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Basic chemically recuperated gas turbines—power plant optimization and thermodynamics second law analysis
Energy 29 (2004) 2385–2395 www.elsevier.com/locate/energy
Basic chemically recuperated gas turbines—power plant optimization and thermodynamics second law analysis Lourenc¸o Gobira Alves , Silvia Azucena Nebra Energy Department of Mechanical Engineering Faculty, State University of Campinas, DE/FEM/UNICAMP, PO Box 6122, CEP 13083-970, Campinas, SP, Brazil
Abstract One of the proposals to increase the performance of the gas turbines is to improve chemical recuperated cycle. In this cycle, the heat in the turbine exhaust gases is used to heat and modify the chemical characteristics of the fuel. One mixture of natural gas and steam receives heat from the exhaust turbine gases; the mixture components react among themselves producing hot synthesis gas. In this work, an analysis and nonlinear optimization of the cycle were made in order to investigate the temperature and pressure influence on the global cycle performance. The chemical composition in the reformer was assumed according to chemical equilibrium equations, which presents good agreement with data from literature. The mixture of hot gases was treated like ideal gases. The maximum net profit was achieved and a thermodynamic second law analysis was made in order to detect the greatest sources of irreversibility. # 2004 Elsevier Ltd. All rights reserved. Keywords: Optimization; Exergy; Chemical recovery; Gas turbine; Power plant
1. Introduction The rational administration of energy resources with views to the improvement of productive processes is the key procedure to maintain competitiveness in global markets. The search for efficiency in the electric area goes not only through new methods and sources of electric production but also through improvements in the current processes. Gas turbines that operate in simple cycle present low efficiency because the turbine exhaust gases come out very hot and this heat is lost in the atmosphere. Better performances are reached with the advanced cycles [1], that take advantage of the energy contained in the turbine exhaust gases to improve the cycle or to transfer heat in combined cycles.
Corresponding author. Tel.: +55-19-37883285; fax: +55-19-32893722. E-mail address: [email protected] (L.G. Alves).
0360-5442/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2004.03.039
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Nomenclature Ca Cc Ce Cv Ech Eph Ex F I Kp N Ntot P P0 T T0 Wc We Wmc Wp Wt Wv ech eph ex h ma mc mv m s z g e DHr,c DHr,r
feeding water cost (US$/kg) acquisition price of the fuel (natural gas) (US$/kg) electric power price (US$/kWh) saturated steam price (US$/kg) chemical exergy (kJ) physical exergy (kJ) total exergy (kJ) exergetic equipment fuel (kJ) irreversibility (kJ) the chemical equilibrium constants molar quantity (kmol) the total moles number (kmol) exergetic equipment product (kJ) reference pressure (kPa) temperature (K) reference temperature (K) air compressor power required (kJ) electric power generated (kJ) methane compressor power required (kJ) water pump power required (kJ) turbine power (kJ) available electric power for sale (KWh) specific chemical exergy (kJ/kg) specific physical exergy (kJ/kg) specific total exergy (kJ/kg) enthalpy (kJ/kmol) feeding water mass (kg) fuel mass used (kg) steam mass available for sale (kg) mass flow (kg) entropy (kJ/kmol-K) optimization objective variable (US$) first law efficiency second law efficiency combustion reaction enthalpy (kJ) reform reaction enthalpy (kJ)
In gas turbines that work in cycle with chemical recovery, the mixture of natural gas (methane) and water absorbs heat contained in the exhaust gases. A reformer is used for this end. The
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mixture of natural gas and water enters on the cold side and it absorbs heat generating the synthesis gas to be burned in the combustion chamber. Cycles of chemical recovery were studied under several aspects. Kesser et al. [2] explored the relationships between the reformer and the turbine for two compressor pressure air ratios. Souza-Santos [3] studied variants of the cycle with chemical recovery taking into account the chemical composition of the natural gas. The physical and chemical aspects of the reformer can be seen in Adelman et al. [4] and Carcasci et al. [5]. Prieto et al. [6] made the Second-Law Analysis of the cycle determining its exergetic efficiency. This work analyzes the influence of methane and water injection in the reformer and the expansion of the turbine in the general performance of the cycle. The net operational profit of the cycle, understood as the difference between the sale of the products and the cost of the inputs all taken in relation to 1 kg of compressed air, was chosen as the optimization parameter.
