Estimating Steam Generation and Gas–Steam Temperature Profiles

Assumption of pinch and approach points will enable one to arrive at the complete gas– steam temperature profiles, steam generation, and duty in each section such as superheater or evaporator as mentioned earlier. This is illustrated by an example.

Example 5.1

Exhaust gas flow from a gas turbine is 100,000 kg/h at 500°C. Gas analysis is % volume

CO 2 = 3, H 2 O = 7, N 2 = 75, O 2 = 15. Steam at 41 kg/cm 2 a and at 375°C is required to be

generated using 105°C feed water. Use a blowdown of 1%. Determine the gas–steam temperature profiles, duty of each section, and steam generation.

268 Steam Generators and Waste Heat Boilers: For Process and Plant Engineers

Solution

Let us assume 10°C (18°F) as the pinch point and 7°C (13.6°F) as the approach point.

Assume that the superheater pressure drop is 1 kg/cm 2 ; the drum pressure will be 42 kg/cm 2 a or saturation temperature is 252°C. Hence, gas temperature leaving the

evaporator is 262°C and water temperature entering the evaporator is 252 − 7 = 245°C. From Appendix F, the exhaust gas specific heat at the average gas temperature of (500 + 262)/2 or 381°C is 0.268 kcal/kg °C. Hence, energy absorbed by the superheater and evaporator = 100,000 × 0.99 × 0.268 × (500 − 262) = 6.32 MM kcal/h (0.99 refers to the 1% heat loss assumed). From steam tables, the enthalpy of superheated steam at 375°C

and 41 kg/cm 2 a is 753.4 kcal/kg and that of feed water at 245°C is 253.5 kcal/kg. Saturated liquid and vapor enthalpy at 42 kg/cm 2 a are 261.8 and 668.8 kcal/kg, respectively. One

can obtain the steam generation W s using the energy absorbed by the superheater and evaporator as follows:

6.32 × 10 6 =W s [(753.4 − 253.5) + 0.01 × (261.8 − 253.5)] = 500 W s or W s = 12,640 kg/h (the blowdown effect is taken care by the second term).

The energy absorbed by the superheater = 12,640 × (753.4 − 668.8) = 1.069 MM kcal/h (1.24 MW). Using a gas specific heat of 0.274 kcal/kg °C at the superheater, we obtain the

gas temperature drop in the superheater as 1.069 × 10 6 /(100,000 × 0.99 × 0.274) = 39.4°C or

gas temperature leaving the superheater is = 460.4°C. The evaporator duty by difference is (6.32 − 1.069) = 5.251 MM kcal/h = 6.11 MW.

The economizer duty = . 1 01 12 640 × , × ( 253 5 105 8 . − . ) = . 1 886 MM kcal/h ( 2 .. 19 MW ) .

Gas temperature drop across the economizer = 1.88 × 10 6 /(100,000 × .99 × 0.26) = 73.3°C

or exit gas temperature from the economizer = 262 − 73.3 = 188.7°C. Thus, the gas and steam temperatures are obtained simply by assuming pinch and approach points. Note that specific heat of gas at the average gas temperature in a given surface is required for the calculation of the gas temperature drop, and hence, the temperature profile evaluation involves a few iterations and is best done using a computer program. The results from HRSG simulation program developed by the author is shown in Figure 5.3. Slight differences are noticed in the results as the program evaluates the gas specific heats more accurately; a few iterations are required to estimate the inlet– exit gas temperatures at each section and the accurate gas specific heat at each section. But the idea is to show that by simply assuming the pinch and approach points, one can establish a design. Note that the program also computes the efficiency of the HRSG as explained in Chapter 3. We can now evaluate the UA value for each section as the log-mean temperature difference (LMTD) for each section is known (counter- flow arrangement is typical in HRSGs for superheater and economizer). Using the results from the program, let us compute the various terms required to perform an off-design evaluation.

Q 1 = 1.24 MW = 1,069,000 kcal/h, Q 2 = 6.11 MW = 5,251,000 kcal/h, Q 3 = 2.19 MW =

1,892,000 kcal/h (sections 1, 2, and 3 are the superheater, evaporator, and economizer, respectively).

Superheater LMTDs: ΔT 1 = [(500 − 375) − (460 − 252)]/ln[(500 − 375)/(460 − 252)] = 163°C. (UA) 1 =Q 1 /ΔT 1 =

1,069,000/163 = 6,558. Program shows a value of 6,607. Evaporator

LMTD ΔT 2 = [(460 − 252) − (262 − 252)]/ln[(460 − 252)/(262 − 252)] = 65.2°C. (UA) 2 =Q 2 /ΔT 2 = 5,251,000/65.2 = 80,536. Program shows a value of 80,645.

HRSG Simulation 269

HRSG performance—Design case

Sh. Evap. Eco. Project—eg1 Units—Metric case—eg1 Remarks-

Amb. temp., °C = 25 Heat loss, % = 1 Gas temp. to HRSG C = 500 Gas ﬂow, kg/h = 100,000

% vol CO 2 = 3. H 2 O = 7. N 2 = 75. O 2 = 15. SO 2 =. ASME eﬀ., % = 64.85 tot duty, MW = 9.6 Surf. Gas temp. Wat./Stm. Duty Pres.

Flow Pstm. Pinch Apprch. US Module no. in/out °C

°C kcal/h °C Sh.

in/out °C MW kg/cm 2 a kg/h

Example 5.1: gas–steam temperature profile in design mode.

Economizer LMTD ΔT 3 = [(262 − 245) − (189 − 105)]/ln[(262 − 245)/(189 − 105)] = 42°C. (UA) 3 =Q 3 /ΔT 3 =

1,892,000/42 = 45,047. Program shows 45,310. The variations are mainly due to rounding off the LMTD values and slight variations in gas specific heats. However, the purpose is to illustrate the methodology. These data will come in handy later when we discuss off-design calculations.

One should understand that the HRSG heating surfaces have been determined indirectly when we selected the pinch and approach points. (UA) is in fact a proxy for the surface area.

270 Steam Generators and Waste Heat Boilers: For Process and Plant Engineers

Estimating Steam Generation and Gas–Steam Temperature Profiles