Energy-Exergy Analysis of Solarized Triple Combined Cycle Having Intercooling, Reheating and Waste Heat Utilization

As the energy demand is increasing, consumption of the fossil fuel is also increasing which in turns increases the environmental hazards as the burning of fossil fuel results in carbon production and other gases which is responsible for global warming and also there is cost which is associated with fossil fuel such as transporting cost, Extracting fossil fuel cost. Further, in view of continued reliance on fossil fuel driven power plants for meeting the power needs, fossil fuels are nearing depletion. Therefore, researchers are moving in the direction to find a sustainable source of energy which is renewable energy resources. The European Commission has an energy strategy of replacing fossil-fuel by increasing utilization of renewable energy resources and cutting down 40% of greenhouse gas emissions and targeting that at least 32% must be shared by renewable energy resources by 2030 [1]. Solar energy is the most promising and secured renewable source of energy needing detailed thermodynamic analysis of cycle based on it. The study of the thermodynamic cycle of a renewable energy source based power plant cannot be completed until the analysis is done by both the first law and second law of thermodynamics as the first law only gives the quantitative value of energy but the second law gives the qualitative value of energy. Exergy efficiency and destruction investigation provide more insight towards ideality. Thus, the exergy investigation serves as a worthwhile tool for enhancing the energy efficiency of large scale thermal energy systems [2].

The literature review shows that the Sanjay [3] carried out the energy and exergy analysis of combined cycle systems with different cycles, operating as a bottoming cycle, and observed that maximum steam is to be generated in case of triple pressure HRSG. Chandra and Kaushik [4] performed the energy and exergy analysis of the closed Brayton cycle with a regenerator, reheater, intercooler, and found that even with zero energy loss in reheater there occurs some exergy losses. Carcasciand and Winchler [5] presented that many times industrial waste has the potential to run low-temperature cycles for that they combined organic Rankine cycle with a gas turbine for converting waste into power as this low-temperature heat discharged can't be utilized with traditional Rankine Cycle. Amiralipoura and Kouhikamali [6] parametrically studied the effect of steam extraction on net power for the amount of water production and concluded that this will lead to a reduction in net power by 5.5 kW. Idrissa and Boulama [7] evaluated the exergy destruction by applying the advanced exergy analysis of components in a closed Brayton cycle power plant and found that the most exergy which is destructed in the combustion chamber is endogenous and unavoidable and further stated that varying the combustion temperature leads to reduce the destruction of the plant. Khan and Tlili [8] did a parametric comparison between steam and gas bottoming cycles and showed that the steam bottoming cycle having higher net-work output as a comparison to the gas bottoming cycle. Yang et al. [9] proposed a four-step investigation process wherein first, it checked the applicability of R1233zd(E) as an alternative to R245fa and compared R1233zd(E) to R245fa experimentally with a conclusion that R1233zd(E) is not only environment friendly but it also leads in thermal efficiency and power output by 3.8% and 4.5% respectively. Coco-Enríquez et al. [10] studied four different configurations based on the s-CO₂ Brayton cycle with reheating and intercooling and found that recuperation in the Brayton cycle leads to higher thermal efficiency compared to the Rankine cycle and combining the s-CO2 to the dual-loop solar field is beneficial in terms of cost of the solar field and thermal efficiency than to coupling of the dual loop solar field to Rankine cycle. Adibhatla and Kaushik [11] explored energy and exergy analysis of the conventional natural gas-fired having steam generation solar field and found that in DSG ISCCPP components the lowest exergetic efficiency is 27.4% for a solar field.