2. Cycle model The cycle presented in this work is a simplification of the gas turbine cycle with chemical recovery. It is assumed that the gases are ideal gases, preserving the variation of the specific heat with the temperature. This hypothesis is fully acceptable for the pressure and temperature ranges of the cycle. Details of the cycle can be seen in Fig. 1. In order to make the case the most general possible, the air compressor flow was taken as reference. The ratio between the mass of methane and the mass of air can vary between 1:100 and 1:40, and the ratio between the mass of methane and the mass of water can vary between 1:3 and 1:7.5. These ratios were taken as the operational base of the turbine. It is not possible to operate economically below this level of methane, and superior levels would also make the temperature surpass 1400 K, the maximum temperature acceptable in the turbine inlet without blades cooling [7]. The amount of injected water also needs to be limited due to the physical parameters of the turbine. Conservative parameters were assumed in turbine and air compressor parameters because the fuel is a synthesis gas and not pure natural gas. The natural gas is composed of several substances, the main one being methane. For this reason, this gas will be adopted as the only component in place of the detailed composition of the natural gas. Besides that, the natural gas composition varies according to its source. In the same way, the composition of the dry air will be adopted as 21% oxygen and 79% nitrogen. After absorbing heat in the reformer, the methane reacts with the steam according to the equations: CH4 þ H2 O ! CO þ 3H2
(1)
CO þ H2 O ! CO2 þ H2
(2)
The reform reaction obeys the equations of chemical balance. The ratio between steam and methane must be high enough to prevent the formation of carbon deposits. In industrial reformers, this range is between 3 and 5. This proportion is used thoroughly for the production
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Fig. 1. Cycle schematic representation.
of hydrogen and for the synthesis of ammonia and methanol [5]. For this case, it is necessary that the catalyst is active at low temperatures, 800 K. The global reaction, written as function of the methane and the steam that enter as products, can be written as: a1 CH4 þ a2 H2 O ! b1 CH4 þ b2 CO þ b3 CO2 þ b4 H2 þ b5 H2 O;
(3)
where a1 and a2 are known amounts of the process feed. To obtain the composition of the gas mixture in the reformer exit, it is necessary to determine the five constants b1 to b5. The stoichiometric balance calculation yields to: a1 ¼ b1 þ b2 þ b3
(4)
4a1 þ 2a2 ¼ 4b1 þ 2b4 þ 2b5
(5)
a2 ¼ b2 þ 2b3 þ b5
(6)
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The other two equations are derived from the equilibrium constants Kp of the reactions 1 and 2. The constant Kp,1 can be written as [5]: Kp;1 ¼
PCO P3H
2
PCH4 PH2 O P20
¼
b2 b34 1 P2out;2 ; 2 b1 b5 Ntot P20
(7)
where Ntot is the total number of moles at equilibrium (b1 þb2 þb3 þb4 þb5 ) and P0 is the reference pressure, usually adopted as 1 atm. The value of Kp,1 is computed using the following correlation from Oertel et al. [8]: 27; 463 Kp;1 ¼ exp 30; 688 : (8) T The second constant Kp,2 can be written as [5]: Kp;2 ¼
PCO2 PH2 bb ¼ 3 4; PCO PH2 O b2 b5
(9)
and the value of Kp,2 at the temperature T is also computed in agreement with the equation [8]: 4084 3765 : (10) Kp;2 ¼ exp T All the thermodynamic properties were calculated based on the Janaf tables, and using the software EES1. The analysis of each element of the cycle supplies the equations that govern the system: Compressor: m1 ðh2 h1 Þ Wc ¼ 0
(11)
s1 ¼ s2;isso ;
(12)
where gc ¼
Wiso h2;iso h1 ¼ ¼ 0:85 Wc h2 h1
is the isentropic efficiency of the compressor, and Wc is the power required by the compressor. Turbine: m3 ðh3 h4 Þ Wc =gG We Wcm Wb ¼ 0
(13)
s3 ¼ s4;isso ;
(14)
where gt ¼
Wt h3 h4 ¼ ¼ 0:9 Wiso h3 h4;iso
is the isentropic efficiency of the turbine, gG ¼ 0:98 is the electric generator efficiency, We is the generated electric power, Wcm and Wb are the power consumed in methane compressor and water pump.
