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Optimum design of dual pressure heat recovery steam generator using non-dimensional parameters based on thermodynamic and thermoeconomic approaches
Applied Thermal Engineering 52 (2013) 371e384
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Optimum design of dual pressure heat recovery steam generator using non-dimensional parameters based on thermodynamic and thermoeconomic approaches Sanaz Naemi a, Majid Saffar-Avval a, *, Sahand Behboodi Kalhori b, Zohreh Mansoori c a b c
Mechanical Engineering Department, Amirkabir University of Technology, Hafez Ave., P.O. Box 15875-4413, Tehran, Iran Lab. for Alternative Energy Conversion, Mechatronic Systems Engineering, School of Engineering Science, Simon Faser University, Canada Energy research center, Amirkabir University of Technology, Iran
h i g h l i g h t s < Presenting thermodynamic and thermoeconomic optimization of a heat recovery steam generator. < Defining an objective function consists of exergy waste and exergy destruction. < Defining an objective function including capital cost and cost of irreversibilities. < Obtaining the optimized operating parameters of a dual pressure heat recovery boiler. < Computing the optimum pinch point using non-dimensional operating parameters.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 May 2012 Accepted 6 December 2012 Available online 21 December 2012
The thermodynamic and thermoeconomic analyses are investigated to achieve the optimum operating parameters of a dual pressure heat recovery steam generator (HRSG), coupled with a heavy duty gas turbine. In this regard, the thermodynamic objective function including the exergy waste and the exergy destruction, is defined in such a way to find the optimum pinch point, and consequently to minimize the objective function by using non-dimensional operating parameters. The results indicated that, the optimum pinch point from thermodynamic viewpoint is 2.5 C and 2.1 C for HRSGs with live steam at 75 bar and 90 bar respectively. Since thermodynamic analysis is not able to consider economic factors, another objective function including annualized installation cost and annual cost of irreversibilities is proposed. To find the irreversibility cost, electricity price and also fuel price are considered independently. The optimum pinch point from thermoeconomic viewpoint on basis of electricity price is 20.6 C (75 bar) and 19.2 C (90 bar), whereas according to the fuel price it is 25.4 C and 23.7 C. Finally, an extensive sensitivity analysis is performed to compare optimum pinch point for different electricity and fuel prices. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Heat recovery steam generator Exergy analysis Optimum pinch point temperature Thermoeconomic analysis
1. Introduction Due to global energy crisis, an increasingly attitude to efficient energy conversion technologies especially Combined Cycle Power Plants (CCPPs) have seen in recent decades, in which gas turbine operating in open cycle is integrated with a steam cycle by means of a Heat Recovery Steam Generator (HRSG). Hereupon, HRSG provides the critical connection between the gas turbine topping cycle and * Corresponding author. Tel.: þ98 21 66405844; þ98 21 66419736. E-mail addresses: [email protected] (S. Naemi), [email protected] (M. SaffarAvval), [email protected] (S. Behboodi Kalhori), [email protected] (Z. Mansoori). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.12.004
the steam turbine bottoming cycle. Undoubtedly, the optimum design of HRSG has a particular interest to improve the performance of heat recovery for maximizing the power generated by steam cycle. Besides, it reduces the environmental impacts of pollutant emissions. In the design of HRSGs, the method to obtain the optimum design usually is a combination of the thermodynamic and economic point of views. The exergy method, which uses the conservation of mass and energy principles together with the second law of the thermodynamics, is a useful tool to identify the locations, types and magnitudes of losses. In the past decade, coupled energy and exergy analyses of different thermal systems have been carried out. Dincer and Rosen