Rovira et al. [12] showed that when solar input is given for saturated steam generation then the highest thermal to electrical efficiency of 44.6% is achieved and the lowest efficiency of 33.5% is obtained when used for water preheating too. Kelly et al. [13] suggested the highly effective method for converting the thermal energy of solar into electricity by feed water extraction from the HRSG’seconomizer and producing saturated steam, and returning steam for superheating and reheating in HRSG by the exhaust of gas turbine. Saghafifarand Gadalla [14] investigated the Maisotsenko bottoming cycle power plant hybridization using a heliostat field collector. Maisotsenko gas turbine cycle also known as M-cycle is a recently proposed bottoming cycle. Kong et al. [15] concluded that the increase in pinch value leads to lowering the second law efficiency for which it used three different heat sources such as hot water, saturated steam, and combined hot water/saturated steam to supply heat at the ORC evaporator and with the heat source temperature varying from 80-110°C, the difference in pinch temperature of the heat source and the evaporating temperature was in the range of 1-10°C. Sachdeva and Singh [22] performed the theoretical analysis based on both the Ist & IInd law of thermodynamics to assess the performance parameters for identifying optimal conditions of the combined cycle configuration. Choi et al. [23] compared the efficiency of the triple combined cycle with carbon captured or without carbon captured and concluded that with carbon capture the 5% less efficiency is achieved and this will decrease with capture increasing rate.

The present paper deals with energy and exergy analysis of a solarized triple combined cycle with intercooling and reheating in the GT cycle combined with steam Rankine cycle and organic Rankine cycle for power with no carbon emission. The system consists of an intercooled-reheat type topping Brayton cycle and two bottoming cycles out of which one is steam run steam Rankine cycle and the other is an organic fluid run organic Rankine cycle. The air run GT cycle employs two stages intercooled compression and reheating during expansion while utilizing the solar energy collected through heliostats and used through a molten salt heat exchanger. During intercooling, the heat rejected in intercooler is utilized in the heat recovery vapour generator (HRVG) in one of the arrangements while in the other arrangement this heat ejected during intercooling is used in heat recovery steam generator (HRSG). Thus, two distinct triple combined cycle arrangements have been analyzed and compared. The considered combined cycle configurations have been analyzed using thermodynamic modeling based on the first law of thermodynamics and the second law of thermodynamics. The results obtained have been analyzed and presented herein to underline the effect of waste heat utilization on triple combined cycle performance which will pave way for power sector professionals to evolve suitable efficient arrangements using solar energy.

The energy and exergy analysis of the proposed intercooled-reheat type gas turbine, steam turbine, and organic Rankine cycle are done using energy balance and exergy balance of each component by thermodynamic modeling through the C program.

Following assumption considered during analysis are listed below:

1. All processes considered here are at a steady-state.
2. Direct Normal Irradiation is considered constant with a value of 1000 W/m².
3. No variation is considered in kinetic energy and potential energy.
4. The chemical exergy of material is neglected.
5. There is no pressure loss considered.
6. Pumps and turbines are adiabatic.
7. The approach temperature is considered negligible.

These are some generalized equation for the components of the considered cycle which are explained below:

Mass balance across components:

$\sum m_{\text {inlet }}=\sum m_{\text {outlet }}$

Energy balance across components:

$\sum E_{\text {inlet }}=\sum E_{\text {outlet }}$

Exergy balance across components:

$\sum E x_{\text {inlet }}=\sum E x_{\text {outlet }}+E_{x_{d}}$

Enthalpy in kJ/kg at each state can be calculated as:

$\mathrm{h}=\int C_{p} \cdot \mathrm{dt}$

Exergy in kJ/kg at each state is given as:-

ex=(h-h_o)-T_o.(s-s_o)

3.1 Heliostat field, central receiver

Energy balance for heliostat field is given by-

$\mathrm{Q}_{\mathrm{max}}=\mathrm{Q}_{\mathrm{rec}}+\mathrm{Q}_{\text {lost }}$     (1)

where,

$Q_{\max }=I . A_{h f}$     (2)

Q_max is the incident solar radiation that will be divided into two parts in which one goes to receiver (solar isolation) and other is lost due to some environmental factors(Irreversibility). After accounting radiation energy losses, energy efficiency of heliostat (η_h) is given by-

η_h=Q_rec/Q_{max     (3)}

Exergy equation related to solar irradiation is -

Exergy_solar=Q_max.(1-(T_o/T_sun))     (4)

Energy balance for receiver is given by-

Q_rec =Q_{rec, abs}+ Q_{rec, loss     (5)}

where, Q_{rec, abs} is the energy that is absorbed by the receiver and Q_{rec, loss} is the energy that is lost due to emissive, reflective, convective, and conductive losses.