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Combustion chamber: m1 h2 þ m15 h15 m3 h3 þ DHr;c ¼ 0
(15)
m2 þ m15 m3 ¼ 0;
(16)
where DHr,c is the combustion reaction enthalpy. Reformer: m3 ðh4 h5 Þ þ m15 ðh15 h14 Þ þ DHr;r ¼ 0;
(17)
where DHr,r is the reform reaction enthalpy. m15 m8 m13 ¼ 0
(18)
m11 m12 m13 ¼ 0
(19)
Evaporator/economizer: m11 ðh11 h10 Þ ¼ m3 ðh5 h6 Þ
(20)
3. Optimization This cycle does not operate in industrial scale, so the equipment price was not estimated. The objective function will be the operational net profit, understood as the revenue of the electric power and saturated steam sale minus the cost of the inputs, feeding water and natural gas: z ¼ Ce Wv þ Cv mv Cc mc Ca ma
(21)
where Ce is electric power price (US$/kWh), Cv is saturated steam price (US$/kg), Cc is acquisition price of the fuel (natural gas) (US$/kg), Ca is feeding water cost (US$/kg), Wv ¼ We Wmc Wp : available electric power for sale (KWh), mc is fuel mass used (kg), mv is steam mass available for sale (kg/s), ma is feeding mass water (kg/s). The costs and prices were assumed according to: Electric energy price: Ce ¼ 102:4 US$=MWh [9]. Natural gas cost: Cc ¼ 0:08015 US$=kg [9]. Steam for sale price: Cv ¼ 0:009 US$=kg, Guarinello et al. [10]. Feeding water cost: Ca ¼ 0:00022 US$=kg, Guarinello et al. [10]. Restrictions of the system: v
T3 < 1400 K (1127 C): the turbine does not bear temperatures superior to that under the risk of thermal fatigue. P2 =P1 14:6: maximum air compressor operational compression ratio [7]. h4 ¼ h3 gt h3 h4;iso . The adiabatic expansion links the variation of the temperature to the pressure. This relationship supplies the smallest value possible for the temperature T4. The
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lower the temperature in the point 4, the higher the electric generation will be, on the other hand, the lower the capacity to generate steam will be. v T6 > 413 K (140 C). This value must be high enough to avoid gas condensation, which causes liquefaction of acid vapors in the stack walls. m12 0. This indicates that the system needs to provide at least the necessary steam to its own cycle. 650 K < T15 < 923 K. The reform temperature should be between these two limits. Below 650 K, the reform does not happen and above 923 K the chemical equilibrium equations are not valid. T 4 T 15 ¼ 20. Imposed condition of the heat transfer in the reformer (pinch point). 0:14 m15 0:25. Turbine operational conditions that regulate the flow and the excess of air. 0:13 m13 0:18. Turbine operational conditions. The optimization was made entirely in EES1 software. 4. Exergetic analysis The importance of the exergetic analysis is to diagnose how much of the theoretical maximum work the system is able to perform. The method of exergetic analysis used consists of evaluating each bearer of energy along the system identifying its chemical composition, physical state and flow rate. In order to analyze the cycle, the system was divided in seven control volumes so that it was possible to identify the performance of each one of those volumes. The following considerations were assumed. v Although the turbine performance is measured at 15 C, standard atmosphere for the calcuv lation of the physical exergies was assumed as T0 ¼ 25 C, P0 ¼ 101:3 kPa and relative humidity of the air 70%, according to standard temperature and pressure used in Szargut tables [11]. Efficiencies determination of each control volume, in agreement with the fuel, product and losses Kotas et al. [12] concept. Calculation of the physical exergy (eph), chemical (ech), and total exergy (ex), according to Szargut et al. [11] formulations: eph ¼ ðh h0 Þ T0 ðs s0 Þ
(22)
ex ¼ eph þ ech
(23)
where the component of the ech refers to the tables reported by Szargut et al. [11]. The gas mixtures from the reformer exit were admitted as mixtures of ideal gases. The gas compositions along the cycle were taken based on the mass balances and considering complete combustion in the combustion chamber. The exergetic efficiency, e, and the irreversibility values, I; in each component will be calculated according to the following: P F I ¼PF e¼
where P is the product and F is the thermodynamic fuel considered in each control volume.
(24) (25)
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The previous considerations lead to: Air compressor: F ¼ Wc
(26)
P ¼ Ex2 Ex1
(27)
Combustion chamber: F ¼ Ex15
(28)
P ¼ Ex3 Ex2
(29)
Turbine: P ¼ Wt
(30)
F ¼ Ex3 Ex4
(31)
Reformer: P ¼ Ex15 Ex8 Ex13
(32)
F ¼ Ex4 Ex5
(33)
Methane compressor: P ¼ Ex8 Ex7
(34)
F ¼ Wmc
(35)
Evaporator/economizer: P ¼ Ex11 Ex10
(36)
F ¼ Ex5 Ex6
(37)
Water pump: P ¼ Ex10 Ex9
(38)
F ¼ Wp
(39)
5. Results and discussions The optimal solution showed that the largest operational net profit is obtained with the largest possible temperature in the turbine inlet associated with the largest ratio compression (14.8) in the air compressor. This solution shows that in this cycle, for the present prices of the electric power and saturated steam, the electricity production is more profitable than the steam production, what makes the system prioritize the electric production without steam surpluses. The net profit found was US$ 0.01245 per compressed air kilogram. The steam-to-methane mol ratio optimal was 7.2. Table 1 presents the thermodynamic values for each point shown in Fig. 1. The chemical composition of the flows is presented in Table 2.
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Table 1 Operational parameters of the cycle Substance
T (K)
m (kg)
P (kPa)
1 (air) 2 (air) 3 (gases) 4 (gases) 5 (gases) 6 (gases) 7 (methane) 8 (methane) 9 (water) 10 (water) 11 (steam) 12 (steam) 13 (steam) 15 (synthesis gas)
298 689 1400 829 689 413 298 415 298 298 485 – 485 809
1 1 1.166 1.166 1.166 1.166 0.020 0.020 0.146 0.146 0.146 0 0.146 0.166
101.3 1500 1477 105.4 103.4 101.3 499.5 2138 199.6 2074 1972 – 1972 1950
The chemical and physical exergy in each main flow along the cycle are shown in Table 3. This system shows a high exergetic and energetic performance. Table 4 shows the exergetic performance and Table 5 shows the main equipment energetic performance. In the hand of the chemical reform, the largest irreversibility source is the group evaporator/ economizer. This is due to the high temperature difference between the hot gases and the steam. When compared to the evaporator/economizer, the reformer presents low irreversibility. This is due to the optimization of the reformer, where there are small temperature differences in the hot side. This conclusion agrees with these obtained by Harvey and Kane, [13], Kesser et al. [2] and Prieto et al. [6]. These results are lower than these of Kesser et al. [2], whose overall cycle performance was 47.6% against 46.5% here. This difference is due to the lower temperature at the turbine inlet assumed in this work. If the turbine has no blade cooling the temperature at the combustion chamber should be lower, that means higher irreversibility at combustion chamber.
