An Accelerating Rate Calorimeter (ARC) tracks a cell's own self-heating rate to find three landmark temperatures: T1 (onset of measurable self-heating, driven by SEI-layer decomposition), T2 (thermal-runaway trigger, once heat generation outruns heat loss) and T3 (the peak temperature reached once stored electrochemical and chemical energy is exhausted). This sim integrates a lumped three-stage Arrhenius kinetic model of that cascade:
dT/dt = [ Σᵢ mᵢ·ΔHᵢ·kᵢ(T)·zᵢ − h·A·(T − T_amb) ] / C
kᵢ(T) = Aᵢ · exp( −Eᵢ / (R·T) ) dzᵢ/dt = −kᵢ(T)·zᵢ
Stage 1 (SEI decomposition): onsets first, small exotherm
Stage 2 (anode–electrolyte reaction): dominant heat, drives runaway
Stage 3 (cathode / separator collapse): fastest kinetics, sets T3 peak
Each stage has its own remaining-reactant fraction z (1 → 0) and Arrhenius rate constant k(T); as the cell warms, k grows exponentially, more reactant converts per second, and more heat is released — a positive feedback loop that only stops once a stage's reactant is used up or heat loss (surface area × your cooling coefficient × ΔT to the chamber) catches up.
- State of charge — scales the reactive mass available to each stage (more stored lithium and electrolyte at high SOC → larger exotherms and an earlier runaway).
- Chamber heating rate — how fast the surrounding oven/chamber ramps, standing in for an external heat source (fire, adjacent cell, hot-box test).
- Heat rejection — the convective heat-loss coefficient h·A; strong cooling can hold a marginal cell below T2 indefinitely.
- Trigger Internal Short — injects an instantaneous ohmic heat pulse, the way a nail-penetration or crush test creates a local short circuit that can kick-start the cascade even from a cool cell.
Numbers are illustrative (they reproduce the right qualitative T1/T2/T3 staging and self-accelerating shape), not a validated fit to one specific commercial cell — real ARC data varies by chemistry, format and manufacturer. Peak temperatures above 700 °C have been measured in real ARC tests of high-SOC NMC/NCA cells.