Batch tank heating and cooling time

It estimates how long a jacketed or coil-heated vessel takes to heat or cool a batch, how much heat and steam the batch uses and what that costs per batch and per year. Use it to plan the production sequence, compare steam with hot water or thermal oil, judge whether more transfer area pays off and check whether a real batch is slower than it should be.

With Kern’s batch equations (Process Heat Transfer, ch. 18), assuming a well-mixed product. With steam, t = C ÷ (U·A) × ln[(Ts − Ti) ÷ (Ts − Tf)], where C is mass times specific heat of the product plus the vessel. In the example, 1,300 gal of product (0.93 Btu/lb·°F) and 2,600 lb of steel heated from 77 °F to 176 °F with 45 psig steam (292 °F), U of 106 Btu/(h·ft²·°F) and 110 ft² of jacket take 33 minutes.

Steam condenses at constant temperature, so only the product temperature changes. A fluid without phase change cools (or warms) as it passes through the jacket and leaves between its inlet and the product temperature; that brings in Kern’s factor K = e^(U·A ÷ ṁ·cp), and fluid flow also limits the duty. In the cooling example, taking the batch from 176 °F to 95 °F with 82 °F tower water at 22,000 lb/h and U of 62 Btu/(h·ft²·°F) takes 3 h 32 min.

The list holds midpoints from Sinnott’s table of typical overall coefficients (Coulson & Richardson, vol. 6): jacket with steam and an aqueous solution, 88 to 123 Btu/(h·ft²·°F) (500 to 700 W/m²K); steam coil in an agitated tank, 141 to 264. It is the main uncertainty: in the example, U 30% lower stretches the batch to 47 minutes and 30% higher cuts it to 25. Calibrate it: log the product temperature at two times in a real batch and adjust U until the curve matches.

In the example the batch uses 1,183 lb of steam including 5% losses to ambient, since each pound of 45 psig steam gives up about 916 Btu as it condenses. Flow is not constant: at the start, with cold product, it reaches 2,877 lb/h and then falls, averaging about 2,150 lb/h. Size the control valve, line, trap and boiler capacity for the peak, not the average.

With steam at $15 per 1,000 lb, the example batch costs $17.75 and 600 batches a year add up to about $10,600. To cut it: insulate the lid and shell (10% to 20% losses on a bare vessel), return condensate to the boiler, keep the jacket clean and drained (working trap and air vent) and do not heat past what the process needs, since the last degrees are the slowest.

The calculation assumes a uniform product with constant U and cp, and ignores air or condensate held in the jacket, products that thicken and reactions that release heat. It is a pre-sizing estimate. A steam jacket is a pressure vessel under the ASME Code: working pressure, relief valve and inspections need a qualified professional, as does the design of new transfer area or an agitator.