Table 2 Molar fraction of the flows in the cycle Substance
Flow 3
Flow 14
Flow 15
CH4 CO2 CO O2 N2 H2 O H2
– 0.0286 – 0.1047 0.6095 0.2572 –
0.1357 – – – – 0.8643
0.0878 0.0356 0.0020 – – 0.7259 0.1486
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Table 3 Exergy along the cycle Flow
Eph (kJ)
Ech (kJ)
Ex (kJ)
1 2 3 4 5 6 7 8 9 10 11 13 15
0 383 1294 332 202 24 5 11 0 0 133 133 155
0 0 63 63 63 63 1056 1056 7 7 7 7 1155
0 383 1356 394 265 87 1061 1067 7 7 140 140 1310
Table 4 Equipment exergetic evaluation Equipment
e (%)
I (kW)
I (%)
Air compressor Combustion chamber Turbine Reformer Methane compressor Evaporator Water pump Stack Cycle
93.2 74.3 94.9 79.7 96.1 74.3 90.0 0 46.5
27.8 336.6 48.7 26.2 0.2 45.8 0.0 86.8 572.2
4.9 58.8 8.5 4.6 0.0 8.0 0.0 15.2 100
Table 5 Equipment energetic performance evaluation Equipment
g (%)
Air compressor Combustion chamber Turbine Methane compressor Water pump Cycle
85 100 90 94.6 90.0 46.8
6. Conclusions This work sought the optimization and exergetic analysis of a simplified gas turbine cycle with chemical recovery.
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The difference between the electric power and saturated steam prices make it more advantageous to produce and trade electric power, in total detriment of the saturated steam production. The development of devices should focus on the equipment that presents the largest exergetic losses, mainly the combustion chamber whose operation is linked to the physical limits of the turbine and reformer. A future suggestion is to improve the cycle system and study the thermoeconomics of this process. Another suggestion is to study sceneries in which the fuel and saturated steam prices are both varied in order to analyze the optimal behavior of this system. 7. Acknowledgments We thank FAPESP and CNPQ for the financial support without which this work would not have been accomplished. We thank Cristiano S. Pinto for the English revision. References [1] Briesch MS, Banister RL, Diakunchak IS, Huber D. A combined cycle designed to achieve greater than 60 percent efficiency. Journal of Engineering for Gas Turbine and Power 1995;117:734–41. [2] Kesser KF, Hoffman MA, Baughn JW. Analysis of a basic chemically recuperated gas turbine power plant. Journal of Engineering for Gas Turbines and Power 1994;116:227–84. [3] Souza-Santos K, Marcio L. A study of thermochemically recuperative power generation systems using natural gas. Fuel 1997;76(7):593–601. [4] Adelman ST, Hoffman MA, Baughn JW. A methane-steam reformer for a basic chemically recuperated gas turbine. Transactions of the ASME 1995;17:16–23. [5] Carcasci C, Facchini B, Harvey S. Design issues and performance of a chemically recuperated aeroderivative gas turbine. Proc Instn. Mech. Engrs 1998;212(A5):315–29. [6] Prieto MGS, Nebra SA, Gallo WLR. Exergetic Analysis of a Gas Turbine Plant with Chemical Recuperation. Proceeding of ENCIT—Eigth Brasilian Congress of Thermal Engineering and Sciences. 1998, p. 1–10. [7] Saravanamuttoo HIH, Rogers GFC, Cohen H. Gas Turbine Theory, fifth ed. Pearson Education—Prentice Hall; 2001. [8] Oertel M, Schmitz J, Weirich W, Jendryssek-Newmann D, Schulten R. Steam Reforming of Natural Gas with Integrated Hydrogen Separation for Hydrogen Production. Chemical Engineering and Technology 1987;10:248–55. [9] EIA—Energy Information Administration. electronic address: http://www.eia.doe.gov, July, 2003. [10] Guarinello Jr FF, et al. Thermoeconomic Evaluation of a Gas Turbine Cogeneration. System Energy Conversion & Management 2000;41:1191–200. [11] Szargut J, Morris DR, Steward FR. Exergy Analysis of Thermal, Chemical, and Metallurgical Processes. Hemisphere Publishing Corporation; 1998. [12] Kotas TJ. The Exergy Method of Thermal Plant Analysis. Tiptree, Essex., UK: Anchor Brandon LTD; 1985. [13] Harvey S, Kane ND. Analysis of a reheat gas turbine cycle with chemical recuperation using ASPEN. Energy Conversion & Management 1998;38(15-17):1671–9.
