Steam Engineering Principles and Heat Transfer

Example​ 2.3.1

A turbine is supplied with superheated steam at 90 bar a @ 450 °C.
The exhaust is at 0.06 bar a (partial vacuum) and 10% wet.
Saturated temperature = 36.2 °C.

2.3.1.1 Determine the Carnot efficiency (η_C)

Examination of th​e figures for either of the cycles indicates that to achieve high efficiency:

• The temperature or energy at the turbine inlet should be as high as possible. This means as high a pressure and temperature as is practically possible. Superheated steam is the simplest way of providing this.
• The temperature or energy in the exhaust must be as low as possible. This means as low a pressure and temperature as is practically possible, and is usually achieved by a condenser on the turbine exhaust.

Notes:

• The figures calculated in Examples 2.3.1.1 and 2.3.1.2 are for thermodynamic efficiency, and must not be confused with mechanical efficiency.
• Although the efficiency figures appear to be very low, they must not be viewed in isolation, but rather used to compare one type of heat engine with another. For example, gas turbines, steam engines and diesel engines.

This may sound a useful increase in energy, but in fact it will actually make life more difficult for the engineer who wants to use steam for heating purposes.

From the energy in the superheat shown, the specific heat capacity can be determined by dividing this value by the temperature difference between saturation temperature (100 °C) and the superheated steam temperature (400 °C):

However, unlike the specific heat capacity of water, the specific heat capacity for superheated steam varies considerably with pressure and temperature and cannot be taken as a constant.

The value of 2.0 kJ/kg °C given above is therefore only the mean specific heat capacity over the specified temperature range for that pressure.

There is no direct relationship between temperature, pressure and the specific heat capacity of superheated steam. There is, however, a general trend towards an increase in specific heat capacity with increasing pressure at low degrees of superheat, but this is not always the case.

Can superheated steam be used in process heat exchangers and other heating processes? 

Although not the ideal medium for transferring heat, superheated steam is sometimes used for process heating in many steam plants around the world, especially in the HPIs (Hydrocarbon Processing Industries) which produce oils and petrochemicals. This is more likely to be because superheated steam is already available on site for power generation, being the preferred energy source for turbines, rather than because it has any advantage over saturated steam for heating purposes. To be clear on this point, in most cases, saturated steam should be used for heat transfer processes, even if it means desuperheating the steam to do so. HPIs often desuperheat steam to within about ten degrees of superheat. This small degree of superheat is removed readily in the first part of the heating surface. Greater amounts of superheat are more difficult, and often uneconomic to deal with and (for heating purposes) are best avoided.

There are quite a few reasons why superheated steam is not as suitable for process heating as saturated steam:

Superheated steam has to cool to saturation temperature before it can condense to release its latent heat (enthalpy of evaporation). The amount of heat given up by the superheated steam as it cools to saturation temperature is relatively small in comparison to its enthalpy of evaporation.

If the steam has only a few degrees of superheat, this small amount of heat is quickly given up before it condenses. However, if the steam has a large degree of superheat, it may take a relatively long time to cool, during which time the steam is releasing very little energy.

Unlike saturated steam, the temperature of superheated steam is not uniform. Superheated steam has to cool to give up heat, whilst saturated steam changes phase. This means that temperature gradients over the heat transfer surface may occur with superheated steam.

In a heat exchanger, use of superheated steam can lead to the formation of a dry wall boiling zone, close to the tube sheet. This dry wall area can quickly become scaled or fouled, and the resulting high temperature of the tube wall may cause tube failure.

This clearly shows that in heat transfer applications, steam with a large degree of superheat is of little use because it:

• Gives up little heat until it has cooled to saturation temperature.
• Creates temperature gradients over the heat transfer surface as it cools to saturation temperature.
• Provides lower rates of heat transfer whilst the steam is superheated.
• Requires larger heat transfer areas.

So, superheated steam is not as effective as saturated steam for heat transfer applications. This may seem strange, considering that the rate of heat transfer across a heating surface is directly proportional to the temperature difference across it. If superheated steam has a higher temperature than saturated steam at the same pressure, surely superheated steam should be able to impart more heat? The answer to this is ‘no’. This will now be looked at in more detail.

It is true that the temperature difference will have an effect on the rate of heat transfer across the heat transfer surface, as clearly shown Equation 2.5.3. 

Equation 2.5.3 also shows that heat transfer will depend on the overall heat transfer coefficient ‘U’, and the heat transfer area ‘A’.

For any single application, the heat transfer area might be fixed. However, the same cannot be said of the ‘U’ value; and this is the major difference between saturated and superheated steam.

The overall ‘U’ value for superheated steam will vary throughout the process, but will always be much lower than that for saturated steam. It is difficult to predict ‘U’ values for superheated steam, as these will depend upon many factors, but generally, the higher the degree of superheat, the lower the ‘U’ value.

Typically, for a horizontal steam coil surrounded with water, ‘U’ values might be as low as 50 to 100 W/m² °C for superheated steam but 1 200 W/m² °C for saturated steam, as depicted in Figure 2.3.4.