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Nomenclature A Af At Ai Ao Aw B b cI cp Cost CostE,j CostE,m CostE,w CostS,b CostS,m c1 c1 c001 c2 c2 d di f ffi ffo fEC fth G h hc hi ho hN km L LEC,w LMTD _ m ME ME,j MS Nb Nd Nw n NTU P0 Q
heat transfer area (m2) fin surface areas (m2/m) total surface area (m2/m) inside surface area (m2/m) obstruction surface area (m2/m) area of tube wall (m2/m) factor used in Grinson’s correlation fin thickness (m) specific cost of exergy loss (US $/kWh) specific heat (kJ kg1 k1) cost of each heat transfer section (US $) cost of economizer joints (US $/kg) cost of tubes and fins (economizer) (US $/kg) cost of welding (economizer) (US $/kg) cost of bending (superheater) (US $/kg) cost of tubes and fins (superheater) (US $/kg) specific heat of water in low pressure economizer (kJ kg1 K1) specific heat of water in high pressure economizer1 (kJ kg1 K1) specific heat of water in high pressure economizer2 (kJ kg1 K1) specific heat of steam in low pressure superheater (kJ kg1 K1) specific heat of steam in high pressure superheater (kJ kg1 K1) tube outer diameter (m) tube inner diameter (m) friction factor inside fouling factors (m2 s K kJ1) outside fouling factors (m2 s K kJ1) thermoeconomic objective function thermodynamic objective function gas mass velocity (kg m2 s1) fin height (m) convection heat transfer coefficient (W m2 K1) inside heat transfer coefficient of tubes (W m2 K1) outside heat transfer coefficient of tubes (W m2 K1) nonluminous heat transfer coefficient (W m2 K1) metal thermal conductivity (W m K1) latent heat of vaporization (kJ/kg) length of welding (m) logarithmic mean temperature difference (for evaporator) (K) mass flow rate (kg s1) mass of tube and fins (economizer) (kg) joint mass for economizer (kg) mass of tube and fins (superheater) (kg) number of bending in superheater number of tubes per row number of tube rows number of fins per meter number of transfer units ambient pressure (kPa) heat transferred (kW)
[1] reviewed application of exergy approach, to analyze and design a wide range of energy conversion systems. Shi and Che [2] conducted energy and exergy analyses of an improved liquefied natural gas fuelled CCPP with a waste heat recovery, considering mass, energy and exergy balances for each component. Cihan et al. [3]
SL ST St S_ gen Tg T0 Tout Tsat1 Tsat2 Tsup1 Tsup2 Tw 0 Tw;in Uo V V* X1 X1ʹ X1ʺ X2 X2ʹ
longitudinal pitch (m) transferred pitch (m) Stanton number rate of entropy generation (kW/K) temperature of flue gas at the considered location (K) ambient temperature (K) flue gas temperature at the economiser outlet (K) saturation temperature of water or steam (low pressure boiler) (K) saturation temperature of water or steam (high pressure boiler) (K) temperature of superheated steam (low pressure superheater) (K) temperature of superheated steam (high pressure superheater) (K) temperature of water at the considered location (K) temperature of water at the entrance of high pressure economizer2 (K) overall heat transfer coefficient (W m2 K1) flue gas velocity (m/s) non-dimensional gas velocity ratio of heat capacities of water and gas stream (LE) ratio of heat capacities of water and gas stream (HE2) ratio of heat capacities of water and gas stream (HE1) ratio of heat capacities of steam and gas stream (LS) ratio of heat capacities of steam and gas stream (HS)
Greek symbols DPg pressure drop (kPa) h fins efficiency s non-dimensional hot flue gas inlet temperature difference ratio ss1 non-dimensional water saturation temperature (LP drum) difference ratio ss2 non-dimensional water saturation temperature (HP drum) difference ratio sh1 non-dimensional HP superheated steam temperature difference ratio sh2 non-dimensional LP superheated steam temperature difference ratio Subscripts g gas HB high pressure boiler (evaporator) HE1 high pressure economizer1 HE2 high pressure economizer2 HS high pressure superheater HRSG heat recovery steam generator I irreversibility in inflow LB low pressure evaporator LE low pressure economizer LS low pressure superheat out outflow w water water in low pressure economizer w1 water in high pressure economizer w2
preformed energy and exergy analyses of a CCPP investigating the potential for improving system efficiency. They indicated that, while the greatest energy loss takes place at the stack, the greatest exergy loss takes place in the combustion chamber of gas turbine and HRSG.