Basic chemically recuperated gas turbines—power plant optimization and thermodynamics second law analysis Lourenc¸o Gobira Alves , Silvia Azucena Nebra Energy Department of Mechanical Engineering Faculty, State University of Campinas, DE/FEM/UNICAMP, PO Box 6122, CEP 13083-970, Campinas, SP, Brazil
Abstract One of the proposals to increase the performance of the gas turbines is to improve chemical recuperated cycle. In this cycle, the heat in the turbine exhaust gases is used to heat and modify the chemical characteristics of the fuel. One mixture of natural gas and steam receives heat from the exhaust turbine gases; the mixture components react among themselves producing hot synthesis gas. In this work, an analysis and nonlinear optimization of the cycle were made in order to investigate the temperature and pressure influence on the global cycle performance. The chemical composition in the reformer was assumed according to chemical equilibrium equations, which presents good agreement with data from literature. The mixture of hot gases was treated like ideal gases. The maximum net profit was achieved and a thermodynamic second law analysis was made in order to detect the greatest sources of irreversibility. # 2004 Elsevier Ltd. All rights reserved. Keywords: Optimization; Exergy; Chemical recovery; Gas turbine; Power plant
1. Introduction The rational administration of energy resources with views to the improvement of productive processes is the key procedure to maintain competitiveness in global markets. The search for efficiency in the electric area goes not only through new methods and sources of electric production but also through improvements in the current processes. Gas turbines that operate in simple cycle present low efficiency because the turbine exhaust gases come out very hot and this heat is lost in the atmosphere. Better performances are reached with the advanced cycles [1], that take advantage of the energy contained in the turbine exhaust gases to improve the cycle or to transfer heat in combined cycles.
Corresponding author. Tel.: +55-19-37883285; fax: +55-19-32893722. E-mail address: [email protected] (L.G. Alves).
0360-5442/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2004.03.039
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Nomenclature Ca Cc Ce Cv Ech Eph Ex F I Kp N Ntot P P0 T T0 Wc We Wmc Wp Wt Wv ech eph ex h ma mc mv m s z g e DHr,c DHr,r
feeding water cost (US$/kg) acquisition price of the fuel (natural gas) (US$/kg) electric power price (US$/kWh) saturated steam price (US$/kg) chemical exergy (kJ) physical exergy (kJ) total exergy (kJ) exergetic equipment fuel (kJ) irreversibility (kJ) the chemical equilibrium constants molar quantity (kmol) the total moles number (kmol) exergetic equipment product (kJ) reference pressure (kPa) temperature (K) reference temperature (K) air compressor power required (kJ) electric power generated (kJ) methane compressor power required (kJ) water pump power required (kJ) turbine power (kJ) available electric power for sale (KWh) specific chemical exergy (kJ/kg) specific physical exergy (kJ/kg) specific total exergy (kJ/kg) enthalpy (kJ/kmol) feeding water mass (kg) fuel mass used (kg) steam mass available for sale (kg) mass flow (kg) entropy (kJ/kmol-K) optimization objective variable (US$) first law efficiency second law efficiency combustion reaction enthalpy (kJ) reform reaction enthalpy (kJ)
In gas turbines that work in cycle with chemical recovery, the mixture of natural gas (methane) and water absorbs heat contained in the exhaust gases. A reformer is used for this end. The
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mixture of natural gas and water enters on the cold side and it absorbs heat generating the synthesis gas to be burned in the combustion chamber. Cycles of chemical recovery were studied under several aspects. Kesser et al. [2] explored the relationships between the reformer and the turbine for two compressor pressure air ratios. Souza-Santos [3] studied variants of the cycle with chemical recovery taking into account the chemical composition of the natural gas. The physical and chemical aspects of the reformer can be seen in Adelman et al. [4] and Carcasci et al. [5]. Prieto et al. [6] made the Second-Law Analysis of the cycle determining its exergetic efficiency. This work analyzes the influence of methane and water injection in the reformer and the expansion of the turbine in the general performance of the cycle. The net operational profit of the cycle, understood as the difference between the sale of the products and the cost of the inputs all taken in relation to 1 kg of compressed air, was chosen as the optimization parameter.
