[Bug]: `Total lithium in electrolyte [mol]` multiplies by the full-cell length `L_x` in half-cell models

[repowazdogz-droid]

PyBaMM Version

main at 258fdc8 (2026-09-05); same code on v26.4.1 (d9e5afb)

Python Version

3.12.13

Describe the bug

Split out from #5700 at @NicolaCourtier's suggestion.

Total lithium in electrolyte [mol] is defined as

L_x = self.param.L_x
A = self.param.A_cc
eps_c_e_av = pybamm.yz_average(pybamm.x_average(eps_c_e))
variables = {"Total lithium in electrolyte [mol]": L_x * A * eps_c_e_av}

(base_electrolyte_diffusion.py, lines 130-135), and L_x = n.L + s.L + p.L unconditionally (geometric_parameters.py, line 34). With {"working electrode": "positive"} the electrolyte lives on whole_cell_domains = ["separator", "positive electrode"], and x_average averages over that domain, but the multiplier is still the three-layer length. In Xu2019 the average is over L_s + L_p = 67 µm and the multiplier is L_n + L_s + L_p = 767 µm, so the electrolyte lithium is overstated by a factor 11.4478.

Effect (Xu2019 half-cell, DFN({"working electrode": "positive"})):

• At t = 0 the electrolyte concentration is uniform, so the electrolyte lithium is exactly A * c_e0 * (eps_s * L_s + eps_p * L_p) = 3.642e-6 mol. The variable reports 4.170e-5 mol.
• Total lithium [mol] = Total lithium in particles [mol] + Total lithium in electrolyte [mol], so it reports 1.356e-4 mol at t = 0 against 9.754e-5 mol from a direct sum (39 % high). Total lithium in particles [mol] is unaffected; a direct sum matches it with coefficient 1.
• Because only the electrolyte term carries the factor, any time variation in Total lithium [mol] that comes from the electrolyte is also scaled by 11.45× relative to the particle term.
• Variables derived from Total lithium [mol], such as Total lithium lost [mol] and Loss of lithium inventory, including electrolyte [%], presumably inherit the factor. I have not checked them individually.

Two reasonable resolutions, and the current state is neither:

1. Multiply by the length of whole_cell_domains rather than L_x (or compute the electrolyte total as an integral over x rather than length × average, which removes the dependence on L_x altogether).
2. Document Total lithium in electrolyte [mol] and Total lithium [mol] as full-cell-only and leave them undefined in half-cell models.

Steps to Reproduce

Run against main 258fdc8; the output is under "Relevant log output".

import pybamm

model = pybamm.lithium_ion.DFN({"working electrode": "positive"})
pv = pybamm.ParameterValues("Xu2019")
sim = pybamm.Simulation(model, parameter_values=pv)
sol = sim.solve([0, 1])

A = pv["Electrode width [m]"] * pv["Electrode height [m]"] * pv["Number of electrodes connected in parallel to make a cell"]
c0 = pv["Initial concentration in electrolyte [mol.m-3]"]
expected = A * c0 * (pv["Separator porosity"] * pv["Separator thickness [m]"]
                     + pv["Positive electrode porosity"] * pv["Positive electrode thickness [m]"])
reported = sol["Total lithium in electrolyte [mol]"].entries[0]
L_x = pv["Negative electrode thickness [m]"] + pv["Separator thickness [m]"] + pv["Positive electrode thickness [m]"]
L_e = pv["Separator thickness [m]"] + pv["Positive electrode thickness [m]"]
print(f"reported at t=0 : {reported:.6e} mol")
print(f"direct sum      : {expected:.6e} mol")
print(f"ratio           : {reported / expected:.6f}   (L_x / (L_s + L_p) = {L_x / L_e:.6f})")

Relevant log output

reported at t=0 : 4.169742e-05 mol
direct sum      : 3.642408e-06 mol
ratio           : 11.447761   (L_x / (L_s + L_p) = 11.447761)

[rtimms]

Thanks, I would prefer option 1.