Fouled Oil Cooler that Cannot Meet its Outlet Specification
A refinery uses a counter-flow shell-and-tube exchanger to cool 1.5 kg/s of hot oil (cp = 2.2 kJ/kg·K) from 160 °C to a required 110 °C before storage. Cooling water enters the tube side at 25 °C at 1.2 kg/s (cp = 4.18 kJ/kg·K). The exchanger was commissioned with U_clean = 450 W/m²·K and 4.4 m² of outside area. After 18 months the oil outlet has crept up to 122 °C, and the downstream line cannot tolerate more than 110 °C for more than 30 minutes before wax crystallises. Inspection shows a 0.2–0.4 mm deposit on the shell side. The plant has three options: (i) clean the bundle, (ii) raise the oil inlet temperature by 10 °C using a preheater, (iii) bypass part of the oil around the exchanger. The exchanger cannot be offline for more than 8 hours, but the cleaning contractor needs 12 hours.
1. From the measured temperatures, determine the current overall heat transfer coefficient and the fouling resistance, and judge whether the shortfall is explained by fouling.
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Heat capacity rates: Ch = 1.5 × 2200 = 3300 W/K; Cc = 1.2 × 4180 = 5016 W/K. The hot stream is Cmin, Cr = 3300/5016 = 0.658.
Measured duty: Q = 3300 × (160 − 122) = 125.4 kW. Water outlet = 25 + 125400/5016 = 50.0 °C.
LMTD for counter-flow: ΔT1 = 160 − 50.0 = 110.0 K; ΔT2 = 122 − 25 = 97.0 K. LMTD = 13.0/ln(110/97) = 13.0/0.1258 = 103.4 K.
U = Q/(A·LMTD) = 125400/(4.4 × 103.4) = 276 W/m²·K.
Fouling resistance: Rf = 1/276 − 1/450 = 0.00362 − 0.00222 = 0.00140 m²·K/W. The deposit therefore adds about 63 % to the clean thermal resistance, roughly three times a typical design fouling allowance of 0.0005. Cleaning the bundle restores U to 450 W/m²·K, and at NTU = 450 × 4.4/3300 = 0.60 with Cr = 0.658, ε = 0.400, giving an oil outlet of 160 − 0.400 × 135 = 106 °C. Cleaning meets the specification with margin, so the shortfall is fully explained by fouling and no other fault needs to be assumed.
2. Evaluate the preheater and bypass options quantitatively.
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For a two-stream exchanger with the hot stream as Cmin, the hot outlet follows Th,out = Th,in(1 − ε) + ε·Tc,in, with ε set by NTU and Cr. At the current fouled condition NTU = 276 × 4.4/3300 = 0.368 and ε = 0.282, so Th,out = 0.718·Th,in + 0.282 × 25.
Preheater: at Th,in = 170 °C, Th,out = 122.1 + 7.05 = 129.2 °C. Raising the inlet temperature raises the outlet temperature by almost the same amount, because the exchanger's effectiveness is unchanged. The preheater makes the problem worse, not better, and adds duty that must later be removed.
Bypass: sending a fraction x of the oil around the exchanger lowers the hot-side capacity rate, which lowers Cr and raises ε, but the mixed outlet is what matters. At x = 0.3, Ch = 2310 W/K, Cr = 0.460, NTU = 0.525, ε = 0.378, exchanger outlet 109 °C, mixed outlet = 0.7 × 109 + 0.3 × 160 = 124 °C. At x = 0.5 the mixed outlet is about 127 °C. Both are worse than the present 122 °C.
Raising cooling-water flow also fails: with Cmin fixed, NTU stays at 0.368 and ε can rise only to 1 − e^−0.368 = 0.308 as Cr → 0, giving a best-case outlet of 160 − 0.308 × 135 = 118 °C. No operating adjustment restores 110 °C.
3. Given the 8-hour outage limit against a 12-hour cleaning job, what do you recommend and what would you monitor?
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None of the online options restores the specification, so the choice is between accepting off-specification oil, deferring production, and removing the constraint permanently. Since the downstream waxing limit is 30 minutes at 110 °C, the process as it stands is already outside its design envelope and the risk is a blocked line, not just poor quality.
Recommendation: negotiate a 12-hour outage or install a spared bundle that can be swapped within 8 hours, and clean now rather than continue operation. In parallel, arrange temporary cooling capacity - for example a plate exchanger rented for the outage window - or route the oil to an alternative tank where it can be held above the waxing temperature and re-cooled later.
Monitoring: log U weekly from inlet and outlet temperatures and a measured water flow, and set a cleaning trigger at U = 340 W/m²·K, which leaves about 10 °C of margin on the outlet. Trend Rf against time to estimate the fouling rate (0.0014 m²·K/W in 18 months) and to justify an antifoulant programme or a larger bundle. Finally, check whether the deposit is organic or inorganic; the antifoulant choice and the cleaning method both depend on that, and the answer is not available from temperatures alone.