Part 1 sized pump P-101. This part sizes the heater it feeds: E-101, a shell-and-tube exchanger that uses low-pressure steam to warm the reactor feed. The method is the same for most heaters and coolers: find the duty, find the temperature driving force, choose an overall heat transfer coefficient, and calculate the area.
Step 1: the duty
The feed of 6,250 kg/h is heated from 20 °C to 80 °C with a heat capacity of 2.0 kJ/kg·K:
Q = ṁ × cp × ΔT = 6,250 × 2.0 × 60 / 3,600 = 208 kW
That matches the stream table in How to Read a PFD and a P&ID. The steam needed is the duty divided by the latent heat of steam at 3.0 barg, about 2,133 kJ/kg: roughly 352 kg/h.
Step 2: the driving force (LMTD)
Heat flows because the steam is hotter than the feed. The difference is not constant along the exchanger, so the design uses the log mean temperature difference:
LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2)
Steam at 3.0 barg condenses at about 143.6 °C. At the feed inlet the difference is 123.6 K; at the outlet it is 63.6 K. The LMTD is 90.3 K. Because the steam condenses at one temperature, flow direction does not matter and no correction factor is needed. For two liquids, a multi-pass exchanger needs a correction factor, F, applied to the LMTD.
Step 3: the overall coefficient (U)
U combines every resistance between the steam and the feed: the condensing film, the tube wall, the liquid film inside the tubes and any fouling. For preliminary sizing, engineers use typical values for the service. For condensing steam heating a light organic liquid in a shell-and-tube exchanger, a few hundred W/m²·K is typical; this example uses 500 W/m²·K. The liquid side controls, so tube velocity matters more than the steam side.
Step 4: the area
From Q = U × A × LMTD:
A = 208,333 / (500 × 90.3) = 4.61 m²
Add a margin for fouling and uncertainty in U. With 20%, the design area is 5.54 m². Margins are better stated as a fouling factor in the U calculation, which makes the reason visible; a flat percentage is acceptable at this stage if the design basis says so.
Step 5: lay out the tubes
The area has to fit a geometry that also gives a sensible tube velocity. With ¾" tubes (inside diameter 15.8 mm) and a target of about 1.0 m/s, the feed needs 11 tubes per pass. With two tube passes that is 22 tubes, and the area requires a tube length of about 4.2 m. A standard length of 4.5 m gives a little more area.
| Item | E-101 value |
|---|---|
| Type | Shell and tube; steam in shell, feed in tubes |
| Duty | 208 kW |
| Steam | 352 kg/h at 3.0 barg (143.6 °C) |
| Feed in / out | 20 / 80 °C |
| LMTD | 90.3 K |
| U assumed | 500 W/m²·K |
| Area, required / design | 4.61 / 5.54 m² |
| Tubes | 22 × ¾" OD, 2 passes, 4.5 m long |
What to check next
- Tube-side pressure drop. Part 1 allowed 50 kPa. At about 1 m/s in two short passes the real figure will be well under that; the vendor's rating confirms it.
- Control. Steam flow is controlled by a valve on the steam inlet, as on the HAZOP's P&ID. At low load, the shell pressure can fall below the condensate return pressure and the exchanger floods with condensate (stall). The condensate system must be designed for it.
- Overpressure. The tube side runs at about 3.5 barg and the shell at 3.0 barg. A burst tube would push feed into the shell. Whether that needs a relief device is one of the cases in pressure relief basics.
- Rating by the vendor. Preliminary sizing gives the area and layout to request quotes. The vendor's thermal rating, with actual film coefficients, is what the purchase order is based on.
Key points
- Duty first: Q = ṁ cp ΔT, and check it against the stream table.
- The driving force is the log mean temperature difference, corrected for flow arrangement where needed.
- U is the uncertain number. Use typical values to start and state the fouling allowance explicitly.
- The area must fit a layout that gives a sensible tube velocity.
Next: Part 3 sizes the feed tank, T-101.
The plant, fluid properties and equipment in this series are an illustrative example. The calculations are preliminary sizing estimates. Final sizing needs vendor data, the applicable codes and a qualified engineer.