2. Cycle model The cycle presented in this work is a simplification of the gas turbine cycle with chemical recovery. It is assumed that the gases are ideal gases, preserving the variation of the specific heat with the temperature. This hypothesis is fully acceptable for the pressure and temperature ranges of the cycle. Details of the cycle can be seen in Fig. 1. In order to make the case the most general possible, the air compressor flow was taken as reference. The ratio between the mass of methane and the mass of air can vary between 1:100 and 1:40, and the ratio between the mass of methane and the mass of water can vary between 1:3 and 1:7.5. These ratios were taken as the operational base of the turbine. It is not possible to operate economically below this level of methane, and superior levels would also make the temperature surpass 1400 K, the maximum temperature acceptable in the turbine inlet without blades cooling [7]. The amount of injected water also needs to be limited due to the physical parameters of the turbine. Conservative parameters were assumed in turbine and air compressor parameters because the fuel is a synthesis gas and not pure natural gas. The natural gas is composed of several substances, the main one being methane. For this reason, this gas will be adopted as the only component in place of the detailed composition of the natural gas. Besides that, the natural gas composition varies according to its source. In the same way, the composition of the dry air will be adopted as 21% oxygen and 79% nitrogen. After absorbing heat in the reformer, the methane reacts with the steam according to the equations: CH4 þ H2 O ! CO þ 3H2
(1)
CO þ H2 O ! CO2 þ H2
(2)
The reform reaction obeys the equations of chemical balance. The ratio between steam and methane must be high enough to prevent the formation of carbon deposits. In industrial reformers, this range is between 3 and 5. This proportion is used thoroughly for the production
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Fig. 1. Cycle schematic representation.
of hydrogen and for the synthesis of ammonia and methanol [5]. For this case, it is necessary that the catalyst is active at low temperatures, 800 K. The global reaction, written as function of the methane and the steam that enter as products, can be written as: a1 CH4 þ a2 H2 O ! b1 CH4 þ b2 CO þ b3 CO2 þ b4 H2 þ b5 H2 O;
(3)
where a1 and a2 are known amounts of the process feed. To obtain the composition of the gas mixture in the reformer exit, it is necessary to determine the five constants b1 to b5. The stoichiometric balance calculation yields to: a1 ¼ b1 þ b2 þ b3
(4)
4a1 þ 2a2 ¼ 4b1 þ 2b4 þ 2b5
(5)
a2 ¼ b2 þ 2b3 þ b5
(6)
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The other two equations are derived from the equilibrium constants Kp of the reactions 1 and 2. The constant Kp,1 can be written as [5]: Kp;1 ¼
PCO P3H
2
PCH4 PH2 O P20
¼
b2 b34 1 P2out;2 ; 2 b1 b5 Ntot P20
(7)
where Ntot is the total number of moles at equilibrium (b1 þb2 þb3 þb4 þb5 ) and P0 is the reference pressure, usually adopted as 1 atm. The value of Kp,1 is computed using the following correlation from Oertel et al. [8]: 27; 463 Kp;1 ¼ exp 30; 688 : (8) T The second constant Kp,2 can be written as [5]: Kp;2 ¼
PCO2 PH2 bb ¼ 3 4; PCO PH2 O b2 b5
(9)
and the value of Kp,2 at the temperature T is also computed in agreement with the equation [8]: 4084 3765 : (10) Kp;2 ¼ exp T All the thermodynamic properties were calculated based on the Janaf tables, and using the software EES1. The analysis of each element of the cycle supplies the equations that govern the system: Compressor: m1 ðh2 h1 Þ Wc ¼ 0
(11)
s1 ¼ s2;isso ;
(12)
where gc ¼
Wiso h2;iso h1 ¼ ¼ 0:85 Wc h2 h1
is the isentropic efficiency of the compressor, and Wc is the power required by the compressor. Turbine: m3 ðh3 h4 Þ Wc =gG We Wcm Wb ¼ 0
(13)
s3 ¼ s4;isso ;
(14)
where gt ¼
Wt h3 h4 ¼ ¼ 0:9 Wiso h3 h4;iso
is the isentropic efficiency of the turbine, gG ¼ 0:98 is the electric generator efficiency, We is the generated electric power, Wcm and Wb are the power consumed in methane compressor and water pump.
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Combustion chamber: m1 h2 þ m15 h15 m3 h3 þ DHr;c ¼ 0
(15)
m2 þ m15 m3 ¼ 0;
(16)
where DHr,c is the combustion reaction enthalpy. Reformer: m3 ðh4 h5 Þ þ m15 ðh15 h14 Þ þ DHr;r ¼ 0;
(17)
where DHr,r is the reform reaction enthalpy. m15 m8 m13 ¼ 0
(18)
m11 m12 m13 ¼ 0
(19)
Evaporator/economizer: m11 ðh11 h10 Þ ¼ m3 ðh5 h6 Þ
(20)
3. Optimization This cycle does not operate in industrial scale, so the equipment price was not estimated. The objective function will be the operational net profit, understood as the revenue of the electric power and saturated steam sale minus the cost of the inputs, feeding water and natural gas: z ¼ Ce Wv þ Cv mv Cc mc Ca ma
(21)
where Ce is electric power price (US$/kWh), Cv is saturated steam price (US$/kg), Cc is acquisition price of the fuel (natural gas) (US$/kg), Ca is feeding water cost (US$/kg), Wv ¼ We Wmc Wp : available electric power for sale (KWh), mc is fuel mass used (kg), mv is steam mass available for sale (kg/s), ma is feeding mass water (kg/s). The costs and prices were assumed according to: Electric energy price: Ce ¼ 102:4 US$=MWh [9]. Natural gas cost: Cc ¼ 0:08015 US$=kg [9]. Steam for sale price: Cv ¼ 0:009 US$=kg, Guarinello et al. [10]. Feeding water cost: Ca ¼ 0:00022 US$=kg, Guarinello et al. [10]. Restrictions of the system: v
