Off-Design Performance Evaluation

Figure 4.29 shows the procedure for evaluating the performance of an HRSG in off-design [2] mode. In physical design, U is computed for each heating surface at the off-design case, and the NTU method is applied to arrive at the performance. In simulation, we correct the design UA value using appropriate factors for gas properties and gas flow and use the NTU

HRSG Simulation 275

HRSG performance—Oﬀ—Design case

Evap. Eco. Project—eg2 Units—Metric case—eg2 Remarks- Amb. temp., °C = 20 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., % = 79.42 tot duty, MW = 16.4 Surf. Gas temp. Wat./Stm. Duty Pres.

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

kcal/h °C Burn 500

in/out °C MW kg/cm 2 a kg/h

Evap. 671 262 216 250 13. 41. 25,033 100 12 33 96,598 1 Eco. 262

62,895 1 Stack gas ﬂow = 100,422 % CO 2 = 3.72 H 2 O = 8.41 N 2 = 74.45 O 2 = 13.41 SO 2 =. Fuel gas: vol%

Methane = 97 Ethane = 2

Propane = 1

LHV - kcal/cu m = 105 LHV - kcal/kg = 11,910 avg air - kg/h = 0

Off-design mode generating 25,000 kg/h steam. method or heat balance to arrive at the duty of each section. First, we compute the factor

F g , which reflects gas properties for each surface as shown later. Then, we compute the transferred duty Q p in the off-design mode either using the expression Q p = (UA)ΔT or the NTU method described in Appendix A. For the superheater, a small correction for actual steam flow to design steam flow is used; for the evaporator and the economizer, this can be neglected. W sp , the steam flow in off-design case, may be known or assumed; if assumed, then a few iterations are required to arrive at the final results as shown in Figure 4.29.

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

HRSG performance—Off—Design case

Evap. Eco. Project—eg2 Units—Metric case—eg2 Remarks-

Amb. temp., °C = 20 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., % = 86.7 tot duty, MW = 26.3 Surf. Gas temp. Wat./Stm. Duty Pres. Flow Pstm. Pinch Apprch. US Module no.

°C kcal/h °C Burn 500

in/out °C

in/out °C MW kg/cm 2 a kg/h

63,339 1 Stack gas ﬂow = 10,1122 % CO 2 = 4.89 H 2 O = 10.7 N 2 = 73.55 O 2 = 10.83 SO 2 =.

Fuel gas: vol% Methane = 97 Ethane = 2

Propane = 1

LHV - kcal/cu m = 105 LHV - kcal/kg = 11,910 avg air - kg/h = 0

Off-design mode generating 40,000 kg/h steam.

From the relation between (UA) d , the design (UA) value, and the (UA) p , (UA) value in the off-design case may be obtained as follows:

 UA Q = (  )

where Q and ΔT are the duty and LMTD in the design case as obtained from Example 5.1; this term (UA) is obtained for each heating surface such as superheater, evaporator, and

HRSG Simulation 277

economizer. Then, we obtain the (UA) p , the (UA) value in off-design or performance mode by using correction factors for gas flow, gas analysis, and steam flow. The steam flow correction is not required for evaporator and economizer.

( )( p = ) d 

(Subscript d stands for design mode and p for off-design or performance mode.) Then, we may either use the equation Q p = (UA) p ΔT p or the NTU method to obtain the duty in the off-design mode. The gas property factor F g is obtained as follows:

Let us check the off-design of the HRSG discussed in Example 5.1 when the firing temperature is 750°C. Results from the computer program are shown in Figure 5.6. Exhaust

gas flow is 100,634 kg/h. Gas analysis after the burner is % volume CO 2 = 4.08, H 2 O = 9.11, N 2 = 74.17, O 2 = 12.62. Steam pressure is the same. Determine the gas–steam profiles and

steam flow. It is seen that the steam temperature is 439°C and steam flow is 23,471 kg/h.

Solution

Several iterations are required to solve the aforementioned problem. However, to explain the off-design calculation procedure, the final results are used.

The NTU method will be applied. For the superheater, the terms (WC) min and (WC) max have to be first obtained. The enthalpy of superheated steam at 439°C is 789.4 kcal/kg and that of saturated steam is 668.8 kcal/kg. Hence, specific heat of steam is (789.4 − 668.8)/(439 − 255) = 0.655 kcal/kg °C. Gas-side specific heat based on the analysis may be shown to be 0.29 kcal/kg°C at the average gas temperature in the superheater.

Gasside WC ( ) = 100 640 0 29 0 99 , × . × . = , 28 893 . Steam side WC ( ) = , 23 471 × 0 . 0 655 = , 15 373 .

( WC ) min = , 15 373 . C = , 15 373 28 893 / , = . 0 532 1 .