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Many researchers have recommended that costs are better distributed among the outputs, if cost accounting is based on the exergy quantity. Ahmadi et al. [4] optimized a CCPP based on exergy, exergoeconomic and environmental impact point of the views; they investigated the influence of supplementary firing on the performance of bottoming cycle and CO2 emissions. Then, they carried out a multiobjective optimization to determine the best design parameters, maximizing the exergy efficiency using a genetic algorithm. Additionally, Ahmadi and Dincer [5] introduced an objective function in terms of dollar per second, including the sum of the operating and maintenance, and capital investment costs. They obtained the optimum key variables by minimizing the objective function using a generic algorithm. They summarized that, by increasing the fuel price, the optimized decision variables in the thermoeconomic design tend to those of the thermodynamic optimum design. Valdes et al. [6] presented a methodology to identify the most relevant design parameters that impact on the thermal efficiency and the economic results of CCPP focusing on the HRSG design. They proposed two different thermoeconomic models aimed to determine whether an increase in the investment is worthy from the economic viewpoint. There are many researches done regarding HRSG systems for minimizing the losses. Nag and De [7] employed thermodynamic analysis to optimize the design and operation of a waste heat recovery boiler without superheater. Authors introduced entropy generation number function of design and operating parameters, and estimated the effect of these parameters on the operation during generation of saturated steam for a steam power cycle. They concluded that, there is an optimum evaporation temperature for minimizing irreversibilities of an HRSG. Moreover, operating the HRSG at full load reduces entropy generation, and also increases the number of transfer units of evaporator and economizer beyond certain cut-off values will have marginal benefit with respect to entropy generation. In and Lee [8] optimized design parameters of HRSGs by minimizing the sum of the destroyed and the lost exergies. They chose a single pressure HRSG system and obtained the optimum evaporation temperature corresponding to maximum useful work for the given condition of inlet water and gas temperatures; Also it is shown the dependency of number of transfer unit (NTU) on the saturation temperature, which is another important factor for determining the optimum conditions, when the construction cost is taken into account besides the operating cost. Butcher and Reddy [9] investigated the impact of different operating conditions such as gas composition, specific heat, pinch point, and gas inlet temperature on the performance of an HRSG. They indicated that, the energetic and exergetic efficiencies of the power plant deeply depend on the exhaust gas composition, specific heat and pinch point. Reddy et al. [10] studied the effects of various non-dimensional operating parameters on the entropy generation number for a single pressure HRSG. They claimed that, the entropy generation number increases with increase in non-dimensional hot flue gas inlet temperature difference ratio. They showed that, the temperature difference between hot gases and water has dominating effect on the entropy generation rate, whereas heat loss to the surroundings, ambient temperature and frictional pressure drop in the unit are not considered as the temperature difference. Guo et al. [11] analyzed waste heat power generation system on the basis of the first law, second law efficiencies and entropy generation. They tried to highlight how some operating parameters, such as the turbine exergy efficiency and pump performance could affect the unit’s performance; however, they did not consider the exergy waste to atmosphere. They concluded that, the optimal
373
operation condition should be achieved at the trade-off between the heat/exergy input and the heatework conversion ability of the unit. Casarosa and Franco [12] investigated different configurations of HRSG systems to minimize exergy losses, taking into account only the irreversibility due to the temperature difference between the hot and cold streams (pressure drop not accounting). Authors optimized the operating parameters for the HRSG on the basis of thermodynamic analysis. All the solutions lead to the zero pinch point and infinite heat transfer surface. They also developed thermoeconomic optimization; depending on the HRSG operating costs, evidently, the pinch point temperature difference in this case is obtained the values different from zero. Franco and Giannini [13] outlined a method to achieve optimum design of convective HRSGs for combined cycles. They obtained the main