"Element potential" equilibrium solver finds incorrect solution for Redlich-Kwong phase

[speth]

System information

• Cantera version: current master (29437ef)
• OS: any
• Python version: 3.8 / any

To Reproduce

import cantera as ct
import numpy as np

gas = ct.Solution('nDodecane_Reitz.cti', 'nDodecane_RK')
reversible = np.array([R.reversible for R in gas.reactions()])
major_species = ['co2','h2o','co','h2','ch4']
TPX = 1100, 200*ct.one_atm, 'CH4:1.0, O2:0.2'

gas.TPX = TPX
gas.equilibrate('TP', solver='element_potential')
rop_ep = gas.net_rates_of_progress[reversible]
X_ep = gas[major_species].X

gas.TPX = TPX
gas.equilibrate('TP', solver='gibbs')
rop_gibbs = gas.net_rates_of_progress[reversible]
X_gibbs = gas[major_species].X

gas.TPX = TPX
gas.equilibrate('TP', solver='vcs')
rop_vcs = gas.net_rates_of_progress[reversible]
X_vcs = gas[major_species].X

gas2 = ct.Solution('nDodecane_Reitz.cti', 'nDodecane_IG')
gas2.TPX = TPX
gas2.equilibrate('TP', solver='gibbs')
rop_ig = gas2.net_rates_of_progress[reversible]
X_ig = gas2[major_species].X

print('Element potential:', X_ep, max(abs(rop_ep)))
print('Gibbs:            ', X_gibbs, max(abs(rop_gibbs)))
print('VCS:              ', X_vcs, max(abs(rop_vcs)))
print('Ideal gas (Gibbs):', X_ig, max(abs(rop_vcs)))

Expected behavior

• Equilibrium mole fractions using the Redlich-Kwong model should be the same for all equilibrium solvers
• Net reaction rate for all reversible reactions should be zero (to within rounding error)
• Equilibrium using the ideal gas and Redlich-Kwong models should be somewhat different

Actual behavior

Element potential: [0.05060651 0.10176701 0.08695059 0.17343714 0.5871918 ] 0.022609974784086218
Gibbs:             [0.05062318 0.10508309 0.08508188 0.16642096 0.59274197] 8.117562178000526e-12
VCS:               [0.05062318 0.10508309 0.08508188 0.16642096 0.59274197] 2.313936819930973e-10
Ideal gas (Gibbs): [0.05060651 0.10176701 0.08695059 0.17343714 0.5871918 ] 2.313936819930973e-10

• Element potential solver gives a solution that is different from the other two solvers
• Net reaction rates are non-zero
• Element potential solution appears to correspond to the ideal gas solution

[decaluwe]

Thanks for raising this, @speth - I think your commentary over on the PengRobinson PR #641 is correct - this has to do with the function RedlichKwongMFTP::setToEquilState making no use of the interaction parameters (a_coeff and b_coeff), no? It appears to just use the reference state data.