A triple-pressure combined-cycle power plant (refer to Figures 5.12 and 5.13c) is operating under the following conditions: • Gas turbine exhaust gas flow rate mg = 540 kg/s • Exhaust gas temperature texh = t1 = 650°C • Live steam condition at HP turbine inlet p1 = 150 bars, t1 = 550°C • Steam

Question

A triple-pressure combined-cycle power plant (refer to Figures 5.12 and 5.13c) is operating under the following conditions:

• Gas turbine exhaust gas flow rate [latex]m_{g}[/latex] = 540 kg/s
• Exhaust gas temperature [latex]t_\mathrm{exh}[/latex] = [latex]t_{1}[/latex] = 650°C
• Live steam condition at HP turbine inlet [latex]p_{1}[/latex] = 150 bars, [latex]t_{1}[/latex] = 550°C
• Steam pressure at intermediate pressure (IP) turbine inlet [latex]p_{2}[/latex] = 20 bars
• Steam pressure at LP turbine inlet [latex]p_{3}[/latex] = 4 bars
• LP steam production rate [latex]m_\mathrm{LP}[/latex] = 11 kg/s
• Condenser pressure [latex]p_\mathrm{c}[/latex] = 0.05 bar
• steam turbine isentropic efficiency [latex]\eta_\mathrm{it}[/latex] = 0.9
• Feedwater temperature [latex]t_\mathrm{fw}[/latex] = [latex]t_{8}[/latex] = 140°C
• Pinch point PP = 10 K

Flue gas specific heat [latex]c_\mathrm{pg}[/latex] = 1.05 kJ/(kg K)
The temperature–heat flux diagram is shown in Figure 5.12.
Calculate (i) the total steam production rate [latex]m_{s}[/latex], (ii) steam turbine power output [latex]P_\mathrm{ST}[/latex], and (iii) steam turbine plant efficiency [latex]\eta_\mathrm{ST}[/latex].

Accepted Answer

1. Steam and water conditions (from water/steam table, Appendix 7 and h–s diagram, Appendix 11)

2. Flue gas temperatures: [latex]t_{1}=610^{\circ}{\sf C},\;t_{2}=t_{13}+\mathrm{PP}=324.65+10=334.65^{\circ}[/latex]C

[latex]t_{4}=t_{11}+\mathrm{PP}=212.37+10=222.37^{\circ}{\mathrm{C}},\;\mathrm{and~}t_{6}=t_{9}+\mathrm{PP}=143.62+10=153.62^{\circ}{\mathrm{C}}[/latex]

3. HP steam production rate

[latex]m_{\mathrm{HP}}\,=\,m_{\mathrm{g}}\mathrm{c}_{\mathrm{pg}}(t_{1}-t_{2})/(h_{14}-h_{13})[/latex]

[latex]=540 imes1.05 imes(610-334.65)/(3465-1.49\mathbf{1}.8)=79.12\,{\mathrm{kg/s}}[/latex]

4. Actual exhaust steam enthalpy

[latex]h_{3}\,=\,h_{2}\,-\,(h_{2}\,-\,h_{3s})\,{\mathbf{h}}_{\mathrm{it}}\,=\,2840\,-\,(2840\,-\,2120)\,0.9\,=\,2192\,{\mathrm{kJ}}/{\mathrm{kg}}[/latex]

5. Actual specific work for the HP and the LP steam turbine

[latex]w_{\mathrm{HP}}\,=\,h_{1}-h_{2}\,=\,3465-2840=585\ \mathrm{kJ}/\mathrm{kg}[/latex]

[latex]w_{\mathrm{LP}}\,=\,h_{2}\,-\,h_{3}\,=\,2840-2\,192\,=\,648\ {\mathrm{kJ}}/{\mathrm{kg}}[/latex]

6. Steam mass flow rate for the HP and the LP steam turbines

[latex]m_{\mathrm{HP}}\,=\,79.12\;\mathrm{kg/s}[/latex]

[latex]m_{\mathrm{LP}}^{\prime}\,=\,m_{\mathrm{H}\mathrm{P}}\,+\,m_{\mathrm{LP}}\,-\,m_{\mathrm{d}}\,=\,79.12\,+\,10.48\,-\,12.59\,=\,77.01\,{\mathrm{kg/s}}\, [/latex]

7. Steam turbine power output

[latex]P_{\mathrm{ST}}\,=\,m_{\mathrm{HP}}{{w}_{\mathrm{H}\mathrm{P}}}+m_{\mathrm{LP}}w_{\mathrm{LP}}\,=79.12 imes585+77.01 imes648=96,189\mathrm{~kW}[/latex]

8. Steam plant efficiency

[latex]\mathbf{h}_{\mathrm{ST}}\,=\,P_{\mathrm{ST}}/Q_{\mathrm{in}}\,=\,P_{\mathrm{ST}}/(m_{\mathrm{g}}c_{\mathrm{pg}}t_{1})=96,189/(540 imes1.05 imes610)=0.278[/latex]

	Working Fluid State	Pressure (bars)	Temperature (°C)
State	Working Fluid State	Pressure (bars)	Temperature (°C)	Enthalpy (kJ/kg)
8	Feedwater	4	110	460.6
9/10	Saturated	4	143.62	604.67/2737.6
	water/steam
11/12	Saturated	20	212.37	908.59/2792
	water/steam
13	Saturated water	150	342.13	1611
14	Live steam	150	550	3449

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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