NovaSolver›Adiabatic Reactor Temperature Rise Simulator Back
Reaction Engineering
Adiabatic Reactor Temperature Rise Simulator
Find out how hot the reaction mixture gets when an exothermic reaction runs without releasing any heat to its surroundings. Adjust the heat of reaction, concentration, conversion, density and heat capacity to see the adiabatic temperature rise ΔT_ad and final reactor temperature update in real time, and gauge the risk of thermal runaway.
Parameters
Heat of reaction ΔH (exothermicity)
kJ/mol
Heat released per mole of reactant that reacts
Initial reactant concentration C0
mol/L
Reactant concentration at the start; lowered by dilution
Conversion X
Fraction of reactant that actually reacts (0–1)
Mixture density ρ
kg/m³
Specific heat capacity c_p
kJ/(kg·K)
Heat needed to raise 1 kg of the mixture by 1 K
Initial temperature T0
°C
Results
—
Adiabatic rise ΔT_ad (K)
—
Final reactor temp. T_final (°C)
—
Max adiabatic rise X=1 (K)
—
Heat released (kJ/L)
—
Heat per mole (kJ/mol)
—
Runaway risk verdict
—
Adiabatic reactor heat-up animation
Inside the adiabatic reactor (a vessel that releases no heat), the exothermic reaction warms the contents from T0 up to T_final. The vessel colour shows the temperature (blue = cool, orange-red = hot).
Adiabatic temperature rise ΔT_ad [K]. −ΔH_rxn: heat of reaction, C0: initial concentration, X: conversion, ρ: density, c_p: specific heat capacity. All released heat is assumed to warm the reaction mixture.
$$T_{final}=T_0+\Delta T_{ad}$$
Final reactor temperature T_final [°C], the initial temperature T0 plus the adiabatic temperature rise.
ΔT_ad is independent of reactor size. It depends only on the chemistry (heat of reaction, concentration, conversion) and the heat capacity of the mixture, so a flask and an industrial reactor give the same value.
What is the Adiabatic Temperature Rise?
🙋
I keep seeing the term "adiabatic temperature rise" in chemical-plant safety discussions. What does it actually mean?
🎓
Roughly speaking, it is "how many degrees the temperature would rise if all the heat from an exothermic reaction had nowhere to go and went entirely into warming the reaction mixture". When a reaction releases heat, you normally dump it outside with cooling water in the jacket. But what if all the cooling fails? The released heat has nowhere to go and warms its own liquid. That worst-case temperature rise is the adiabatic temperature rise, ΔT_ad.
🙋
I see, the worst case. When I raise the heat of reaction ΔH on the left, ΔT_ad keeps growing. Why is a big value a problem?
🎓
Because the temperature rise itself sets off a chain reaction. The reaction rate rises exponentially with temperature — that is the Arrhenius law. So a small temperature increase makes the reaction faster, faster reaction means more heat, and that heat raises the temperature again. This positive feedback is "thermal runaway". The larger ΔT_ad is, the higher the temperature the system reaches once it enters that loop. A 200 K rise starting from 25 °C lands you at 225 °C — hot enough to boil the solvent or trigger decomposition side reactions.
🙋
Wait — if a higher temperature makes the reaction even faster, that loop never stops. So bigger reactors are more dangerous?
🎓
Good question. Actually ΔT_ad itself does not depend on reactor size — notice there is no volume in the formula. A 1 L flask and a 10 m³ reactor give the same ΔT_ad for the same concentration and reaction. But whether it actually reaches that temperature is another matter. A large reactor has a small surface area relative to its volume, so the heat-transfer area for shedding heat is relatively too small. The bigger it is, the closer it is to adiabatic. A reaction that was safe in the lab running away as soon as it is scaled up — that is the scariest pattern in practice.
🙋
That is alarming. So how do I make ΔT_ad smaller?
🎓
The clearest way is to dilute the reactants. Lower the initial concentration C0 on the left and you will see ΔT_ad fall in proportion — the formula has ΔT_ad proportional to C0. Move C0 on the chart below and a straight proportional line appears. Then there is stronger cooling, and semi-batch operation — feeding the reactant in slowly rather than all at once. If you charge everything at once, unreacted reactant piles up in the reactor as "stored heat". If cooling stops and that stored amount reacts all at once, you get the worst kind of runaway. So the golden rule is to dose it in and never build up that reservoir.
🙋
Conversion X affects the result too. What is the "maximum adiabatic rise" at X=1?
🎓
It is ΔT_ad for X=1, meaning the reactant reacts 100% completely. Normal operation often stops at, say, 80% conversion, but for safety assessment you work with the worst case: "what if it all reacts?". If reactant that had been accumulating unreacted suddenly reacts to completion, you can get the full temperature rise of this maximum value. So in design you check against the maximum adiabatic rise at X=1, not the current ΔT_ad — confirming that even at that temperature nothing breaks, boils or decomposes.
Frequently Asked Questions
The adiabatic temperature rise is how much the temperature of the reaction mixture would climb if none of the heat released by the reaction could escape. It is calculated as ΔT_ad = (−ΔH_rxn)·C0·X / (ρ·c_p), where −ΔH_rxn is the heat of reaction, C0 is the initial reactant concentration, X is the conversion, ρ is the density and c_p is the specific heat capacity. Because it represents the worst case — how hot the batch gets if all cooling stops — it is regarded as the single most important number for the safety of an exothermic reaction.
