A steam power plant operates on ideal Rankine cycle using reheater and regenerative feed water heaters. It has one open feed heater. Steam is supplied at 150 bar and 600°C. The condenser pressure is 0.1 bar. Some steam is extracted from the turbine at 40 bar for closed feed water heater and

Question

A steam power plant operates on ideal Rankine cycle using reheater and regenerative feed water heaters. It has one open feed heater. Steam is supplied at 150 bar and 600°C. The condenser pressure is 0.1 bar. Some steam is extracted from the turbine at 40 bar for closed feed water heater and remaining steam is reduced at 40 bar to 600°C. Extracted steam is completely condensed in this closed feed water heater and is pumped to 150 bar before mixing with the feed water heater. Steam for the open feed water heater is bled from L.P. turbine at 5 bar. Determine :

(i) Fraction of steam extracted from the turbines at each bled heater, and

(ii) Thermal efficiency of the system.

Draw the line diagram of the components and represent the cycle on T-s diagram.

(i) Fraction of steam extracted from the turbines at each bled heater, and

(ii) Thermal efficiency of the system.

Draw the line diagram of the components and represent the cycle on T-s diagram.

Accepted Answer

The arrangement of the components is shown in Fig. 12.41 (a) and the processes are represented on T-s diagram as shown in Fig. 12.41 (b).

From h-s chart and steam tables we have enthalpies at different points as follows :

[latex]\left.\begin{array}{ll}h_1=3578 \mathrm{~kJ} / \mathrm{kg} ; & h_2=3140 \mathrm{~kJ} / \mathrm{kg} ; \h_3=3678 \mathrm{~kJ} / \mathrm{kg} ; & h_4=3000 \mathrm{~kJ} / \mathrm{kg} ; \h_5=2330 \mathrm{~kJ} / \mathrm{kg} ; &\end{array} ight\}[/latex] From h-s chart

[latex]\left.\begin{array}{rl}h_{f 1}( ext { at } 150 \mathrm{bar}) & =1611 \mathrm{~kJ} / \mathrm{kg} \h_{f 2}( ext { at } 40 \mathrm{bar}) & =1087.4 \mathrm{~kJ} / \mathrm{kg} ; h_{f 4}( ext { at } 5 \mathrm{bar})=640.1 \mathrm{~kJ} / \mathrm{kg} ; \h_{f 5} & =h_{f 6}( ext { at } 0.1 \mathrm{bar})=191.8 \mathrm{~kJ} / \mathrm{kg}\end{array} ight\}[/latex] Steam tables

(i) Fraction of steam extracted from the turbines at each bled heater [latex]\mathrm{m}_1, \mathrm{~m}_2[/latex] :

Considering energy balance for closed feed heater, we have :

[latex]m_1\left(h_2-h_{f 2} ight)=\left(1-m_1 ight)\left(h_{f 2}-h_{f 4} ight)[/latex]

[latex]m_1(3140-1087.4)=\left(1-m_1 ight)(1087.4-640.1)[/latex]

or [latex]2052.6 m_1=\left(1-m_1 ight) imes 447.3[/latex]

∴ [latex]m _1=0.179[/latex] kg/kg of steam supplied by the boiler.

Considering energy balance for open feed heater, we have :

[latex]m_2\left(h_4-h_{f 4} ight)=\left(1-m_1-m_2 ight)\left(h_{f_4}-h_{f 6} ight)[/latex]

or [latex]m_2\left(h_4-h_{f 4} ight)=\left(1-m_1-m_2 ight)\left(h_{f 4}-h_{f 5} ight)[/latex] [latex]\left(\because \quad h_{f 6}=h_{f 5} ight)[/latex]

or [latex]m_2(3000-640.1)=\left(1-0.179-m_2 ight)(640.1-191.8)[/latex]

or [latex]2359.9 m_2=\left(0.821-m_2 ight) imes 448.3=368.05-448.3 m_2[/latex]

∴ [latex]m _2=0.131[/latex] kg/kg of steam supplied by boiler.

(ii) Thermal efficiency of the system, [latex]\eta_{ ext {thermal }}[/latex] :

Total work done per kg of steam supplied by the boiler

[latex]=1 imes\left(h_1-h_2 ight)+\left(1-m_1 ight)\left(h_3-h_4 ight)+\left(1-m_1-m_2 ight)\left(h_4-h_5 ight)[/latex]

= (3578 – 3140) + (1 – 0.179)(3678 – 3000) + (1 – 0.179 – 0.131)(3000 – 2330)

= 438 + 556.64 + 462.3 = 1456.94 kJ/kg

Work done by the pump [latex]P_1[/latex]

[latex]W_{P 1}=v_{w 1}\left(1-m_1-m_2 ight)(5-0.1) imes 10^5 imes 10^{-3}[/latex] kJ/kg

= [latex]\frac{1}{1000}(1-0.179-0.131)(5-0.1) imes 10^5 imes 10^{-3}=0.338[/latex] kJ/kg

[latex]\left[ ext { Taking } v_{w 1}=v_{w 2}=v_{w 3}=\frac{1}{1000} m ^3 / kg ight][/latex]

Work done by the pump [latex]P_2[/latex],

[latex]W_{P 2}=v_{w 2}\left(1-m_1 ight)(150-5) imes 10^5 imes 10^{-3}[/latex] kJ/kg

= [latex]\frac{1}{1000}(1-0.179)(150-5) imes 10^5 imes 10^{-3}=11.9[/latex] kJ/kg

Work done by pump [latex]P_3[/latex],

[latex]W_{P 3}=v_{w 3} imes m_1 imes(150-40) imes 10^5 imes 10^{-3}[/latex] kJ/kg

Total pump work [latex]=W_{P 1}+W_{P 2}+W_{P 3}[/latex]

= 0.338 + 11.9 + 1.97 = 14.21 kJ/kg of steam supplied by boiler

∴ Net work done by the turbine per kg of steam supplied by the boiler,

[latex]W_{ ext {net }}=1456.94-14.21=1442.73[/latex] kJ/kg

Heat of feed water extering the boiler

[latex]=\left(1-m_1 ight) imes 1611+m_1 imes 1611=1611[/latex] kJ/kg

Heat supplied by the boiler per kg of steam,

[latex]Q_{s 1}=h_1-1610=3578-1610=1968[/latex] kJ/kg

[latex]Q_{s 2}=[/latex] Heat supplied in the reheater

[latex]=\left(1-m_1 ight)\left(h_3-h_ ho ight)=(1-0.179)(3678-3140)[/latex]

= 441.7 kJ/kg of steam supplied by the boiler

[latex]Q_{s t}[/latex] (Total heat supplied) [latex]=Q_{s 1}+Q_{s 2}=1968+441.7=2409.7[/latex] kJ/kg

∴ [latex]\eta_{ ext {thermal }}=\frac{W_{ ext {net }}}{Q_{s t}}=\frac{1442.73}{2409.7}=0.5987[/latex] or 59.87%.

Question 12.26: A steam power plant operates on ideal Rankine cycle using re...

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