Taking into account receiver efficiency-

η_rec=Q_{rec, abs}/Q_{rec.     (6)}

3.2 Air property model

Here Brayton cycle having working fluid as air having a molar composition of 0.21 O₂ and 79 N₂. The specific heat of air is a function of temperature expressed as [16]-

C_p(T), kJ/kg-K=0.98964-5.344x10^-5T+3.39x10^-7T²-1.344x10-¹⁰T³     (7)

3.3 Topping cycle

Here Topping cycle considered is the Brayton cycle with air its working fluid which is powered by solar energy with a provision of no carbon emission. Intercooling and Reheating are taken.

Considering polytropic efficiency of compressor the temperature at the exit of the compressor is obtained as-

$\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\left(\frac{\mathrm{P}_{2}}{\mathrm{P}_{1}}\right)^{\left[\frac{\gamma-1}{\gamma \cdot \eta p o l y_{-} c}\right]}$     (8)

Considering Intercooling, the air at state 2 is cooled to the temperature of ambient by exchanging its heat into HRVG to the organic working fluid.

T₃=T₁     (9)

Energy balance across compressor can be obtained as-

m₁.h₁+W_c=m₂.h₂     (10)

Exergy balance across compressor can be obtained as-

m₁.ex₁+W_c=m₂.ex₂+Exd,_c     (11)

Second law efficiency of the compressor is given as-

$\eta_{I I, C o m p}=\frac{e x_{2}-e x_{1}}{\frac{W_{C}}{m_{a i r}}}$     (12)

Energy balance across intercooler for both layout1a and layout 1b is given by-

m₂.h₂+ m₂₃.h₂₃= m₃.h₃+m₂₄.h₂₄    (13)

Considering polytropic efficiency for gas turbine, the exit temperature of the turbine after the expansion is obtained as-

$\frac{T_{5}}{T_{6}}=\left(\frac{P_{5}}{P_{6}}\right)^{\left[\frac{\gamma-1}{\gamma}\right] \cdot \eta_{\text {poly_turb }}}$     (14)

Considering perfect reheating,

T₅=T₇     (15)

Turbine inlet temperature is given by-

Q_max.η_h.η_{r =}m_air.(h₅-h₄)+m_air.(h₇-h₆)     (16)

Energy balance across Gas turbine

m₅.h₅=m₆.h₆+W_{gt     (17)}

Exergy balance for Gas turbine-

m₅.ex₅₌m₆.ex₆+W_gt+ Exd,_turb     (18)

Second law efficiency of the turbine is given as-

$\eta_{I I, t u r b}=\frac{\frac{W_{g t}}{m_{a i r}}}{e x_{5}-e x_{6}}$     (19)

Thus the net work output of the topping cycle is,

W_net=W_gt-W_c     (20)

Gas turbine cycle’s energy efficiency is expressed by-

η_gt=W_net/Q_max     (21)

3.4 Heat recovery steam generator

When intercooling heat is used in HRSG as shown in figure 1b, the exhaust of GT cycle at state 8 goes to HRSG for exchanging its heat with water delivered by feed pump at state 18 for steam generation and exit at state 9.

The energy balance across HRSG when intercooling heat is used in HRSG given by-

$\begin{array}{c}

\epsilon_{H R S G} \cdot\left(\mathrm{m}_{8} \cdot \mathrm{h}_{8}+\mathrm{m}_{24} \cdot \mathrm{h}_{24}-\mathrm{m}_{9} \cdot \mathrm{h}_{9}\right)=\left(\mathrm{m}_{10} \cdot \mathrm{h}_{10}+\mathrm{m}_{12} \cdot \mathrm{h}_{12}\right)- \\

\left(\mathrm{m}_{11} \cdot \mathrm{h}_{11+} \mathrm{m}_{18} \cdot \mathrm{h}_{18}\right)

\end{array}$     (22)