operating parameters of the HRSG and a detailed design of the components concerning the geometric variables of the heat transfer sections, in order to minimize the pressure drop of the elements of the HRSG. Franco and Russo [14] preformed the thermodynamic and thermoeconomic optimizations; the purpose of thermodynamic optimization was to diminish energy losses, expressed on exergy basis, while the aim of the thermoeconomic optimization was to minimize a cost function; sum of the cost of exergy inefficiencies and the cost of HRSG. In their method, the cost of every section is considered proportional to the heat transfer area, and exergy losses are computed as the selling price of the desired plant output, i.e., the electrical energy is estimated about three times of the cost of fuel per unit of energy. Similarly, Casarosa et al. [15] developed another HRSG design optimization methodology to meet both thermodynamic and economic objectives simultaneously. Hajabdollahi et al. [16] modeled an HRSG with a typical geometry and a number of pressure levels used at CCPPs, and developed a thermodynamic model and thermoeconomic optimization. They conducted exergoeconomic analysis and multi-optimization of an HRSG through energy and exergy, and compared their results with data provided from a power plant situated near the Caspian Sea in Iran. They introduced a new objective function (the total cost per unit of steam produced exergy). Then, optimum design parameters are selected when objective function is minimized while HRSG exergy efficiency is maximized. Authors summarized that an increase in high and low pressure drums increases exergy efficiency, while an increase in pinch point decreases exergy efficiency. Additionally, an increase in the HRSG inlet gas enthalpy results in an increase of the exergy efficiency. In the present work, as the first step, the thermodynamic model of a dual pressure HRSG coupled with a heavy duty gas turbine [17] was developed, and exergy waste and exergy destruction were computed for different pinch points of four pressure levels. In the second step, a thermodynamic objective function was proposed to minimize the exergy losses of dual pressure HRSGs to obtain the optimum design. In this regards, the effects of non-dimensional parameters on the HRSG performance were discussed. As expected, an increase in the efficiency of an HRSG can be achieved by reducing exergy losses through the heat recovery process. In the next step, optimum design of HRSG regarding financial considerations was investigated. A proper trade-off between the efficiency and the capital cost of equipment requires that some additional losses of exergy must be tolerated in order to reduce the capital cost. Therefore, the cost of exergy losses recast to operating cost of HRSG, and combined with the HRSG installation costs. To convert the exergy losses into cost, two strategies were employed; one based on electricity tariff, another based on fuel price. Finally, a sensitivity analysis was carried out to see how electricity tariff and fuel price affect on the optimum value of pinch point.
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2. Thermodynamic simulation
_ g cpg Tg;in Tg;out Q ¼ m
(1)
_ w cpw Tw;out Tw;in Q ¼ m
(2)
Fig. 1 reveals the schematic diagram of a dual pressure HRSG which will be simulated to find the optimum design. According to Fig. 1, gas turbine exhaust gases meet high pressure superheater (HS), high pressure boiler (HB), high pressure economizer2 (HE2), low pressure superheater (LS), high pressure economizer1 (HE1), low pressure boiler (LB) and low pressure economizer (LE) through the HRSG from left to right (hot side to cold side). Important operating parameters of HRSG are pinch point, approach point and gas side pressure drop through the HRSG. Fig. 2 describes the sketch of temperature profile for a dual pressure HRSG. As can be clearly seen, pinch point is the difference between the gas temperature leaving the evaporator and the saturation temperature corresponding to the steam pressure at drum, and approach temperature is the difference between the saturation temperature and temperature of drum inlet water. Karthikeyan et al. [18] investigated the performance simulation of an HRSG to see how pinch point and approach point affect the mass of steam generation and also temperature profiles across the HRSG. They concluded that, low pinch point increases steam production rate. On the other hand, although pinch point reduction leads to improvement of HRSG’s first law efficiency, it increases evaporating area causing greater expense for the heat transfer material.
Detailed formulations used to compute each resistance can be found in Appendix A and [19]. The characteristics of exhaust gases and physical properties of HRSG tubes and fins are given in the beginning of Results and discussion section.
