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Shell and Tube Heat Exchanger Sizing

Duty, LMTD, U, surface and pressure drop in stainless

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What size shell and tube do you need?

Four quantities set the surface

Sizing starts with the duty: Q equals flow times specific heat times temperature change. For water that reduces to gpm × 500 × temperature change in °F, giving Btu/h, so 50 gpm cooled through 30°F is 50 × 500 × 30 = 750,000 Btu/h. The surface then follows from A = Q / (U × LMTD × F): the duty divided by the overall coefficient U, the log mean temperature difference, and a correction factor F for multi-pass flow.

U is built from the film coefficient on each side, the resistance of the tube wall and a fouling factor for each fluid. The film coefficients depend on velocity, viscosity and conductivity, which is why the tube count, passes and baffle spacing are chosen together with the surface rather than after it. Pressure drop is the constraint that stops velocity being raised without limit.

Grade enters the sizing through wall resistance: 304L and 316L conduct about 9.4 Btu/h-ft-°F, so a stainless bundle carries more surface than copper would for the same duty. Grade limits are set out on Material & Construction.

Stainless adds one term that matters. A 0.065 in. wall of 316L, at about 9.4 Btu/h-ft-°F, has a resistance of about 0.00058 h·ft²·°F/Btu, the same order as a water fouling factor, while the same copper wall at about 230 is near 0.00002. A stainless bundle therefore carries more surface for the same duty, and a thinner tube wall recovers some of it.

Shell & Tube Construction
Stainless steel shell and tube heat exchanger
500
Btu/h per gpm of water per degree F
0.00058
wall resistance of a 0.065 in. 316L tube
0.001–0.002
water fouling factor, h·ft²·°F/Btu
3–8 ft/s
usual tube velocity range for water

Worked example: steam heating water in 316L tubes

Illustrative only. The real selection is run on rating software against the actual fluids, with film coefficients calculated rather than assumed, and no performance is promised from this arithmetic.

Condition Typical value
Duty 60 gpm × 500 × 80°F = 2,400,000 Btu/h
Water side 60 gpm heated from 60°F to 140°F in 316L tubes
Steam side 15 psig saturated steam on the shell, condensing at 250°F; about 2,540 lb/h
LMTD End differences of 190°F and 110°F give about 146°F; F = 1 with condensing steam
Clean U, assumed 400 Btu/h·ft²·°F for this illustration
Fouling factor 0.001 h·ft²·°F/Btu on the water side, giving a design U of about 286
Surface required 2,400,000 / (286 × 146) = about 57 ft²
Without fouling About 41 ft²; the fouling factor adds about 40% surface
One layout 38 tubes, 3/4 in. OD, 16 BWG, 8 ft, two passes: about 60 ft² at roughly 3.4 ft/s
LMTDabbreviation

Log mean temperature difference: the effective driving force between the hot and cold streams, found from the temperature difference at each end of the exchanger as the larger minus the smaller, divided by the natural log of their ratio. Multi-pass shells multiply it by a correction factor F, usually kept above about 0.8.

How a shell and tube sizing is run

What to send

A sizing needs both fluids, both flows and enough temperatures to close the heat balance: both flows and three of the four temperatures, or one flow and all four. Everything else shapes the selection.

  • Fluids, with concentration, viscosity and specific heat if not water, glycol or steam
  • Flows and inlet and outlet temperatures on each side
  • Operating and design pressure and temperature, and allowable pressure drop, each side
  • Chloride, pH, solids and fouling history, which set the grade and fouling factor
  • Codes, connections, orientation and the space available, including pull clearance

From duty to surface

With one stream condensing, F is 1 and the LMTD stands as calculated. With two liquids in a shell with two or more tube passes, the streams are partly in paralell flow and F falls below 1; when it drops under about 0.8, or the outlet temperatures cross, the selection moves to shells in series or a counterflow arrangement. Fouling factors of 0.001–0.002 h·ft²·°F/Btu are common for tower water and process liquids, and they are applied per side, not stacked on a percentage margin.

Passes, baffles, tube size and length

Tube passes set tube-side velocity: water is kept at about 3–8 ft/s, the low end where erosion is a concern and the high end for fouling control. More passes raise velocity and the film coefficient and also pressure drop, which rises roughly with the square of velocity. Baffle spacing and cut do the same job on the shell side. Tubes of 3/4 in. or 1 in. OD are common, 5/8 in. in compact units, and a longer, slimmer shell is usually cheaper per square foot if the plant can give it the length and the pull space.

The mistake: margin piled on margin

An inquiry that asks for a 0.002 fouling factor, 25% excess surface and the highest flow the plant might ever see gets a unit that runs at low velocity in normal service. Low velocity fouls faster, so the oversizing creates the fouling it was meant to cover. State the normal duty, the worst realistic case and the fouling history, and let one fouling factor carry the margin. When you are ready, send the duty for a quote.

Questions on sizing a stainless bundle

That depends on duty, temperature difference and U, not on pipe size or flow alone. Work out the duty from flow and temperature change, then the LMTD from the four temperatures; with a typical stainless steam-to-water U in the low hundreds, the surface follows. The worked example on this page lands near 57 ft² for 2,400,000 Btu/h.

Because the wall itself resists heat flow. At about 9.4 Btu/h-ft-°F against roughly 230 for copper, a 0.065 in. stainless wall adds a resistance comparable to a fouling factor. The difference is largest on duties where both film coefficients are high, such as condensing steam against fast-moving water, and smallest where a viscous fluid controls U.

For tower water and most process liquids, 0.001–0.002 h·ft²·°F/Btu on that side, lower for clean closed loops and condensing steam. Choose from your own cleaning history where you have it. Specify the fouling factor or a surface margin, not both, because stacking them oversizes the unit and slows the fluid enough to foul it faster.

Yes, if both flows are known: the heat balance gives the fourth temperature, since the heat lost by one stream equals the heat gained by the other. With only one flow, all four temperatures are needed so the other flow can be calculated. With fewer data than that, the duty is not defined.

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