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This article discusses the significance of pinch and approach points in gas turbine Hrsgs. Unlike conventional steam generators,where the inlet gas temperatures are very high,namely adiabatic combustion temperatures of the fuel fired(3200-3400 F),the gas turbine exhaust inlet gas temperature to the Hrsg is very low,on the order of 850-1000 F. This creates a problem. We cannot arbitrarily assume an exit gas temperature to determine the steam flow.In steam generators for example,if the feed water temperature is say 240 F,an exit gas temperature of 300 to 350 F is feasible. There are a few reasons for this,such as the low ratio of gas/steam and capacity of heat sink in the form of economizer.A lot of energy is transferred to the steam before the flue gases enter the economizer,while in Hrsgs,it could be very small due to the low inlet gas temperature.This in turn affects the energy absorbed in economizer and hence the Hrsg exit gas temperature.Hence gas/steam profiles cannot be easily predicted.If we arbitrarily assume an exit gas temperature,we can get into either a temperature cross situation(explained later) or the economizer could be steaming. Hence the right way is to determine the steam generation and gas/steam profiles using pinch and approach points
Table of suggested Pinch and Approach points
 item  pinch point , F approach point,F
 evaporator type  bare        finned
  inlet gas temp,F
  1200-1800 130-150      30-60     40-70
   700-1200  80-130      10-30    10-40
As shown in the figure above,pinch point is the difference between the gas temperature leaving the evaporator and the saturation temperature,while approach point is the difference between the water temperature leaving the economizer and saturation temperature. If these values are reasonably assumed,then we obtain a thermodynamically feasible temperature profile.
Pinch and approach points are to a great extent dependent on the inlet gas temperature and whether the evaporator is bare or finned.These values are shown in the table above and are based on the author's experience. For example in incineration plants,the gas inlet temperature could be 1600 F. Here we cannot assume a pinch point of 20 F and approach of 20 F as it will lead to an exit gas temperature below the feed water temperature.This is explained below!.Also,with bare tubes,if we go for a small pinch point,the module size becomes too large. In typical gas turbine Hrsgs using finned evaporators,10-30 F pinch and approach points are reasonable and can be achieved in the unfired mode.
Pinch and approach points are selected in unfired mode at "Design" gas flow,inlet gas temperature conditions.Once they are assumed,the surface areas of the Hrsg evaporator,superheater and economizer are indirectly fixed or considered selected .
Once selected,pinch and approach will vary with other conditions of gas flow,steam parameters. That is,we select pinch and approach only once and in other "Off-Design cases",we have to use an iterative procedure to arrive at the gas/steam temperature profiles and steam generation.The HRSG simulation program does just that.
Pinch and approach shuld be selected in the unfired gas turbine mode(even if the Hrsg operates in fired mode) and preferably at the lowest inlet gas temeprature to avoid steaming in the economizer(discussed later).If they are selected in the fired mode,we have to perform a number of calculations to check if the steam temperature can be achieved in the unfired mode,whether the economizer does not steam in unfired mode etc.
Some engineers with little experience in gas turbine Hrsg performance aspects assume an exit gas temperature and compute the steam generation without going through the pinch,approach point calculations. This can lead to problems as discussed below.
Neglecting heat loss and blow down for simplicity and considering the superheater and evaporator in the figure above ,we have:
WgxCpgx(tg1-tg3)=Wsx(hs2-hw2)   (1)
considering the entire Hrsg,
WgxCpgx(tg1-tg4)=Wsdx(hs2-hw1)    (2)
where Wg,Ws are the gas and steam flow,lb/h
hs2,hw2,hw1 are the enthalpies of final steam,water leaving and entering economizer,btu/lb
Dividing (1) by (2) and neglecting variations in specific heat Cpg:
(tg1-tg3)/(tg1-tg4)=(hs2-hw2)/(hs2-hw1) = K        (3)
Note that K is a function of steam and water parameters only.
For steam generation to occur and for a thermodynamically feasible temperature profile,two conditions must be met: tg3>ts,ts being saturation temperature and tg4>tw1.If pinch and approach are arbitrarily selected,it is likely one of them can fail.Hence all these values are intimately related. Table below shows typical K values and exit gas temperatures at various pressures.

press,psig steam temp,F sat temp,F K exit gas temp,F
100 338 338 0.904 300
150 366 366 0.8754 313
250 406 406 0.8337 332
400 448 448 0.7895 353
400 600 450 0.8063 367
600 490 490 0.74 373
600 750 492 0.7728 398
[basis: pinch point=20 F,approach point=15 F,inlet gas=900 F,feed water=230 F]
The following points may be noted:
1.As steam pressure and steam temperature increase,the exit gas temperature increases. That is,we cannot get 300 F exit gas when generating 600 psig,750 F steam! Hence the purpose of Hrsg simulation is to arrive at the proper  gas/steam profiles and steam generation. I have seen several specifciations written by consultants,where a 300 F economizer exit gas temperature is specified in a high pressure system. If one computes steam generation based on 300 F exit gas,he will be in a rude shock as 300 F cannot be thermodynamically achieved at high pressures!
2.Why can't we get 300 F exit gas at 600 psig,750 F steam conditions?
 K=0.7728  Let us try to compute tg3 from tha above equation for K.
0.7728=(900-tg3)/(900-300) or tg3=436 F,which is below the saturation temperature of 492 F.This is called Temperature Cross!!
3.What should be done to achieve 300 F in the above case?
Increase tg1 by supplementary firing. say tg1=1600 F. Then (1600-tg3)/(1600-300)=0.7728 or tg3=595 F. pinch point=(595-492)=103 F. Note that as inlet gas temperature increases the pinch point increases and the exit gas temperature decreases.This aspect was discussed in the article on  Generating steam efficiently in cogeneration plants .
4.Let us say that at 1600 F gas inlet someone selected 20 F pinch.What happens?
tg3=492+20=512 F
(1600-512)/(1600-tg4)=0.7728 or tg4=192 F,which is below the feed water temperature of 230 F and hence not feasible if the approach point were 20 F. So let us calculate what should be the approach point.
At 600 psig,750 F,hs2=1379 btu/lb. hw1=200 btu/lb. K=(1600-512)/(1600-1300)=0.836 or hw2=393 btu/lb. This corresponds to a water temperature of 416 F or an approach point of 76 F. This is the reason we select pinch and approach in unfired modes as we have no clue as to the exit gas temperature or pinch point or approach point in fired conditions!
Now in order to estimate the correct gas/steam temperature profile we first obtain the steam flow from equation(1)above.All other variables are known except steam flow. Then using (2),the exit gas temperature is found.This is the "DESIGN" profile.The HRSG simulation program  may be used to determine the steam generation,temperature profiles in unfired "Design" as well as in unfired,fired "Off-Design" conditions for complex Hrsgs.
Boilers,HRSGS,Steam Plant Calculations
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