A single-pressure HRSG of a combined-cycle power plant is operating under the following conditions: • Gas turbine exhaust gas mass flow rate mexh = mg = 640 kg/s • Exhaust gas temperature texh = t1 = 660°C • Superheated steam pressure p6 = 100 bars and temperature t6 = 550°C • Steam turbine

Question

A single-pressure HRSG of a combined-cycle power plant is operating under the following conditions:

• Gas turbine exhaust gas mass flow rate [latex]m_{exh}[/latex] = [latex]m_{g}[/latex] = 640 kg/s
• Exhaust gas temperature [latex]t_{exh}[/latex] = [latex]t_{1}[/latex] = 660°C
• Superheated steam pressure [latex]p_{6}[/latex] = 100 bars and temperature [latex]t_{6}[/latex] = 550°C
• Steam turbine isentropic efficiency [latex]\eta_{it}[/latex] = 0.9
• Condenser pressure [latex]p_{2}[/latex] = 0.04 bar
• Feedwater temperature [latex]t_{4}[/latex] = 130°C
• Pinch point PP = 10 K
• Specific heat of exhaust gas [latex]c_{pg}[/latex] = 1.05 kJ/(kg K)

Calculate (a) the rate of steam production, (b) the stack gas temperature, (c) the rate of heat release with stack gas in the atmosphere, (d) the actual steam turbine power output, and (e) the thermal efficiency of the steam power cycle.

Accepted Answer

1. Steam and water parameters: (i) live steam enthalpy [latex]h_{6}[/latex] = 3500 kJ/kg and turbine exhaust steam enthalpy at p = 0.04 bar [latex]h_{2s}[/latex] = 2005 kJ/kg (both from h–s diagram, Appendix 11), (ii) feedwater enthalpy [latex]h_{4}[/latex] =[latex]\mathrm{c}_\mathrm{pw}[/latex][latex]t_{4}[/latex] = 4.187 × 130 = 544.3 kJ/kg, (iii) saturation temperature at [latex]p_{5}[/latex] = 100 bars is [latex]t_{5}[/latex] = 311°C, and (iv) saturated water enthalpy [latex]h_{5}[/latex] = 1408 kJ/kg (from water/steam table, Appendix 7).

2. With the state designation according to Figure 5.7, the flue gas temperature at state 2 is

[latex]t_{2}=t_{5}+\mathrm{PP}=311+10=321^{\circ}C[/latex]

3. Energy balance for the superheater and evaporator of the HRSG yields steam production rate

[latex]m_{s}\,=\,m_{\mathrm{g}}c_{\mathrm{pg}}(t_{1}-t_{2})/(h_{\mathrm{6}}-h_{5})[/latex]

[latex]m_{s}\,=\,640 imes1.05 imes(660-321)/(3500-1408)=108.9\,\mathrm{kg/s}[/latex]

4. Rate of heat recovery in the HRSG

[latex]Q_{\mathrm{HRSG}}=m_{s}(h_{\mathrm{6}}-h_{4})=108.9 imes(3500-544.3)=321,860\,\mathrm{kW}[/latex]

5. Stack gas temperature

[latex]t_{3}\,=\,t_{1}-Q_{\mathrm{HRSG}}/(m_{\mathrm{g}}c_{\mathrm{pg}})=660-321,860/(640 imes1.05)=181^{\circ}C[/latex]

7. With exhaust steam enthalpy after isentropic expansion [latex]h_{2s}[/latex] = 2005 kJ/kg, the actual power output of steam turbine is

[latex]P_{ST}\,=\,m_{s}(h_{1}-h_{2s})\mathbf{h}_{\mathrm{it}}\,=\,108.9 imes(3500-2005) imes[/latex]0.9

[latex]=\,146,525\,\mathrm{kW}\cong\,146.5\,\,\mathrm{MW}[/latex]

8. Heat input rate in HSRG is equal to the total enthalpy of gas turbine exhaust gas, that is

[latex]Q_{\mathrm{in}}\,=\,m_{\mathrm{g}}c_\mathrm{pg}t_\mathrm{exh}\,=\,640 imes1.05 imes660\,=\,443,520\,\mathrm{kJ}/s[/latex]