A runaway happens when the heat generated by the reaction exceeds the reactor's ability to remove it. The reaction rate rises exponentially with temperature following the Arrhenius law, so a small temperature increase accelerates the heat release, which pushes the temperature still higher — a positive feedback loop. Once heat removal can no longer keep up, the temperature surges, triggering side reactions, decomposition, boiling and pressure rise. The larger the adiabatic temperature rise, the higher the temperature reached once this loop sets in, and the more dangerous it becomes.
No. The adiabatic temperature rise ΔT_ad is fixed by the chemistry — heat of reaction, initial concentration and conversion — together with the thermal properties of the mixture, its density and heat capacity. There is no volume or reactor size in the formula, so a 1 L flask and a 10 m³ industrial reactor give the same ΔT_ad for the same concentration and reaction. How hot it actually gets, however, depends on heat removal: larger reactors have a smaller heat-transfer area relative to their volume, so cooling is less effective and the system behaves more like an adiabatic one.
There are three main defences. First, reactor cooling — removing the generated heat through a jacket or internal coils. Second, dilution of the reactants — lowering the initial concentration C0 directly reduces the adiabatic temperature rise itself. Third, semi-batch (dosing) operation — feeding the reactant in slowly so that unreacted material never accumulates in the reactor. Accumulated unreacted material is a stored reservoir of potential heat that, if cooling fails, can react all at once and fuel a runaway. The ΔT_ad from this tool is the starting point for comparing the effect of these measures quantitatively.
Real-World Applications
Batch manufacture of pharmaceuticals and fine chemicals: The production of drug intermediates and agrochemicals uses many strongly exothermic reactions — nitration, sulfonation, diazotization and more. Their adiabatic temperature rise often exceeds 100 K, so ΔT_ad must always be estimated before fixing the operating conditions. Working out "how hot it gets if cooling fails" with a calculation like this tool, and then checking whether the solvent boils or a secondary decomposition starts at that temperature, is the first step of process safety.
Reaction-hazard assessment and scale-up: A lab flask has a large surface area and cools naturally, so reactions that did not run away in the laboratory can still cause accidents the moment they are scaled up to a large reactor that behaves adiabatically. ΔT_ad is calculated from a heat of reaction measured in a reaction calorimeter such as the RC1, and combined with hazard-class schemes like Stoessel's criticality classes to decide the scale, concentration and dosing rate that can be operated safely.
Temperature control of polymerization processes: The polymerization of styrene and acrylic monomers is strongly exothermic, and as conversion proceeds the viscosity rises, degrading both mixing and heat removal. Knowing the adiabatic temperature rise lets engineers predict how high the temperature climbs during a cooling failure and whether it leads to a runaway gel effect (the Trommsdorff effect), informing decisions on emergency shutdown or the addition of a short-stop agent.
Self-heating assessment in storage and transport: Unstable substances such as organic peroxides and nitro compounds slowly decompose and release heat even in storage. The adiabatic temperature rise concept also underpins the interpretation of adiabatic storage tests and the assessment of the SADT (self-accelerating decomposition temperature), which set safe storage temperatures, package sizes and transport conditions.
Common Misconceptions and Pitfalls
The biggest misconception is running a safety assessment with the steady-state conversion. Even if you normally operate at 80% conversion, the figure to look at for safety is X=1 — the maximum adiabatic temperature rise if all of the reactant reacts to completion. Reactant that accumulated unreacted during a cooling failure suddenly reacting at once is the textbook runaway scenario. That is exactly why this tool shows the "maximum adiabatic temperature rise (X=1)" on a separate card — always base the design reference temperature on this maximum, never on the current ΔT_ad.
Next, the assumption that ΔT_ad alone tells you whether something is safe or dangerous. ΔT_ad tells you how high the temperature could ultimately reach, but it says nothing about how fast it gets there. In a real runaway, the rate of temperature rise (heat-release rate) and when a secondary decomposition begins in that temperature range — the TMR_ad, the time to maximum rate under adiabatic conditions — are decisive. Even a small ΔT_ad leaves no room for people to intervene if it is reached in a very short time. ΔT_ad is a starting point and must always be assessed together with heat-release rate, reaction kinetics and secondary-decomposition data.
Finally, dilution does not always make things safe. It is true that lowering the initial concentration C0 reduces the adiabatic temperature rise in proportion. But adding more solvent reduces the output per reactor charge, increasing the number of batches and sometimes the number of operator exposures. And if the solvent itself is flammable or toxic, dilution brings in a different risk. Dilution, cooling and dosing (semi-batch) each have their merits and side effects, so choosing the best combination for a given reaction means weighing ΔT_ad, heat-removal capacity, productivity and solvent hazards together.
How to Use
Enter reaction enthalpy (ΔH_rxn) in kJ/mol using the dhNum field; typical range for exothermic syntheses is −100 to −500 kJ/mol
Set initial reactant concentration (c₀) in mol/L; for batch polymerization feeds, use 1–8 mol/L
Input conversion fraction (X) as decimal 0–1; at X=0.8 a 300 kJ/mol ester hydrolysis releases 240 kJ/L
Specify mixture density (ρ) in kg/L and heat capacity (Cp) in kJ/(kg·K); water is 1.0 kg/L and 4.18 kJ/(kg·K)
Simulator calculates adiabatic temperature rise ΔT_ad = (−ΔH_rxn × c₀ × X) / (ρ × Cp) and final temperature