0 ( − C ) = ..468

NTU = (UA) p /C min . (UA) p is the corrected (UA) for the fired case. To obtain this, we

need to know the (UA) d in the unfired or design case; from Figure 5.3, it is 6607 for the

superheater. Using the gas properties from Appendix F, it may be shown that at 480°C

(average gas temperature in the design mode of superheater), F g = 0.160 and in the off-

design mode (at 700°C), F g = 0.1777. Then, using (5.10),

, 6 607 ( 100 634 100 000 , / , ) ( . 0 1777 0 16 /. ) ( , 23 471 12 / , 70 ) = 8079 . NTU = , 8 079 15 373 0 5255 /, = . (see Appendix A)

UA = ×

∈= 1 − exp NTU { − (  1 − C ) }  / 1  −

C exp NTU { ( 1 − C ) } 

=  1 − exp ( − 0 . 5255 × . 00 468 )  /  − 1 0 532 . exp ( − . 0 5255 0 468 × . ) 

Q 1 = duty of superheater = . 0 3715 15 373 × , × ( 751 255 − ) = . 2 833 M M M kcal/h = . 3 294 MW

Exit gas temperature = 751 2 833 10 100 634 0 − × 6 . ° / , / .. / 99 0 29 652 . = C . Exit steam temperature =

° 255 2 833 10 23 471 + . × 6 /, / . 00 655 439 = C

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

HRSG performance—Off—Design case

Sh. Evap. Eco. Project—eg3 Units—Metric case—eg3 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., % = 79.42 tot duty, MW= 18.7 Surf. Gas temp. Wat./Stm. Duty Pres. Flow Pstm. Pinch Apprch.

US Module no. in/out °C

kcal/h °C Burn 500

in/out °C MW kg/cm 2 a kg/h

45,577 1 Stack gas ﬂow = 100,634 % CO 2 = 4.08 H 2 O = 9.11 N 2 = 74.17 O 2 = 12.62 SO 2 =.

Fuel gas: vol% Methane = 97 Ethane = 2

Propane = 1

LHV - kcal/cu m = 105 LHV - kcal/kg = 11,910 avg air - kg/h = 0 751

Fired performance of Example 5.1 HRSG.

HRSG Simulation 279

Evaporator Assume that F g values have been computed in the design and off-design modes.

( 0 65 UA )

, 80 645 ( . 0 16 0 1509 / . )( 100 634 100 000 , / , ) = , 85 860 . l n n   ( −

g 2 − 255 )   = , 85 860 100 634 0 2763 / , / . /0 . = 99 3 119 . o or t g2 = 273 C Q 2 = Dut y = 100 634 0 99 , × . × ( 652 273 − ) × . 0 2763 10 432 = . MM k kcal/h = 12 13 . MW

652 255 ° ) / ( t

Economizer

. ( 0 65 UA )

Gas side (WC) = 100,640 × 0.2625 × 0.99 = 26,153. Enthalpy of water at 216°C and 105°C are 221.2 and 105.9 kcal/kg, respectively. Hence, C pw = (221.2 − 105.9)/(216 − 105) = 1.0387 kcal/kg °C. Gas side specific heat is 0.2625 kcal/kg °C.

( WC ) gas = , 10 0634 0 99 0 2625 26 152 × . × . = , † ( WC ) water = , 23 706 1 0387 × . = = , 24 623

C min = , 24 623 . C = , 24 623 26 152 0 9287 /, = . . NTU = , 45 886 24 6 /, 223 1 8635 = .

∈=  1 − exp NTU { − ( 1 − C ) }  /  1 −

C exp NTU { ( 1 − C ) } 

=  1 − exxp ( − . 1 8635 0 0713 × . )  /  − 1 0 9287 . exp ( − . 1 8635 0 0713 × . )  = 0 .6666 Q 3 = duty of economizer = . 0 666 24 623 × , × ( 273 105 − ) = . 2 755 MM kcal / /h = 32 . MW

Exit gas temperature = 273 2 755 10 100 634 0 2625 − × 6 . ° / , / . /0 .. = 99 168 C

° Exit water temperature 105 2 755 10 24 623 217 . /, C

Total duty = 2.833 + 10.432 + 2.755 = 16.02 MM kcal/h. Steam generation based on

enthalpy pickup = 16.02 × 10 6 /(789.4 − 105.9) + 0.01 × (265.9 − 221.2)] = 23,422 kg/h

The results appear to be fine, as seen in Figure 5.6. Note that the manual method is tedious as several iterations are required to arrive at the final results, particularly if one had to compute the firing temperature and burner duty for a desired amount of steam. In such a case, we have to assume some firing temperature and compute the burner duty and exhaust gas analysis (as shown in Chapter 1); then, check the duty of each heating surface and steam generation, and if the required and estimated steam flows do not match, another revision of firing temperature is required, and the earlier process has to be repeated. Hence, a computer program is required to handle such prob- lems. The purpose of the exercise is to explain the procedure for off-design calculations, knowing the design data and thermal performance.

Off-Design Performance Evaluation