What is the tube temperature to be considered in the calculation of shell and tube heat exchangers?

This question comes out many times in the work of heat exchanger designers. The answer is needed whichever is the pressure vessel standard to be used.

The normal situation in which the engineer charged of the mechanical design of shell and tube heat exchangers finds himself is the following: a specification containing two columns, tube side and shell side: in each column there is a design temperature, a design pressure, a test pressure, a corrosion allowance and so on: however, nothing is generally specified about the design temperature of the walls which are common to both sides, such as, in the case of shell and tube heat exchangers, the tubes and the tubesheets.

Well, in order to avoid mistakes, the answer could be: take the higher temperature between the tube side and the shell side temperature. But which is the consequence of this choice when one of the temperatures is much higher than the other one? In the case of a firetube boiler (which at the end is also a shell and tube exchanger), you have combustion gases on the tube side, at temperatures around 1000°C, while the design temperature of the shell side is much lower, possibly below 300°C, depending on the steam pressure. It is clear that in a unit like this the real average tube temperature is determined by the two side coefficients: the tube side convective coefficient of combustion gases at high temperatures, which is normally very low; and the shell side boiling coefficient of water, which  is much higher, at least until the water is present in both the liquid and vapour phase: in fact the operating temperature of a single fluid present in two phases and heated by any source will not change, at least until both phases are present, because, at a given pressure, all the heat received will be used to cause the evaporation of the liquid phase instead of an increase of its temperature.

Consequently, the average tube temperature will be closer to the temperature of the boiling water: in firetube boilers it is common practice to consider a tube temperature only 25°C higher than the temperature of the boiling water. The temperature will start to increase only when all the liquid is totally evaporated: but in this case the heat transfer coefficient will become much lower, and the tube wall temperature consequently higher.

Well, the Pressure Equipment Directive classifies these units as “units with the risk of overheating”, that is, units where the temperature of some component is normally kept under safe limits in their normal operating condition, because they are fitted with particular safety devices capable to assure this situation (for the case of steam generators as the firetube boilers, the safety devices must assure that the water level is always sufficient to cover all the tubes).

Note that many refinery heat exchangers are heated by process gases at temperatures comparable to the one of combustion gases, and therefore also normal refinery shell and tube heat exchangers may be subject to the risk of overheating: for these units the design tube temperature must be provided in the thermal specification. Failure to specify this temperature, would lead to the very unlogic assumption that the tube design temperature is the one of the hot side fluid, with the consequence that the tube material should be able to support this temperature: in other words, tubes that are normally made of carbon or low alloy steels should be made of very special heat resistant Nickel-Chrome-Molybdenum-Iron alloys.

Moreover, when such units are heat exchangers with fixed tubesheets (that is, with the tubesheets rigidly connected to the tubes and to the shell), the differential thermal expansion between shell and tubes would generate very high thermal stresses which in practice do not exist: which involves the need to specify not only a tube design temperature, but also a tube (and a shell) average metal temperature in service conditions, needed to evaluate these stresses. Of course, in this case all the possible operating conditions must be evaluated, particularly start-up and shutdown, in which the average wall temperatures could be different from the normal operation. For this reason, a suitable information can only be given by the thermal designer (but in many cases this information is missing, so that the mechanical designer is not always able to fulfil his task).

A slightly different situation is the one of the tubesheets: in fact , while in the tubes the surface in contact with the hot fluid is almost the same as the one of the cold fluid (except for the difference between inside and outside tube diameter), when the hot fluid flows in the tubes the cylindrical surface of the portion of tube inside the tubesheet, through which most of the heat is transferred to the tubesheet material, is higher in thick than in thin tubesheets: in other words, thick tubesheets crossed by the hot fluid will be heated at a temperature much higher than the one of the tubes, so that the calculation must be able to generate thin tubesheets, as in the case of firetube boilers.

This situation may lead, for very special process units, to the use of finite element calculations either for the evaluation of the operating tubesheet temperature or for the consequent mechanical calculation of stresses, since the normal software used for the thermal design of heat exchangers generally gives the tube and shell average metal temperatures, but doesn’t give information on the tubesheet operating temperature.


25.01.2023                                                                                                                Fernando Lidonnici