The energy balance across HRSG when intercooling heat is used in HRVG given by-

$\begin{array}{c}

\epsilon_{H R S G} \cdot\left(\mathrm{m}_{8} \cdot \mathrm{h}_{8}-\mathrm{m}_{9} \cdot \mathrm{h}_{9}\right)=\mathrm{m}_{10} \cdot \mathrm{h}_{10}+\mathrm{m}_{12} \cdot \mathrm{h}_{12}- \\

\left(\mathrm{m}_{11} \cdot \mathrm{h}_{11+} \mathrm{m}_{18} \cdot \mathrm{h}_{18}\right)

\end{array}$     (23)

Exergy balance across HRSG when intercooling heat is used in HRSG is given by-

(m₈.ex₈)+(m₁₁.ex₁₁) +(m₁₈.ex₁₈)+(m_24.ex₂₄)=(m₉.ex₉)+(m₁₀.ex₁₀)+(m₁₂.ex₁₂)+Exd,_{HRSG     (24)}

Exergy balance across HRSG when intercooling heat is used in HRVG is given by-

(m₈.ex₈)+(m₁₁.ex₁₁)+(m₁₈.ex₁₈)=(m₉.ex₉)+(m₁₀.ex₁₀)+(m₁₂.ex₁₂)+Exd,_{HRSG     (25)}

Second law efficiency of HRSG is-

$\eta_{I I, H R S G}=1-\left(\mathrm{Exd}, \mathrm{HRSG} / \mathrm{av}, \mathrm{H}_{\mathrm{RSG}}\right)$     (26)

For Figure 1(a)

av,_HRSG=(ex₈- ex₉).m_air     (27)

For Figure 1(b)

av,_HRSG=(ex₈+ex₂₄-ex₉).m_air     (28)

3.5 Bottoming cycle

There are two bottoming cycles. One is the steam run steam Rankine cycle (SRC) and the other is an organic fluid run organic Rankine cycle (ORC).

3.5.1 SRC

Here a reheat Rankine cycle with steam bleeding for deaeration is combined with a topping cycle through HRSG.

(1) HPST

Energy balance in high pressure steam turbine is given by-

m₁₀.h₁₀=m₁₁.h₁₁+W_HPST     (29)

Considering the isentropic efficiency of the turbine

$\eta_{i s e n, H P S T}=\left(\mathrm{h}_{10}-\mathrm{h}_{11}\right) /\left(\mathrm{h}_{10}-\mathrm{h}_{11, \mathrm{is}}\right)$     (30)

Exergy balance for High Pressure steam turbine-

m₁₀.ex₁₀=m₁₁.ex₁₁+W_HPST+Exd,_HPST     (31)

Exd,_HPST is exergy destruction across high pressure steam turbine.

Second law efficiency of high pressure steam turbine:

$\eta_{\mathrm{IL}, \mathrm{HPST}}=\frac{\frac{W_{H P S T}}{m_{\text {steam }}}}{e x_{10}-e x_{11}}$     (32)

where, η_II,HPST is the second law efficiency of HPST

(2) LPST

Energy balance in low pressure steam turbine is given by-

m₁₂.h₁₂=m₁₃.h₁₃₊m₁₄.h₁₄+W_LPST     (33)

m₁₃=fr.m₁₂     (34)

m₁₄=(1-fr).m₁₂     (35)

Perfect reheating is considered, so the temperatures at state 10 and 12 are same.

T₁₀=T₁₂     (36)

Taking isentropic efficiency of the turbine

$\eta_{i s e n, L P S T}=\left(\mathrm{h}_{12}-\mathrm{h}_{13}\right) /\left(\mathrm{h}_{12}-\mathrm{h}_{13 \mathrm{is}}\right)$     (37)

Exergy balance for low pressure steam turbine

$m₁₂.ex₁₂=m₁₃.ex₁₃+m₁₄.ex₁₄+W_LPST+Exd,_LPST$     (38)

Exd,_LPST is exergy destruction across low pressure steam turbine

Second law efficiency of low pressure steam turbine-

$\eta_{\mathrm{II}, \mathrm{LPST}}=\frac{\frac{W_{L P S T}}{m_{\text {steam }}}}{e x_{12}-e x_{14}}$     (39)

