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.
FACTS ABOUT PINCH AND APPROACH POINTS
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.
WHY HRSG EXIT GAS TEMPERATURES CANNOT BE ASSUMED
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:
W_gxC_pgx(tg₁-tg₃)=W_sx(hs₂-hw₂)   (1)
considering the entire Hrsg,
W_gxC_pgx(tg₁-tg₄)=W_sdx(hs₂-hw₁)    (2)
where W_g,W_s are the gas and steam flow,lb/h
hs_2,hw_2,hw₁ are the enthalpies of final steam,water leaving and entering economizer,btu/lb
Dividing (1) by (2) and neglecting variations in specific heat C_pg:
(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.
 
    EFFECT OF STEAM PARAMETERS ON EXIT GAS TEMPERATURE