For steam to oil applications, the ‘U’ values might be considerably less, perhaps as low as 20 W/m² °C for superheated steam and 150 W/m² °C for saturated steam.

In a shell and tube heat exchanger, 100 W/m² °C for superheated steam and 500 W/m² °C for saturated steam can be expected. These figures are typical; actual figures will vary due to other design and operational considerations.

Although the temperature of superheated steam is always higher than saturated steam at the same pressure, its ability to transfer heat is therefore much lower. The overall effect is that superheated steam is much less effective at transferring heat than saturated steam at the same pressure. The next Section ‘Fouling’ gives more detail.

Not only is superheated steam less effective at transferring heat, it is very difficult to quantify using Equation 2.5.3, Q̇ = U A ΔT, as the temperature of the steam will fall as it gives up its heat while passing along the heating surface.

Predicting the size of heat transfer surfaces utilising superheated steam is difficult and complex. In practice, the basic data needed to perform such calculations is either not known or empirically obtained, putting their reliability and accuracy in doubt.

Clearly, as superheated steam is less effective at transferring heat than saturated steam, then any heating area using superheated steam would have to be larger than a saturated steam coil operating at the same pressure to deliver the same heat flowrate.

If there is no choice but to use superheated steam, it is not possible to maintain steam in its superheated state throughout the heating coil or heat exchanger, since as it gives up some of its heat content to the secondary fluid, it cools towards saturation temperature. The amount of heat above saturation is quite small compared with the large amount available as condensation occurs.

The steam should reach saturation relatively soon in the process; this allows the steam to condense to produce higher heat transfer rates and result in a higher overall ‘U’ value for the whole coil, see Figure 2.3.5.

To help to enable this, superheated steam used for heat transfer purposes should not hold more than about 10 °C of superheat.

If this is so, it is relatively easy and practical to design a heat exchanger or a coil with a heating surface area based upon saturated steam at the same pressure, by adding on a certain amount of surface area to allow for the superheat. Using this guideline, the first part of a coil will be used purely to reduce the temperature of superheated steam to its saturation point. The rest of the coil will then be able to take advantage of the higher heat transfer ability of the saturated steam. The effect is that the overall ‘U’ value may not be much less than if saturated steam were supplied to the coil.

From practical experience, if the extra heating area needed for superheated steam is 1% per 2 °C of superheat, the coil (or heat exchanger) will be large enough. This seems to work up to 10 °C of superheat. It is not recommended that superheated steam above 10 °C of superheat be used for heating purposes due to the probable disproportionate and uneconomic size of the heating surface, the propensity for fouling by dirt, and the possibility of product spoilage by the high and uneven superheat temperatures.

As the actual enthalpy of the steam at 1 bar g is less than the enthalpy of dry saturated steam at 1 bar g, then the steam is not superheated and still retains a proportion of moisture in its content.

Since the total enthalpy after the pressure reducing valve is less than the total enthalpy of steam at 1 bar g, the steam is still wet.

Determine the degree of superheat after the valve.

As in the previous example (2.3.4), the specific enthalpy of dry saturated steam (h_g) at 1 bar g is 2 706.7 kJ/kg.

The actual total enthalpy of the steam is greater than the total enthalpy (h_g) of dry saturated steam at 1 bar g. The steam is therefore not only 100% dry, but also has some degree of superheat.

The excess energy = 2 741.7 - 2 706.7 = 35 kJ/kg, and this is used to raise the temperature of the steam from the saturation temperature of 120 °C to 136 °C.

Example 2.3.6 Perfect isentropic expansion resulting in work

Consider the perfect expansion of steam through a turbine. Initially the pressure is 50 bar a, the temperature is 300 °C, and the final pressure is 0.04 bar a.
As the process is a perfect expansion, the entropy remains constant. The final condition can then be found by dropping vertically downwards from the initial condition to the 0.04 bar a constant pressure line (see Figure 2.3.9).

At the initial condition, the entropy is approximately 6.25 kJ/kg °C. If this line is followed vertically downwards until 0.04 bar a is reached, the final condition of the steam can be evaluated. At this point the specific enthalpy is 1 890 kJ/kg, and the dryness fraction is 0.72 (see Figure 2.3.9).

The final condition can also be determined by using the superheated steam tables.

At the initial condition (50 bar a/300 °C): h_g = 2 927 kJ/kg

and s_g = 6.212 kJ/kg °C

For dry saturated steam 0.04 bar a: s_f = 0.422 kJ/kg °C

s_fg = 8.051 kJ/kg °C

and s_g = 8.473 kJ/kg °C

Since the entropy of dry saturated steam at 0.04 bar a (8.473 kJ/kg °C) is greater than the entropy of the superheated steam at 50 bar a/300 °C (6.212 kJ/kg °C), it follows that some of the dry saturated steam must have condensed to maintain the constant entropy.

As the entropy remains constant, at the final condition:

These answers correspond closely with the results obtained using the Mollier chart. The small difference in value between the two sets of results is to be expected, considering the inaccuracies involved in reading off a chart such as this.