

Run the following command to install

pip3 install SeaFreeze

seafreeze.seafreeze: calculating thermodynamic and elastic properties of a phase of water

Usage

The main function of SeaFreeze is seafreeze.seafreeze, which has the following parameters:

• PT: the pressure (MPa) and temperature (K) conditions at which the thermodynamic quantities should be calculated -- note that these are required units, as conversions are built into several calculations This parameter can have one of the following formats:
  • a 1-dimensional numpy array of tuples with one or more scattered (P,T) tuples
  • a numpy array with 2 nested numpy arrays, the first with pressures and the second with temperatures -- each inner array must be sorted from low to high values a grid will be constructed from the P and T arrays such that each row of the output will correspond to a pressure and each column to a temperature
• phase: indicates the phase of H₂O. Supported phases are
  • 'Ih' - from Feistel and Wagner, 2006
  • 'III' - from Journaux et al, 2019
  • 'V' - from Journaux et al, 2019
  • 'VI' - from Journaux et al, 2019
  • 'water1' - extends to 500 K and 2300 MPa; from Bollengier et al 2019
  • 'water2' - extends to 100 GPa; from Brown 2018
  • 'water_IAPWS95' - LBF representation of IAPWS 95; from Wagner and Pruß, 2002

The output of the function is an object with properties corresponding to the following thermodynamic quantities (all but the last three are from lbftd):

• G: Gibbs energy in J kg^-1
• rho: density in kg m^-3
• vel: sound speed in m s^-1
• Cp: isobaric specific heat in J kg^-1 K^-1
• Cv: isochoric specific heat in J kg^-1 K^-1
• alpha: thermal expansivity in K^-1
• U: internal energy in J kg^-1
• A: Helmholtz energy in J kg^-1
• H: enthalpy in J kg^-1
• S: entropy in J kg^-1 K^-1
• Kt: isothermal bulk modulus in MPa
• Kp: pressure derivatives of isothermal bulk modulus (dimensionless)
• Ks: isotropic bulk modulus in MPa
• V: unit volume in m³ kg^-1
• Vp: compressional wave velocity in m s^-1
• Vs: shear wave velocity in m s^-1
• shear: shear modulus in MPa

Example

import numpy as np
import seafreeze as sf

# list supported phases
sf.phases.keys()

# evaluate thermodynamics for ice VI at 900 MPa and 255 K
PT = np.empty((1,), np.object)
PT[0] = (900, 255)
out = sf.seafreeze(PT, 'VI')
# view a couple of the calculated thermodynamic quantities at this P and T
out.rho     # density
out.Vp      # compressional wave velocity

# evaluate thermodynamics for water at three separate PT conditions
PT = np.empty((3,), np.object)
PT[0] = (441.0858, 313.95)
PT[1] = (478.7415, 313.96)
PT[2] = (444.8285, 313.78)
out = sf.seafreeze(PT, 'water1')
# values for output fields correspond positionally to (P,T) tuples 
out.H       # enthalpy

# evaluate ice V thermodynamics at pressures 400-500 MPa and temperatures 240-250 K
P = np.arange(400, 501, 2)
T = np.arange(240, 250.1, 0.5)
PT = np.array([P, T])
out = sf.seafreeze(PT, 'V')
# rows in output correspond to pressures; columns to temperatures
out.A       # Helmholtz energy
out.shear   # shear modulus

seafreeze.whichphase: determining the stable phase of water

Usage

Seafreeze also includes a function to determine which of the supported phases is stable under the given pressure and temperature conditions. The function seafreeze.whichphase has a single parameter, PT, which requires the same format as in the seafreeze.seafreeze function.

The output of the function is a Numpy array with an integer indicating the phase number corresponding to the PT input. The phase number 0 means liquid water, phase number 1 means ice Ih, phase number 3 means ice III, etc.

• for a list of scattered (P,T) conditions, each value corresponds to the same index in the input
• for a grid of PT conditions, each row corresponds to a pressure and each column to a temperature from the input.

seafreeze.phasenum2phase can be used to map output phase numbers to a phase.
Each item in this dictionary has the phase number as its key and the phase as the value.

Example

import numpy as np
import seafreeze as sf

# determine the phase of water at 900 MPa and 255 K
PT = np.empty((1,), np.object)
PT[0] = (900, 255)
out = sf.whichphase(PT)
# map to a phase using phasenum2phase
sf.phasenum2phase[out[0]]


# determine phase for three separate (P,T) conditions
PT = np.empty((3,), np.object)
PT[0] = (100, 200)
PT[1] = (400, 250)
PT[2] = (1000, 300)
out = sf.whichphase(PT)
# show phase for each (P,T)
[(PT, sf.phasenum2phase[pn]) for (PT, pn) in zip(PT, out)]

# find the likely phases at pressures 0-5 MPa and temperatures 240-300 K
P = np.arange(0, 5, 0.1)
T = np.arange(240, 300)
PT = np.array([P, T])
out = sf.whichphase(PT)

Change log

Changes since 0.9.0

• 0.9.1: add whichphase function

Changes from 0.8

• rename function get_phase_thermodynamics to seafreeze
• reverse order of PT and phase in function signature
• remove a layer of nesting (seafreeze.seafreeze rather than seafreeze.seafreeze.seafreeze)