9. Thermal efficiency of the steam turbine plant

[latex]{\mathbf h}_{\mathrm{th}}\,=\,P_\mathrm{ST}/Q_{\mathrm{in}}\,=\,146,525/443,520\,=\,0.274[/latex]

Appendix 7: Thermodynamic Properties of Saturated Water and Saturated Water Vapor— Pressure Table
p	t	${{v}}_\mathrm{f}$	${{v}}_\mathrm{g}$	$\mathbf{\rho}_{g}$	${{h}}_\mathrm{f}$	${{h}}_\mathrm{g}$	^{${{h}}_\mathrm{fg}$}	${{s}}_\mathrm{f}$	${{s}}_\mathrm{g}$
bar	°C	dm³/kg	m³/kg	kg/m³	kJ/kg	kJ/kg	kJ/kg	kJ/(kg K)	kJ/(kg K)
0.010	6.9808	1.0001	129.20	0.007739	29.34	2514.4	2485.0	0.1060	8.9767
0.020	17.513	1.0012	67.01	0.01492	73.46	2533.6	2460.2	0.2607	8.7246
0.030	24.100	1.0027	45.67	0.02190	101.00	2545.6	2444.6	0.3544	8.5785
0.040	28.983	1.0040	34.80	0.02873	121.41	2554.5	2433.1	0.4225	8.4755
0.050	32.898	1.0052	28.19	0.03547	137.77	2561.6	2423.8	0.4763	8.3960
0.060	36.183	1.0064	23.74	0.04212	151.50	2567.5	2416.0	0.5209	8.3312
0.070	39.025	1.0074	20.53	0.04871	163.38	2572.6	2409.2	0.5591	8.2767
0.080	41.534	1.0084	18.10	0.05523	173.86	2577.1	2403.2	0.5925	8.2296
0.090	43.787	1.0094	16.20	0.06171	183.28	2581.1	2397.9	0.6224	8.1881
0.10	45.833	1.0102	14.67	0.06814	191.83	2584.8	2392.9	0.6493	8.1511
0.20	60.086	1.0172	7.650	0.1307	251.45	2609.9	2358.4	0.8321	7.9094
0.30	69.124	1.0223	5.229	0.1912	289.30	2625.4	2336.1	0.9441	7.7695
0.40	75.886	1.0265	3.993	0.2504	317.65	2636.9	2319.2	1.0261	7.6709
0.50	81.345	1.0301	3.240	0.3086	340.56	2646.0	2305.4	1.0912	7.5947
0.60	85.954	1.0333	2.732	0.3661	359.93	2653.6	2293.6	1.1454	7.5327
0.70	89.959	1.0361	2.365	0.4229	376.77	2660.1	2283.3	1.1921	7.4804
0.80	93.512	1.0387	2.087	0.4792	391.72	2665.8	2274.0	1.2330	7.4352
0.90	96.713	1.0412	1.869	0.5350	405.21	2670.9	2265.6	1.2696	7.3954
1.0	99.632	1.0434	1.694	0.5904	417.51	2675.4	2257.9	1.3027	7.3598
1.5	111.37	1.0530	1.159	0.8628	467.13	2693.4	2226.2	1.4336	7.2234
2.0	120.23	1.0608	0.8854	1.129	504.70	2706.3	2201.6	1.5301	7.1268
2.5	127.43	1.0675	0.7184	1.392	535.34	2716.4	2181.0	1.6071	7.0520
3.0	133.54	1.0735	0.6056	1.651	561.43	2724.7	2163.2	1.6716	6.9909
3.5	138.87	1.0789	0.5240	1.908	584.27	2731.6	2147.4	1.7273	6.9392
4.0	143.62	1.0839	0.4622	2.163	604.67	2737.6	2133.0	1.7764	6.8943
4.5	147.92	1.0885	0.4138	2.417	623.16	2742.9	2119.7	1.8204	6.8547
5.0	151.84	1.0928	0.3747	2.669	640.12	2747.5	2107.4	1.8604	6.8192
6.0	158.84	1.1009	0.3155	3.170	670.42	2755.5	2085.0	1.9308	6.7575
7.0	164.96	1.1082	0.2727	3.667	697.06	2762.0	2064.9	1.9918	6.7052
8.0	170.41	1.1150	0.2403	4.162	720.94	2767.5	2046.5	2.0457	6.6596
continued