(3) Condenser

Energy balance for condenser is given by-

m₁₄.h₁₄=m₁₅.h₁₅+Q_cond     (40)

Exergy balance across condenser

$\mathrm{m}_{14} \cdot \mathrm{ex}_{14}=\mathrm{m}_{15} \cdot \mathrm{ex}_{15+} \mathrm{Q}_{\text {cond }}\left(1-\frac{T_{o}}{T_{\text {space }}}\right)+\mathrm{Exd}_{\text {,cond }}$     (41)

(4) Pump

Energy balance for pump yields,

m₁₇.h₁₇+W_pump=m₁₈.h₁₈    (42)

$\mathrm{W}_{\text {pump }}=\mathrm{m}_{15} .\left(\mathrm{h}_{18}-\mathrm{h}_{17}\right)=\int v \cdot d p$     (43)

(5) Deaerator

Energy balance across deaerator is given by-

m₁₃.h₁₃+m₁₅.h₁₅=m₁₇.h₁₇     (44)

(6) Condensate extraction pump

Energy balance for pump yields,

m₁₅.h₁₅+W_CEP=m₁₆.h_{16    （(45)}

Energy efficiency of steam Rankine cycle is given as -

$\eta_{\mathrm{I}, \mathrm{SRC}=} \frac{W_{H P S T}+W_{L P S T^{-}} W_{p u m p}-W_{C E P}}{\left(h_{8}-h_{9}\right) \cdot m_{a i r}}$ (46)

(7) Heat recovery vapour generator

The exhaust air at state 9 goes to HRVG and exits at state 1. During state 9 to state 1 the exhaust heat is used in the evaporation of the organic fluid R1233zd(E).

The energy balance across HRVG when intercooling heat is used in HRVG given by-

$\epsilon_{\mathrm{HRVG}}\left(\mathrm{m}_{9} \cdot \mathrm{h}_{9}+\mathrm{m}_{24} \cdot \mathrm{h}_{24}-\mathrm{m}_{25} \cdot \mathrm{h}_{25}-\mathrm{m}_{1} \cdot \mathrm{h}_{1}\right)=\mathrm{m}_{\text {oxc } \cdot}\left(\mathrm{h}_{19}-\mathrm{h}_{22}\right)$     (47)

The energy balance across HRVG when intercooling heat is used in HRSG given by-

$\epsilon_{\mathrm{HRVG}}\left(\mathrm{m}_{9} \cdot \mathrm{h}_{9}-\mathrm{m}_{1} \cdot \mathrm{h}_{1}\right)=\mathrm{m}_{\text {orc. }}\left(\mathrm{h}_{19}-\mathrm{h}_{22}\right)$     (48)

Exergy balance across HRVG when intercooling heat is used in HRVG is given by-

m₉.ex₉+m₂₄.ex₂₄+m₂₂.ex₂₂=m₁.ex₁+m₁₉.ex₁₉+m₂₅.ex₂₅+Exd,_HRVG     (49)

Exergy balance across HRVG when intercooling heat is used in HRSG is given by-

m₉.ex₉+m₂₂.ex₂₂=m₁.ex₁+m₁₉.ex₁₉+Exd,_HRVG     (50)

Second law efficiency of HRVG is-

$\eta_{I I, H R V G}=1-(\mathrm{Exd}, \mathrm{HRVG} / \mathrm{av}, \mathrm{HRVG})$      (51)  

For layout 1(a)

av,_HRVG= (ex₉+ex₂₄- ex₂₅-ex₁).m_air     (52)

For Figure 1(b)

av,_HRVG= (ex₉-ex₁).m_air     (53)

3.5.2 Organic rankine cycle

Organic Rankine cycle is the second bottoming cycle which is a low temperature cycle work on organic fluid R1233zd(E).

