Open Validation of Arrhenius Thermal Runaway Calibration for Lithium-Ion Cells

A Benchmark Against a Public ARC Dataset

Abstract

Accurate prediction of battery thermal runaway is a prerequisite for Hazard Mitigation Analysis (HMA) mandated by NFPA 855 for most battery energy storage system (BESS) installations; UL 9540A provides the standardized test method for thermal runaway fire propagation characterization. Arrhenius kinetic parameters (activation energy Ea, pre-exponential factor A, reaction enthalpy ΔH, and heat capacity Cp) required for CFD source-term generation (FLACS, KFX) are typically obtained by fitting an adiabatic thermal runaway ODE to Accelerating Rate Calorimetry (ARC) data. Despite its central role in fire safety engineering, no openly reproducible benchmark of this calibration procedure — with released code and raw results — exists, to our knowledge, for modern 21700 lithium-ion cells. We present Calor, an open inverse-analysis workflow that fits a two-state adiabatic ODE (y = [T, α], n = 1) to public ARC time-series data using a three-stage optimizer (L-BFGS-B → Nelder-Mead → default-value fallback). Applied to five cell chemistries from the Zenodo 21700 ARC dataset (DOI: 10.5281/zenodo.7707929, CC BY 4.0), the workflow achieves range-normalized RMSE (NRMSE) ranging from 0.076 (NMC) to 0.304 (LFP) for the four chemistries with meaningful fits. One chemistry, NCA-HEI, produced a complete non-fit: the reaction progress variable α remains essentially zero throughout the ARC window (α_f ≈ 0), with simulated peak temperature 139 °C versus measured 484 °C (absolute RMSE ≈ 97 K); its low range-normalized NRMSE (0.257) reflects the large temperature-range denominator rather than fit quality. We characterize two identifiability limits: (i) an Arrhenius compensation effect, along which Ea and log10(A) co-vary at near-constant NRMSE so that individual kinetic parameters are not uniquely resolved while the temperature trajectory is; and (ii) an extrapolation gap between the directly data-constrained quantity — the realized temperature rise α_f·ΔTad, where α_f is the reaction fraction reached in the ARC window — and ΔTad = ΔH/Cp itself, which is an extrapolation to full reaction completion (α→1); the ratio of ΔTad to the directly observed temperature rise is approximately 2.1× for NMC and 1.6× for NCA-HEII. Both limits manifest in the collapse of per-parameter bootstrap confidence intervals to near-zero width. We provide the calibration code and benchmark results as a demonstration of an openly reproducible calibration workflow.