p	t	${{v}}_\mathrm{f}$	${{v}}_\mathrm{g}$	$\mathbf{\rho}_{g}$	${{h}}_\mathrm{f}$	${{h}}_\mathrm{g}$	^{${{h}}_\mathrm{fg}$}	${{s}}_\mathrm{f}$	${{s}}_\mathrm{g}$
bar	°C	dm³/kg	m³/kg	kg/m³	kJ/kg	kJ/kg	kJ/kg	kJ/(kg K)	kJ/(kg K)
9.0	175.36	1.1213	0.2148	4.655	742.64	2772.1	2029.5	2.0941	6.6192
10.0	179.88	1.1274	0.1943	5.147	762.61	2776.2	2013.6	2.1382	6.5828
11	184.07	1.1331	0.1774	5.637	781.13	2779.7	1998.5	2.1786	6.5497
12	187.96	1.1386	0.1632	6.127	798.43	2782.7	1984.3	2.2161	6.5194
13	191.61	1.1438	0.1511	6.617	814.70	2785.4	1970.7	2.2510	6.4913
14	195.04	1.1489	0.1407	7.106	830.08	2787.8	1957.7	2.2837	6.4651
15	198.29	1.1539	0.1317	7.596	844.67	2789.9	1945.2	2.3145	6.4406
16	201.37	1.1586	0.1237	8.085	858.56	2791.7	1933.2	2.3436	6.4175
17	204.31	1.1633	0.1166	8.575	871.84	2793.4	1921.5	2.3713	6.3957
18	207.11	1.1678	0.1103	9.065	884.58	2794.8	1910.3	2.3976	6.3751
19	209.80	1.1723	0.1047	9.555	896.81	2796.1	1899.3	2.4228	6.3554
20	212.37	1.1766	0.09954	10.05	908.59	2792.2	1888.6	2.4469	6.3367
25	223.94	1.1972	0.07991	12.51	961.96	2800.9	1839.0	2.5543	6.2536
30	233.84	1.2163	0.06663	15.01	1008.4	2802.3	1793.9	2.6455	6.1837
40	250.33	1.2521	0.04975	20.10	1087.4	2800.3	1712.9	2.7965	6.0685
50	263.91	1.2858	0.03943	25.36	1154.5	2794.2	1639.7	2.9206	5.9735
60	275.55	1.3187	0.03244	30.83	1213.7	2785.0	1571.3	3.0273	5.8908
70	285.79	1.3513	0.02737	36.53	1267.4	2773.5	1506.0	3.1219	5.8162
80	294.97	1.3842	0.02353	42.51	1317.1	2759.9	1442.8	3.2076	5.7471
90	303.31	1.4179	0.02050	48.79	1363.7	2744.6	1380.9	3.2867	5.6820
100	310.96	1.4526	0.01804	55.43	1408.0	2727.7	1319.7	3.3605	5.6198
110	318.05	1.4887	0.01601	62.48	1450.6	2709.3	1258.7	3.4304	5.5595
120	324.65	1.5268	0.01428	70.01	1491.8	2689.2	1197.4	3.4972	5.5002
130	330.83	1.5672	0.01280	78.14	1532.0	2667.0	1135.0	3.5616	5.4408
140	336.64	1.6106	0.01150	86.99	1571.6	2642.4	1070.7	3.6242	5.3803
150	342.13	1.6579	0.01034	96.71	1611.0	2615.0	1004.0	3.6859	5.3178
200	365.70	2.0370	0.00587	170.2	1826.5	2418.4	591.9	4.0149	4.9413
220	373.69	2.6714	0.00373	268.3	2011.1	2195.6	184.5	4.2947	4.5799
221.2	374.15	3.17	0.00317	315.5	2107.4	2107.4	0	4.4429	4.4429
Note: 1. Symbols: t, temperature; p, pressure; v, specific volume; h, specific enthalpy; s, specific entropy. 2. Subscripts: f, saturated liquid water; g, dry saturated water vapor; ρ, density; fg, phase change from liquid to vapor.

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