(1) ORC vapor turbine

Energy balance across ORC vapor turbine is given as-

m₁₉.h₁₉=m₂₀.h₂₀+W_,orct     (54)

Exergy balance across ORC vapor turbine

m₁₉.ex₁₉=m₂₀.ex₂₀+W_,orct+Exd_,orct     (55)

Second law efficiency of ORC vapor turbine is given as-

$\eta_{\mathrm{II}, \text { orct }}=\frac{\frac{W_{\text {orct }}}{m_{\text {orc }}}}{e x_{19}-e x_{20}}$     (56)

(2) ORC condenser

Conservation of energy across ORC condenser

m₂₀.h₂₀=m₂₁.h₂₁+Q_cond,orc     (57)

Exergy balance across orc condenser

m₂₀.ex₂₀=m₂₁.ex₂₁+Q_cond,orc+ Exd_cond,orc     (58)

(3) ORC pump

Conservation of energy across ORC Pump

m₂₁.h₂₁=m₂₂.h₂₂+W_orc,pump     (59)

Energy efficiency of Organic Rankine cycle is given as-

$\eta_{\mathrm{I}, \mathrm{ORC}}=\frac{W_{\text {orct }}-W_{\text {orc }, \text { pump }}}{\left(h_{9}-h_{1}\right) \cdot m_{\text {air }}}$     (60)

3.6 Overall cycle

The net-work output from the considered combined cycle comprises of the work output from intercooled-reheat type Brayton cycle, reheat SRC, and ORC along with the heat in the condensers of the bottoming cycles.

W,_overall=$\begin{array}{rl}

W_{g t}+W_{H P S T}+W & W_{L P S T}+W_{\text {orct }}+Q_{\text {cond }} \\

& +Q_{\text {cond,orc }}-W_{c}-W_{p}-W_{C E P} \\

& -w_{\text {Orc,pump }}

\end{array}$    (61)

Overall cycle efficiency is given as-

$\begin{array}{c}

W_{g t}+W_{H P S T}+W_{L P S T}+W_{\text {orct }}+Q_{\text {cond }} \\

\eta_{I, \text { overall }}=\frac{+Q_{\text {cond,orc }}-W_{c}-W_{p}-W_{C E P}-w_{\text {Orc,pump }}}{Q_{\max }}

\end{array}$     (62)

Overall exergy efficiency is given as-

$\begin{array}{r}

W_{g t}+w_{H P S T}+W_{L P S T}+w_{\text {orct }}+Q_{\text {cond }} \cdot\left(1-\frac{T 0}{\text { Tspace }}\right) \\

\eta_{\text {II }, \text { exergy }}=\frac{+Q_{\text {cond,orc. }}\left(1-\frac{\text { To }}{\text { Tspace }}\right)-W_{c}-W_{p}-W_{C E P}-W_{\text {orc,pump }}}{Q_{\max } \cdot\left(1-\frac{T 0}{\text { Tspace }}\right)}

\end{array}$     (63)

The following conclusion has been drawn from the considered solarized triple combined cycle having intercooling, reheating, and waste heat utilization:

1. There is no emission of carbon as only air is treated as a working fluid in the topping cycle. Hence it is an environment-friendly combined cycle whose exhaust air potential is used for using low GWP refrigerant R1233zd(E) in the low-temperature cycle.
2. The use of intercooler reduces the work requirement of the compressor and the use of intercooling heat helps in enhancing energy efficiency.
3. In the present study, it is analyzed after a comparative study that using intercooling heat in HRSG increases energy efficiency, and this efficiency increases with increasing CPR. And in this case, the exergy destruction in HRSG is more than in HRVG.
4. The maximum energy efficiency of 64.15% is achieved at 16 CPR & 300 K ambient temperature when intercooling heat is used in HRSG and the maximum overall exergetic efficiency of 39.72% is achieved at 16 CPR. While maximum energy efficiency of 63.54% is achieved at 8 CPR & 300 K ambient temperature when intercooling heat is utilized in HRVG and maximum overall exergetic efficiency of 38.37% is achieved at 14 CPR &300 K ambient temperature.
5. While analyzing the exergy destruction in different components it is found that when intercooling heat is utilized in heat recovery steam generator, then the most exergy is destructed in HRSG to the tune of 50% followed by 11% in the compressor and lowest exergy destruction of 1% is observed in HRVG. On the other hand when intercooling heat is utilized by HRVG then maximum exergy destruction of 17% takes place in compressors.