2.1. Energy balance
2.2. Gas side pressure drop
The first step to simulate the HRSG is to balance the mass and energy on different heat transfer sections. In this study, the logarithmic means temperature difference (LMTD) method is used to size the heat transfer area. Additionally, some of the main assumptions to derive the mathematical modeling are listed below:
Undoubtedly, when the flue gas is passing through the HRSG, the pressure inevitably drops; therefore, exhaust gas should leave the turbine with a pressure more than the ambient to compensate this drop, this reduces the electricity generation; hence, the reduction of the gas side pressure drop is essential and plays important role as designing and operating parameters of HRSGs. Eq. (6) is used to estimate the pressure drop of each heat transfer section [19].
The system is assumed to be steady state. The exhaust gas mass flow rate, temperature and chemical composition are known. The staggered pitch tubes with solid fins are considered. The natural circulation is assumed for evaporator. The pressure drop of the flue gas across the HRSG is taken into account, whereas the pressure drop in water side is negligible. There is no external heat loss except the outflow of the exhaust gas which enters the stack. Energy balance in all heat transfer surfaces between the hot and cold streams (gas side and water/steam side) can be expressed as Eqs. (1) and (2):
The designing method is based on logarithmic means temperature difference, therefore the heat transfer areas are obtained by Eq. (3):
Q ¼ Uo A LMTD
(3)
where Uo is total heat transfer coefficient and LMTD is logarithmic mean temperature difference as Eqs. (4) and (5):
1 At At At d d 1 ¼ þ f fi þ f fo þ ln þ hi Ai Ai Aw 24km Uo di hho LMTD ¼
DPg ¼
Tg;in Tw;out Tg;out Tw;in " # Tg;in Tw;out ln Tg;out Tw;in
fg þ a G2 NL 500rg
(4)
(5)
(6)
Calculations of fg and a are reported in Ref. [19]. 3. Thermodynamic optimization Minimization of exergy losses ensures that the HRSG will operate efficiently. The exergy losses of HRSG were chosen as the objective function, that can successfully measure both the quality
Fig. 1. Schematic diagram of a dual pressure HRSG.
S. Naemi et al. / Applied Thermal Engineering 52 (2013) 371e384
375
Fig. 2. Gas and steam temperature profile of dual pressure HRSG.
and quantity of energy flow in the HRSG. Although this approach is not acceptable financially, it proposes a rough design criterion to define operating parameters of the HRSG. Exergy losses consist of two terms: exergy destruction and exergy out flow waste. First term is due to the irreversibility of the heat transfer process and pressure drops which leads to destruction of a substantial proportion of the input exergy through the HRSG. Second term is because of the hot gas outflow leaving the stack which is referred as exergy waste. Exergy destruction is expressed as Eq. (7):