T3 < 1400 K (1127 C): the turbine does not bear temperatures superior to that under the risk of thermal fatigue. P2 =P1 14:6: maximum air compressor operational compression ratio [7]. h4 ¼ h3 gt h3 h4;iso . The adiabatic expansion links the variation of the temperature to the pressure. This relationship supplies the smallest value possible for the temperature T4. The
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lower the temperature in the point 4, the higher the electric generation will be, on the other hand, the lower the capacity to generate steam will be. v T6 > 413 K (140 C). This value must be high enough to avoid gas condensation, which causes liquefaction of acid vapors in the stack walls. m12 0. This indicates that the system needs to provide at least the necessary steam to its own cycle. 650 K < T15 < 923 K. The reform temperature should be between these two limits. Below 650 K, the reform does not happen and above 923 K the chemical equilibrium equations are not valid. T 4 T 15 ¼ 20. Imposed condition of the heat transfer in the reformer (pinch point). 0:14 m15 0:25. Turbine operational conditions that regulate the flow and the excess of air. 0:13 m13 0:18. Turbine operational conditions. The optimization was made entirely in EES1 software. 4. Exergetic analysis The importance of the exergetic analysis is to diagnose how much of the theoretical maximum work the system is able to perform. The method of exergetic analysis used consists of evaluating each bearer of energy along the system identifying its chemical composition, physical state and flow rate. In order to analyze the cycle, the system was divided in seven control volumes so that it was possible to identify the performance of each one of those volumes. The following considerations were assumed. v Although the turbine performance is measured at 15 C, standard atmosphere for the calcuv lation of the physical exergies was assumed as T0 ¼ 25 C, P0 ¼ 101:3 kPa and relative humidity of the air 70%, according to standard temperature and pressure used in Szargut tables [11]. Efficiencies determination of each control volume, in agreement with the fuel, product and losses Kotas et al. [12] concept. Calculation of the physical exergy (eph), chemical (ech), and total exergy (ex), according to Szargut et al. [11] formulations: eph ¼ ðh h0 Þ T0 ðs s0 Þ
(22)
ex ¼ eph þ ech
(23)
where the component of the ech refers to the tables reported by Szargut et al. [11]. The gas mixtures from the reformer exit were admitted as mixtures of ideal gases. The gas compositions along the cycle were taken based on the mass balances and considering complete combustion in the combustion chamber. The exergetic efficiency, e, and the irreversibility values, I; in each component will be calculated according to the following: P F I ¼PF e¼
where P is the product and F is the thermodynamic fuel considered in each control volume.
(24) (25)
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The previous considerations lead to: Air compressor: F ¼ Wc
(26)
P ¼ Ex2 Ex1
(27)
Combustion chamber: F ¼ Ex15
(28)
P ¼ Ex3 Ex2
(29)
Turbine: P ¼ Wt
(30)
F ¼ Ex3 Ex4
(31)
Reformer: P ¼ Ex15 Ex8 Ex13
(32)
F ¼ Ex4 Ex5
(33)
Methane compressor: P ¼ Ex8 Ex7
(34)
F ¼ Wmc
(35)
Evaporator/economizer: P ¼ Ex11 Ex10
(36)
F ¼ Ex5 Ex6
(37)
Water pump: P ¼ Ex10 Ex9
(38)
F ¼ Wp
(39)
5. Results and discussions The optimal solution showed that the largest operational net profit is obtained with the largest possible temperature in the turbine inlet associated with the largest ratio compression (14.8) in the air compressor. This solution shows that in this cycle, for the present prices of the electric power and saturated steam, the electricity production is more profitable than the steam production, what makes the system prioritize the electric production without steam surpluses. The net profit found was US$ 0.01245 per compressed air kilogram. The steam-to-methane mol ratio optimal was 7.2. Table 1 presents the thermodynamic values for each point shown in Fig. 1. The chemical composition of the flows is presented in Table 2.
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Table 1 Operational parameters of the cycle Substance
T (K)
m (kg)
P (kPa)
1 (air) 2 (air) 3 (gases) 4 (gases) 5 (gases) 6 (gases) 7 (methane) 8 (methane) 9 (water) 10 (water) 11 (steam) 12 (steam) 13 (steam) 15 (synthesis gas)
298 689 1400 829 689 413 298 415 298 298 485 – 485 809
1 1 1.166 1.166 1.166 1.166 0.020 0.020 0.146 0.146 0.146 0 0.146 0.166
101.3 1500 1477 105.4 103.4 101.3 499.5 2138 199.6 2074 1972 – 1972 1950
The chemical and physical exergy in each main flow along the cycle are shown in Table 3. This system shows a high exergetic and energetic performance. Table 4 shows the exergetic performance and Table 5 shows the main equipment energetic performance. In the hand of the chemical reform, the largest irreversibility source is the group evaporator/ economizer. This is due to the high temperature difference between the hot gases and the steam. When compared to the evaporator/economizer, the reformer presents low irreversibility. This is due to the optimization of the reformer, where there are small temperature differences in the hot side. This conclusion agrees with these obtained by Harvey and Kane, [13], Kesser et al. [2] and Prieto et al. [6]. These results are lower than these of Kesser et al. [2], whose overall cycle performance was 47.6% against 46.5% here. This difference is due to the lower temperature at the turbine inlet assumed in this work. If the turbine has no blade cooling the temperature at the combustion chamber should be lower, that means higher irreversibility at combustion chamber.
