What is TMRad? Time to Maximum Rate, TD24 and Adiabatic Temperature Rise

TMRad is usually measured with adiabatic calorimetry — an accelerating rate calorimeter (ARC) or similar instrument — which holds the sample in near-adiabatic conditions and records temperature and pressure as self-heating accelerates. Because the test cell itself absorbs some heat, results are corrected using the phi factor (φ = 1 + mass × heat capacity of the cell ÷ mass × heat capacity of the sample) to represent a large, truly adiabatic plant vessel.

At screening stage TMRad can be estimated from differential scanning calorimetry (DSC) kinetic data using the zero-order approximation TMRad ≈ cp·R·T² / (q·Ea), where cp is the specific heat, T the start temperature in kelvin, q the specific heat release rate at that temperature, and Ea the activation energy. The estimate is only as good as the kinetic data behind it, so it is used to decide whether adiabatic testing is needed, not to replace it.

TD24 is the temperature at which TMRad equals 24 hours. The reasoning is practical: if a cooling failure leaves the mixture at or below TD24, there is roughly a day to restore cooling, transfer or quench the batch before a runaway develops. Widely used assessment methods treat a TMRad above 24 hours as a low probability of runaway, and below about 8 hours as a high probability.

The adiabatic temperature rise is the temperature increase if all the reaction heat stays in the mass: ΔTad = Q / cp, where Q is the specific heat of reaction (J/kg) and cp the specific heat capacity (J/kg·K). A ΔTad above about 200 K is generally treated as high severity, and below about 50 K as low.

For semi-batch processes what matters is how much unreacted material has accumulated when cooling fails. The Maximum Temperature of the Synthesis Reaction (MTSR) is the process temperature plus the accumulated fraction times ΔTad. Comparing MTSR with TD24 tells you whether a cooling failure in the desired reaction can go on to trigger a secondary decomposition.

Stoessel's widely used approach ranks a process into five criticality classes by comparing four temperatures: the process temperature, the MTSR, the maximum technical temperature (MTT — usually the boiling point or the relief set temperature), and TD24. In class 1, the least critical, the MTSR stays below both the MTT and TD24, so a cooling failure neither boils the mass nor triggers decomposition. In class 5, the most critical, the MTSR exceeds TD24 and decomposition can be triggered before evaporative cooling or relief can act — the process needs redesign or strong technical safeguards.

The class determines what protection is appropriate: from simple operating limits in class 1, through reliance on evaporative cooling and a correctly sized relief system in the intermediate classes, to changes in dosing strategy, concentration or process route in class 5.