Why Cannot We Arbitrarily Select the Pinch and Approach Points?

Let us see the basic equations involved in arriving at the gas–steam temperature profiles. From Figure 5.2, considering the superheater and evaporator,

W g × C pg × ( t g 1 − t g 3 ) = Wh s ( so − h w 2 ) (5.1)

Considering the entire HRSG and neglecting blowdown and heat losses,

W g × C pg × t g 1 − t g 4 = Wh s ( so − h w 1 ) (5.2)

Dividing (5.1) by (5.2) and neglecting the variations in C pg , we have

( t g 1 − t g 3 ) = ( h so − h w 2 ) =

K ( (5.3)

t g 1 − t g 4 ) ( h so − h w 1

Note that factor K is a function of steam–water properties alone. For steam generation to occur and for a feasible temperature profile, two conditions must be met:

t > t (5.4)

t 4 t g > w 1 (5.5) It is possible that if pinch and approach points are arbitrarily selected, one of these condi-

tions will not be met. This is called temperature cross situation. K value has been com- puted for various steam pressures and presented in the following text for a specific case of an HRSG.

It is seen from Table 5.2 that as the steam pressure increases, the exit gas temperature increases. If steam is superheated, then the exit gas temperature is even higher for the same pressure. This is due to the simple fact that with a superheater for a given pinch point, the energy absorbed by the superheater and evaporator is the same, while the enthalpy absorbed by steam is more and hence less steam is generated. Lesser water flow through economizer in turn means smaller heat sink and hence higher exit gas temperature.

TABLE 5.2

K Values (482°C Gas Inlet, 110°C Feed Water, 11°C Pinch, and 8.3°C Approach)

Pressure kg/cm 2 g (kPa) (psig)

Steam Temp., °C (°F)

Sat. Temp., °C (°F)

K Exit Gas, °C (°F)

Saturated

HRSG Simulation 271

Hence, one cannot arbitrarily select an exit gas temperature in a single-pressure HRSG.

A temperature profile analysis is required. One may develop such a table for any exhaust gas conditions. The author has seen a few specifications where consultants call out for an exit gas temperature, which cannot be obtained at a given pressure due to the limitation

of pinch point (say, 140°C exit gas temperature from economizer at 28 kg/cm 2 g saturated steam conditions with about 480°C–490°C gas inlet temperature and 110°C feed water inlet).

Example 5.2

Check the exit gas temperature for 689 kPa (100 psig) saturated steam using 11°C pinch and 8.3°C approach points.

t s = 170°C. t g3 = 181°C. Using (5.3), (482 − 181)/(482 − t g4 ) = 0.904 or t g4 = 149°C as shown in Table 5.2. We cannot get much lower than this.

Example 5.3

Why cannot we obtain an exit gas temperature of 149°C when the steam pressure is 4137 kPa (600 psig) and steam temperature is 399°C? K is 0.7728.

Using (5.3), let us see what should be t g3 to obtain this desired t g4 . (482 − t g3 )/(482 − 149) = 0.7728. t g3 = 225°C. This is an example of temperature cross situation. The pinch

point is negative. Saturation temperature is 255°C, while the gas temperature leaving the evaporator is 225°C, which is not feasible. Hence, exit gas temperature should be higher than 203°C.

Example 5.4

What should be done to obtain an exit gas temperature of 149°C in the earlier case? Let us raise the inlet gas temperature to say 870°C. Then,

(870 − t g3 )/(870 − 149) = 0.7728 or t g3 = 312°C. This is feasible as t g3 is above the saturation

temperature of 254°C. So supplementary firing helps increase the steam generation and thus provides a larger heat sink at the economizer that enables cooling of the exhaust gas to a lower temperature. Higher the gas inlet temperature, lower the economizer exit gas temperature in single-pressure HRSGs.

Example 5.5

Is it possible to have a pinch point of 11°C with 870°C inlet gas temperature? t g3 is then 255 + 11 = 266°C. (870 − 266)/(870 − t g4 ) = 0.7728 or t g4 = 88°C, which is impossible as it is below the feed

water temperature of 110°C, another case of temperature cross! So low pinch points cannot be achieved with high inlet gas temperatures. This was also suggested in Table 5.1. Hence, these are basic principles to be kept in mind by process engineers while trying to develop gas–steam temperature profiles for their HRSGs. The important point to be kept in mind is that pinch and approach points should be selected in the unfired mode of HRSG. Then, the values suggested in Table 5.1 can be achieved.

Why Cannot We Arbitrarily Select the Pinch and Approach Points?