E_ Destruction ¼ T0 S_ LEC þ S_ LB þ S_ LS þ S_ HE1 þ S_ HE2 þ S_ HB þ S_ HS
_ g cpg ln E_ waste ¼ T0 m
fth ¼
Hence, the total exergy destruction rate can be expressed as Eq. (9):
2 6_ E_ destruction ¼ T0 S_ gen;destruction ¼ T0 4m w c1 ln
Tsat1 Tw;in
! þ
_ w1 L1 m Tsat1
00 1 Tsup1 T _ w2 c001 ln @ w;in A _ w1 c2 ln þm þm Tsat1 Tsat1 0 1 _ L Tsup2 m BT C _ w2 _ w2 þm c1 ln @ 0 sat2 A þ w2 2 þ m c2 ln Tsat2 Tsat2 T w;in 3 ! Tg;out P0 þ DP 7 _ g cpg ln _ g Rln þm þm (9) 5 P0 Tg;in
Additionally, the exergy waste due to the external irreversibility can be obtained by Eq. (10) [8]:
! _ w1 L1 m Tsat1 þ _ g cpg Tsat1 m Tw;in 00 1 _ w2 c001 _ w1 c2 Tsup1 T w;in m m A þ þ ln ln @ _ g cpg _ g cpg m m Tsat1 Tsat1 0 1 _ w2 _ w2 L2 _ w2 Tsup2 m c1 B Tsat2 C m m c2 ln @ 0 þ ln þ þ A _ g cpg _ g cpg Tsat2 m _ g cpg m m Tsat2 T w;in Tg;out T0 T R P0 þ DP þ þ ln 0 þ ln (11) Tg;in cpg T0 P0
_ w c1 m E_ destruction þ E_ waste ¼ ln _ g cpg T0 _ g cpg m m
(7)
(8)
(10)
Accordingly, the thermodynamic objective function (fth) of HRSG can be formulated as Eq. (11):
where entropy generation in a counter flow heat exchanger is calculated by Eq. (8) [20]:
T T P _ p 1 ln 1;out þ mc _ p 2 ln 2;out ðmRÞ _ 1 ln 1;out S_ gen ¼ mc T1 T2 P1 P2;out _ 2 ln ðmRÞ P2
T0 _ g cpg Tg;out T0 þm Tg;out
The fth depends on different variables; thus, non-dimensional parameters are defined to study the impact of these variables on the fth. Those non-dimensional parameters are: nondimensional hot flue gas inlet temperature difference ratio (s), non-dimensional water saturation temperature difference ratio (sS), non-dimensional superheated steam temperature difference ratio (sh), ratio of heat capacities of water and gas stream (X1), ratio of heat capacities of steam and gas steam (X2), NTUHS, NTUHB, NTUHE1, NTUHE2, NTULE, NTULB, NTULS and nondimensional gas velocity (V*), which are defined by Eqs. (12)e (24).
s¼
Tg;in T0 T0
(12)
ss1 ¼
Tsat1 Tw;in Tw;in
(13)
ss2 ¼
Tsat2 Tw;in Tw;in
(14)
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sh1 ¼
Tsup1 Tw;in Tw;in
(15)
sh2 ¼
Tsup2 Tw;in Tw;in
(16)
where s is non-dimensional hot flue gas inlet temperature difference ratio and ss is non-dimensional water saturation temperature difference ratio.
_ w c1 m _ g cpg m
(17)
X1 ¼
_ w2 m c1 _ g cpg m
(18)
X100 ¼
_ w2 c001 m _ g cpg m
(19)
X1 ¼ 0
T1 ¼
V V * ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 St U0 P0 cpg f h0 r R
(23)
NTU ¼ NTUHS þ NTUHB þ NTUHE1 þ NTUHE2 þ NTULS þ NTULB þ NTULE
(24)
