Inconsistent thermo calculations in BinarySolutionTabulatedThermo

[speth]

Problem description

For the BinarySolutionTabulatedThermo phase:

• molar volume computed using the volume_mole function (in Python) disagrees with calculating the mole fraction weighted sum of the partial molar volumes.
• molar enthalpy computed using the enthalpy_mole function disagrees with calculating the mole fraction weighted sum of the partial molar enthalpies.

Steps to reproduce

# setup
>>> import cantera as ct
>>> p = ct.Solution('lithium_ion_battery.yaml', 'anode')
>>> p.TPX = 350, 10*101325, [0.9, 0.1]

# molar volume
>>> p.volume_mole
0.0341882587444934
>>> sum(p.partial_molar_volumes * p.X)
0.03449907488986783

# molar enthalpy
>>> p.enthalpy_mole
1475155.1278555722
>>> sum(p.partial_molar_enthalpies * p.X)
1475438.5688689428

System information

• Cantera version: 2.6.0 and main at 8fbb4bc

Additional context

This was discovered as part of #1299, which implements Cantera/enhancements#114.

[dschmider-HSOG]

Hi Ray,

I came across this issue and had a look at the behavior. The composition of the phase that is used for the test ([0.9 0.1]) lies outside the provided molefraction in ‘lithium_ion_battery.yaml’. When calling p.volume_mole, BinarySolutionTabulatedThermo::interpolate is invoked, which currently does not extrapolate and therefore caps values below and above the provided molefractions. p.partial_molar_volumes is also capped but since the partial molar volumes are anyways constant in this case, it doesn’t matter. Therefore, p.volume_mole and sum(p.partial_molar_volumes * p.X) return different values.
If the test is done at a different composition within the provided range, for example [0.7 0.3], the results are equivalent for both p.volume_mole and sum(p.partial_molar_volumes * p.X).

I also applied this test to a phase with tabulated molar-volume (‘BinarySolutionTabulatedThermo.yaml’). At molefractions that are provided in the table, p.volume_mole and sum(p.partial_molar_volumes * p.X) are equivalent but at values in-between the tabulated points, the results deviate slightly as a consequence of interpolation (see zoomed-in plot).

Worse, however, is that the enthalpy doesn’t match. This made me notice, that there are still some getter methods concerning (molar) quantities, that have to be overloaded in BinarySolutionTabulatedThermo to be able to handle non-linear molar volumes, namely:

• getChemPotentials
• getChemPotentials_RT
• getPartialMolarEnthalpies
• getPureGibbs
• getGibbs_RT
• getIntEnergy_RT
• getIntEnergy_RT_ref

Currently, these methods still use m_speciesMolarVolume as implemented in IdealSolidSolnPhase where I guess it should actually be the partial molar volume at the current state, since it is no longer necessarily constant.

A possible solution to fix the missing extrapolation behavior could be to automatically append the pure species values of the tabulated quantities at molefractions 0 and 1 during initThermo. Additionally, if the user already provides tabulated data for the whole range from 0 to 1 it should be checked for consistency with the pure species values provided in the species section.
I think this might also be related to Issue #1303

Best regards,
David