Unsteady State Operations

What defines steady-state operation mathematically?

\frac{dn}{dt} = 0

What defines unsteady-state operation mathematically?

\frac{dn}{dt} \neq 0

What does the accumulation term represent?

\frac{dn}{dt}

n is moles of species in the reactor
t is time

When is a reactor unsteady?

\frac{d(\text{any state variable})}{dt} \neq 0

During which operating phases is unsteady state unavoidable?

Start-up, shutdown, and disturbances

Why are transient conditions often the most dangerous?

T(t),\; C(t),\; -r_A(t) \text{ change rapidly}

What is the general unsteady-state mole balance for species j?

\frac{dnj}{dt} = F{j,\text{in}} - F{j,\text{out}} + rj V

F{j,\text{in}}, F{j,\text{out}} are molar flow rates
r_j is rate of generation of species j
V is reactor volume

Why can no terms be cancelled in unsteady-state balances?

\frac{dn_j}{dt} \neq 0

What is the key difference between steady and unsteady mole balances?

Presence of the accumulation term

What changes in the energy balance under unsteady-state operation?

\frac{dE}{dt} \neq 0

What does the unsteady-state energy balance include?

Enthalpy in, enthalpy out, heat transfer, reaction heat, energy accumulation

Why does temperature become a dynamic variable?

\frac{dT}{dt} \neq 0

Why does unsteady-state behaviour lead to coupled equations?

-rA = f(CA,T), \quad CA = CA(t), \quad T = T(t)

Why is unsteady-state analysis required for start-up?

CA(0),\; T(0) \neq C{A,\text{ss}},\; T_{\text{ss}}

Why can reaction continue after feed is stopped?

F{\text{in}} = 0,\; nA > 0

What causes overshoot in unsteady CSTRs?

Q{\text{gen}}(t) > Q{\text{rem}}(t)

Why are exothermic CSTRs especially sensitive during transients?

-rA(T) \propto e^{-Ea/(RT)}

What is meant by stable reactor operation?

\text{Small disturbance} \Rightarrow \text{return to steady state}

What is meant by unstable reactor operation?

\text{Small disturbance} \Rightarrow \text{growing deviation}

Why can stability only be assessed using unsteady-state analysis?

\text{Stability} = f!\left(\frac{d(\cdot)}{dt}\right)

What phenomenon can instability lead to in exothermic reactors?

T(t) \uparrow \Rightarrow \text{thermal runaway}

Why are steady-state models still widely used?

\frac{dn}{dt} = 0 \Rightarrow \text{simpler design equations}

For what purposes are unsteady-state models essential?

Safety analysis, control design, start-up and shutdown planning

When must unsteady-state modelling be used?

\text{Start-up, shutdown, disturbances, control}

Why do most industrial accidents occur during transient operation?

T(t),\; C(t),\; Q(t) \text{ not yet controlled}

What is the key limitation of steady-state reactor models?

\frac{dn}{dt} \text{ assumed } = 0

What is the central role of unsteady-state analysis?

\text{Predict dynamics, stability, and safety}

One-sentence exam answer for unsteady-state operation

Unsteady-state operation accounts for time-dependent changes in reactor conditions during start-up, shutdown, and disturbances, and is essential for analysing reactor stability and safety