Table 2 Molar fraction of the flows in the cycle Substance
Flow 3
Flow 14
Flow 15
CH4 CO2 CO O2 N2 H2 O H2
– 0.0286 – 0.1047 0.6095 0.2572 –
0.1357 – – – – 0.8643
0.0878 0.0356 0.0020 – – 0.7259 0.1486
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Table 3 Exergy along the cycle Flow
Eph (kJ)
Ech (kJ)
Ex (kJ)
1 2 3 4 5 6 7 8 9 10 11 13 15
0 383 1294 332 202 24 5 11 0 0 133 133 155
0 0 63 63 63 63 1056 1056 7 7 7 7 1155
0 383 1356 394 265 87 1061 1067 7 7 140 140 1310
Table 4 Equipment exergetic evaluation Equipment
e (%)
I (kW)
I (%)
Air compressor Combustion chamber Turbine Reformer Methane compressor Evaporator Water pump Stack Cycle
93.2 74.3 94.9 79.7 96.1 74.3 90.0 0 46.5
27.8 336.6 48.7 26.2 0.2 45.8 0.0 86.8 572.2
4.9 58.8 8.5 4.6 0.0 8.0 0.0 15.2 100
Table 5 Equipment energetic performance evaluation Equipment
g (%)
Air compressor Combustion chamber Turbine Methane compressor Water pump Cycle
85 100 90 94.6 90.0 46.8
6. Conclusions This work sought the optimization and exergetic analysis of a simplified gas turbine cycle with chemical recovery.
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The difference between the electric power and saturated steam prices make it more advantageous to produce and trade electric power, in total detriment of the saturated steam production. The development of devices should focus on the equipment that presents the largest exergetic losses, mainly the combustion chamber whose operation is linked to the physical limits of the turbine and reformer. A future suggestion is to improve the cycle system and study the thermoeconomics of this process. Another suggestion is to study sceneries in which the fuel and saturated steam prices are both varied in order to analyze the optimal behavior of this system. 7. Acknowledgments We thank FAPESP and CNPQ for the financial support without which this work would not have been accomplished. We thank Cristiano S. Pinto for the English revision. References [1] Briesch MS, Banister RL, Diakunchak IS, Huber D. A combined cycle designed to achieve greater than 60 percent efficiency. Journal of Engineering for Gas Turbine and Power 1995;117:734–41. [2] Kesser KF, Hoffman MA, Baughn JW. Analysis of a basic chemically recuperated gas turbine power plant. Journal of Engineering for Gas Turbines and Power 1994;116:227–84. [3] Souza-Santos K, Marcio L. A study of thermochemically recuperative power generation systems using natural gas. Fuel 1997;76(7):593–601. [4] Adelman ST, Hoffman MA, Baughn JW. A methane-steam reformer for a basic chemically recuperated gas turbine. Transactions of the ASME 1995;17:16–23. [5] Carcasci C, Facchini B, Harvey S. Design issues and performance of a chemically recuperated aeroderivative gas turbine. Proc Instn. Mech. Engrs 1998;212(A5):315–29. [6] Prieto MGS, Nebra SA, Gallo WLR. Exergetic Analysis of a Gas Turbine Plant with Chemical Recuperation. Proceeding of ENCIT—Eigth Brasilian Congress of Thermal Engineering and Sciences. 1998, p. 1–10. [7] Saravanamuttoo HIH, Rogers GFC, Cohen H. Gas Turbine Theory, fifth ed. Pearson Education—Prentice Hall; 2001. [8] Oertel M, Schmitz J, Weirich W, Jendryssek-Newmann D, Schulten R. Steam Reforming of Natural Gas with Integrated Hydrogen Separation for Hydrogen Production. Chemical Engineering and Technology 1987;10:248–55. [9] EIA—Energy Information Administration. electronic address: http://www.eia.doe.gov, July, 2003. [10] Guarinello Jr FF, et al. Thermoeconomic Evaluation of a Gas Turbine Cogeneration. System Energy Conversion & Management 2000;41:1191–200. [11] Szargut J, Morris DR, Steward FR. Exergy Analysis of Thermal, Chemical, and Metallurgical Processes. Hemisphere Publishing Corporation; 1998. [12] Kotas TJ. The Exergy Method of Thermal Plant Analysis. Tiptree, Essex., UK: Anchor Brandon LTD; 1985. [13] Harvey S, Kane ND. Analysis of a reheat gas turbine cycle with chemical recuperation using ASPEN. Energy Conversion & Management 1998;38(15-17):1671–9.