Process Safety · Lesson 4 of 9 · 16 min read

Cooling failure and thermal runaway

Heat of reaction, ΔTad, accumulation, cooling capacity, MTSR and TMRad: the cooling-failure scenario step by step.

Educational overview. The principles here are general and simplified, and the figures and rules of thumb are typical values, not limits for your plant. Decisions need process-specific data, the applicable codes and standards, and a qualified assessment.

The scenario

The question is always the same: the cooling fails at the worst possible moment. What happens? Answering it in a structured way gives you the four temperatures of the Stoessel diagram.

1The reaction runs at the process temperature T_p.

2Cooling fails. Dosing stops (it must be interlocked). The unreacted reagent still in the reactor reacts adiabatically and the temperature climbs to the MTSR.

3If the MTSR is high enough, a decomposition or secondary reaction starts. How long that takes is the TMR_ad at the MTSR.

4On the way, the batch may reach its boiling point or relief pressure, the MTT, which can act as a barrier (lesson 5).

1 · How much energy? Heat of reaction and ΔT_ad

Q′_rx = c · (−ΔH_r) / ρ [kJ/kg] (c in mol/m³, ρ in kg/m³)
ΔT_ad = Q′_rx / c′_p [K]
c′_p,mix = Σ m_i·c′_p,i / Σ m_iFrom reaction calorimetry: Q_rx = ∫ q_rx dt (the area under the heat-flow curve). For a roughly constant heat flow during dosing, Q_rx ≈ q_rx × t_dosing.

2 · Can the plant cool it? Cooling capacity

q_ex = U · A · (T_r − T_c)U is the overall heat-transfer coefficient (typically 100–400 W/m²·K for jacketed vessels with organic batches), A the wetted jacket area (it grows as you dose), T_c the coolant temperature. Keep the cooling capacity at least 20 % above the maximum heat release rate.

In a semi-batch reaction that keeps pace with the dosing, the heat release rate is roughly the total heat divided by the dosing time. That gives the shortest dosing time the cooling can handle:

t_dosing,min = Q_rx,total / (q_ex / 1.2)

🧮 Shortest dosing time for the available cooling

From the total reaction heat and the reactor’s cooling capacity.

Educational screening tool Results are illustrative and depend on the stated assumptions. They are not a substitute for a qualified process-safety assessment, the applicable design code, vendor data, laboratory testing or engineering review.

Reaction heat Q′_rx (kJ/kg) Final batch mass (kg) U (W/m²·K) Jacket area A (m²) Reaction temperature T_r (°C) Coolant temperature T_c (°C) Safety margin (%)

3 · How hot can it get? Accumulation and MTSR

In a batch (all reagents charged, then heated) everything is unreacted at the start: X_acc = 100 %. In a semi-batch the dosed reagent may react instantly or may pile up. The fraction that has been added but not yet reacted is the accumulation. It is measured in the reaction calorimeter by comparing the heat released with the amount dosed.

MTSR = T_p + X_acc,max · ΔT_ad

Colder is not automatically safer.

Lowering T_p slows the reaction, so more reagent accumulates. Many runaways happened in reactions run “cold for safety”, sometimes with a stopped agitator or a forgotten catalyst, where the reagent sat unreacted and then reacted all at once.

4 · How much time is left? TMR_ad and TD24

For a decomposition with an initial heat release rate q′₀ (W/kg) at temperature T₀, the adiabatic time to maximum rate is approximately:

TMR_ad = c′_p · R · T₀² / (q′₀ · E_a)
q′(T) = q′₀ · exp[ (E_a/R)·(1/T₀ − 1/T) ]Zero-order, adiabatic approximation (T in kelvin). TD24 is the temperature at which TMR_ad = 24 h: below it, a decomposition develops slowly enough to restore control. As a rough rule the heat release rate doubles every 10 K (van ’t Hoff), so TMR_ad roughly halves.

🧮 TMR_ad and TD24 from one measurement

Enter a heat release rate measured at one temperature (isothermal DSC or ARC) and the activation energy.

Measured at T₀ (°C) Heat release rate q′₀ (W/kg) Activation energy E_a (kJ/mol) c′_p (kJ/kg·K) Check temperature (°C), e.g. MTSR

✍️ Check yourself: Semi-batch, T_p = 50 °C, ΔT_ad = 160 K, maximum accumulation 30 %. What is the MTSR?

MTSR = 50 + 0.30 × 160 = 98 °C. Only the unreacted part can heat the batch after the cooling fails.

✍️ Check yourself: Cooling capacity is 60 kW and the batch releases 720 MJ in total. With a 20 % margin, the shortest dosing time is about…

Usable capacity = 60 / 1.2 = 50 kW. 720,000 kJ / 50 kW = 14,400 s = 4 h. That is valid only if the reaction keeps pace with the dosing.

Key takeaways

Cooling-failure scenario: T_p → MTSR (accumulated reagent reacts) → decomposition after TMR_ad.
ΔT_ad = Q′ / c′_p; MTSR = T_p + X_acc·ΔT_ad.
Cooling capacity q_ex = UA(T_r − T_c), with a ≥ 20 % margin, sets the shortest dosing time.
Lower T_p can mean more accumulation and a higher MTSR.
TD24 (TMR_ad = 24 h) is the stability limit to compare the MTSR with.