Reactor Runaway After Cooling Water Fouling
A 10 m³ stirred batch reactor runs a first-order exothermic reaction (ΔH = -180 kJ/mol, Ea = 95 kJ/mol, A = 4.2×10^11 s⁻¹) at 150 °C using jacket cooling water at 25 °C. Over six weeks the jacket-side fouling factor has degraded from 5000 to 900 W/m²·K. Operators report the reactor now reaches 150 °C but the temperature creeps to 168 °C after 40 minutes, then rises sharply. The jacket area is 12 m², overall U (clean) is 600 W/m²·K, and the heat release at 150 °C is 85 kW. The cooling water flow is at design rate and the jacket inlet temperature is unchanged.
1. Diagnose whether this is a control problem or a heat-transfer capacity problem, and quantify the evidence.
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Compute the required UA. At 150 °C with jacket at 25 °C, ΔT = 125 K. Required UA = Q/ΔT = 85,000/125 ≈ 680 W/K. Clean UA = 600 × 12 = 7200 W/K, which is ample. With fouling: 1/U_f = 1/600 + 1/900 − 1/5000... actually the fouling resistance adds in series: R_f = 1/900 − 1/5000 ≈ 0.000911 m²·K/W, so U_f = 1/(1/600 + 0.000911) ≈ 1/(0.001667+0.000911) = 388 W/m²·K. UA_f = 388 × 12 = 4660 W/K, still above 680 W/K. So UA is not limiting at steady state: the symptom is the reactor temperature drifting upward while the jacket is at design flow, which is the signature of a heat-generation curve that has shifted relative to the removal line. The 18 K creep over 40 min followed by acceleration is runaway behavior, not a fouling capacity limit. The fouling is real but secondary - check the actual cause: a degraded jacket flow, a partially closed valve, or a controller setpoint/measurement error. The evidence points to a control or flow-distribution fault masquerading as fouling.
2. If the fouling is confirmed but the runaway persists, what operating change would you make and what is the safety case?
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The runaway margin is the difference between the heat-removal line slope and the heat-generation curve slope at the operating point. Lower the jacket inlet temperature (or increase cooling flow) to steepen the removal line. If the jacket water is at 25 °C, you can't go much lower, so instead reduce the batch charge or the initial initiator concentration to lower the generation curve. The safety case: calculate the adiabatic temperature rise from ΔH and the charge. For a 10 m³ batch at, say, 1000 kg/m³ and 5 mol/L reactant, the total heat is 5×10^3 mol/m³ × 10 m³ × 180 kJ/mol = 9×10^6 kJ; with cp ≈ 3.5 kJ/kg·K and 10,000 kg, ΔT_ad ≈ 257 K - far beyond any relief capacity. So the correct action is to stop the batch, cool to a safe hold, and re-establish the heat-removal line before restarting. Fouling is a contributing factor but not the root cause.