Heat and temperature

Temperature is the strongest lever on a reactor. With Ea = 80 kJ/mol, going from 300 K to 320 K multiplies k by e^[(80,000 ÷ 8.314) × (1/300 − 1/320)] ≈ 7.4. A small temperature change can mean a much smaller reactor, or a much faster reaction than you planned.

Most industrial reactions are exothermic. If no heat is removed (an adiabatic reactor), the heat goes into the fluid: ΔT_ad = (−ΔH) × C_A0 × X ÷ (ρ × cp). For ΔH = −100 kJ/mol, C_A0 = 2000 mol/m³ (2 mol/L) and a water-like liquid (ρ × cp = 4180 kJ/(m³·K)), full conversion heats it by 100 × 2000 ÷ 4180 = 47.8 K.

To hold a temperature, heat has to be removed as fast as it's made: through a cooling jacket, internal coils, an external exchanger, or by boiling off some liquid (reflux cooling). Heat made grows exponentially with temperature (Arrhenius); heat removed grows only in proportion to the temperature difference with the coolant.

That mismatch is how thermal runaway starts. If the reactor gets a bit hotter than planned, the reaction speeds up, makes more heat, gets hotter still, and the loop takes off. Pressure rises with temperature, and the result can be a burst vessel. Several of the worst chemical accidents, including Seveso in 1976, began this way.

Designers check the worst case: what if the cooling fails? If the adiabatic temperature rise could reach a dangerous decomposition or boiling point, they add protection: dosing the reactant slowly so little is ever unreacted, emergency cooling, inhibitor injection, and relief valves sized for the runaway. The Process design course goes on into safety.