PSE Lab · Amirkabir University of Technology (Tehran's Polytechnic)

CSTR Thermal Runaway

Continuous stirred-tank reactor with an exothermic reaction. Tune the kinetics, feed and cooling, set the simulation time, then solve the stiff ODE system with the built-in adaptive solver.

Open Loop Closed Loop

Simulation Control

Playback replays the solved trajectory. Press Solve after changing parameters (they also auto-solve).

Simulation Time & Solver

t_end — Simulation Time (s)

Type the simulation time and press Enter to apply.

Method
Accuracy (tolerance)
Ready.

Reactor Parameters

CAin — Feed Conc. 1.00
q — Flow (m³/s) 100
V — Volume (m³) 100
Ti — Feed Temp (K) 350
Tc — Coolant Temp (K) 305
UA — Heat Transfer (W/K) 50.0k
k₀ — Pre-exponential (1/s) 7.2e10
E/R — Activation (K) 8750
ΔHr — Heat of Reaction -5.0e4
ρ — Density (kg/m³) 1000
Cp — Heat Capacity 0.239

Initial Conditions

CA0 (mol/L)
T0 (K)

Initial state y(0) = [CA0, T0] passed to the ODE solver. Type an exact value or drag the slider.

CSTR Mole & Energy Balance dCA/dt = (q/V)(CAin − CA) − k·CA
dT/dt = (q/V)(Ti − T) − ΔHr·k·CA/(ρCp)
     + UA(Tc − T)/(ρCpV)
k = k₀·exp(−E/R·T)
Stiff system. The Arrhenius term makes the Jacobian grow by orders of magnitude during ignition, so an L-stable implicit method is required.

CSTR Schematic

LIVE
M Feed · CAin, Ti Product out Coolant in Coolant out T (K) 324 CA = 0.877 T = 324.5 K
t0.00 s
CA0.877
T324.5 K
dT/dt0.0 K/s
Peak Temp
— K
Time to Peak
— s
Final T
— K
Final CA
—
Conversion
— %
Max dT/dt
— K/s
Solver
—
Steps
—

Parameters & Equations

The open-loop reactor model and the stiff ODE solver used to integrate it.

Reactor Model

Mole balance dCA/dt = (q/V)(CAin − CA) − k·CA
Energy balance dT/dt = (q/V)(Ti − T) − ΔHr·k·CA/(ρCp) + UA(Tc − T)/(ρCpV)
Arrhenius rate k = k0·exp(−(E/R)/T) The state is y = [CA, T]; this is a stiff, non-linear system.

Numerical Solver

Adaptive integration of dy/dt = f(t, y) RK45 — explicit Dormand–Prince (non-stiff)
TR-BDF2 — implicit, L-stable (stiff)
Error is controlled by rtol/atol; the step size adapts to the local error.

Accuracy: Fast (rtol 1e-4), Balanced (1e-6, default), Accurate (1e-7).

Reactor Parameters

SymbolMeaningDefault
CAinFeed concentration1.00 mol/L
qVolumetric flow100 m³/s
VReactor volume100 m³
TiFeed temperature350 K
TcCoolant temperature305 K
UAHeat-transfer coefficient5.0×10⁴ W/K
k0Pre-exponential factor7.2×10¹⁰ 1/s
E/RActivation temperature8750 K
ΔHrHeat of reaction−5.0×10⁴
ρDensity1000 kg/m³
CpHeat capacity0.239

Initial Conditions & Simulation

SymbolMeaningDefault
CA0Initial concentration0.87725 mol/L
T0Initial temperature324.475 K
tendSimulation time20 s

Press Solve to integrate the system over [0, tend], then Run to replay the trajectory in real time.