By considering a small element length dx for each heat transfer surface, and by making energy balance for the element and integrating between the limits (inlet and outlet flue gas temperature in each heat transfer surface), and by further simplification, the temperature of the flue gas at the exit of each heat transfer section can be expressed in term of other operating parameters as Eqs. (25)e(30). Gas temperature at entrance of high pressure (boiler) evaporator:
0 0 0 X2 exp NTUHS 1 þ X 2 T0 ðs þ 1Þ Tw;in ðsh2 þ 1Þ X 2 Tw;in ðsh2 þ 1Þ T0 ðs þ 1Þ (25)
0
X2 1
Gas temperature at entrance of high pressure economizer2:
_ c m X2 ¼ w1 2 _ g cpg m
(20)
_ w2 m c2 _ g cpg m
(21)
0
X2 ¼
where X1 is ratio of heat capacities of water and gas stream and X2 is ratio of heat capacities of steam and gas steam. NTUHS, NTUHB, NTUHE1, NTUHE2, NTULE, NTULB, NTULS and non-dimensional gas velocity:
R ln Cpg
1þ
DPg
P0
¼
R DPg ¼ ðNTUÞV * Cpg P0
(22)
T2 ¼exp ðNTUHBÞ
0 8 0
0 8 0
T0 ðs þ 1Þ Tw;in ðsh2 þ 1Þ X exp ðNTUHBÞexp NTUHS 1 X < 2 2 0 0 0 0 1 T3 ¼ X1 exp NTUHE2 1 X1 : X1 1 X2 1 0
9 exp ðNTUHBÞ X 2 Tw;in ðsh2 þ 1Þ T0 ðs þ 1Þ Tw;in ðss2 þ 1Þ½1 exp ðNTUHBÞ= 0 0 0 þ þ ; X1 1 X2 1 X1 1
0 0 0 Tw;in ðss2 þ 1Þ X 1 X 1 exp NTUHE2 1 X 1 0 þ X1 1
(27)
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377
Gas temperature at entrance of high pressure economizer2:
8 < T4 ¼ ½X2 exp ðNTULS2ð1 X2 ÞÞ 1 T ðs þ 1Þ Tw;in ðsh2 þ 1Þ : 0 0
0 0 0 X 1 exp NTUHE2 1 X 1 1 X 2 exp ðNTUHBÞexp NTUHS 1 X 2 0 0 X1 1 X 2 1 ðX2 1Þ
0
0
0 0 0 1 X 2 Tw;in ðsh2 þ 1Þ T0 ðs þ 1Þ X 1 exp NTUHE2 1 X 1 1 exp ðNTUHBÞ X 1 exp NTUHE2 1 X 1 0 0 0 þ þ X 1 1 ðX2 1Þ X1 1 X 2 1 ðX2 1Þ
0 0 0 9 Tw;in ðss2 þ 1Þ X 1 X 1 exp NTUHE2 1 X 1 = 0 Tw;in ðss2 þ 1Þ ½1 exp ðNTUHBÞ þ ; X 1 1 ðX2 1Þ þ Tw;in ðsh1 þ 1Þ
X2 X2 exp ½NTULSð1 X2 Þ ðX2 1Þ (28)
Gas temperature at entrance of low pressure boiler (evaporate):
0
0 0 80 X 1 X exp ðNTUHBÞ exp NTUHS 1 X exp NTUHS 1 X < 2 2 1 1 0 0 T5 ¼ X100 exp NTULS 1 X100 1 00 : X1 1 X 2 1 ðX2 1Þ X1 1 ½X2 exp ðNTULSð1 X2 ÞÞ 1 T0 ðs þ 1Þ Tw;in ðsh2 þ 1Þ
0 0
0 1 X 2 Tw;in ðsh2 þ 1Þ T0 ðs þ 1Þ exp ðNTUHBÞ X 1 exp NTUHE2 1 X 1 0 0 þ ½X2 exp ðNTULSð1 X2 ÞÞ 1 X1 1 X 2 1 ðX2 1Þ X100 1
0 0 1 ½X2 exp ðNTULSð1 X2 ÞÞ 1 X 1 exp NTUHE 1 X 1 0 Tw;in ðs þ 1Þ½1 exp ðNTUHBÞ þ X 1 1 ðX2 1Þ X100 1
0 0 ½X2 exp ðNTULSð1 X2 ÞÞ 1 X 1 exp NTUHE2 1 X 1 1 0 þ Tw;in ðss2 þ 1Þ X 1 1 ðX2 1Þ X100 1 0 X 00 X200 exp NTUHE1 1 X100 ½X X2 exp ðNTULSð1 X2 ÞÞ 00 00 þ Tw;in ðsh1 þ 1Þ 2 þ T w;in 1 X1 1 ðX2 1Þ X1 1
Gas temperature at entrance of low pressure economizer:
T6 ¼ T5 exp ðNTULBÞ þ Tw;in ðss1 þ 1Þ½1 exp ðNTULBÞ
(30)
The energy balance across the low pressure evaporator can be written as Eq. (31):
_ w1 L1 ¼ m _ g cpg ðT5 T6 Þ m
(31)
(29)
Therefore, the latent heat of vaporization (L1), can be expressed as Eq. (32):
L1 ¼
C2 ½1 exp ðNTULBÞ T5 Tw;in ðss1 þ 1Þ X2
L1 is simplified as Eq. (33):
(32)
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0 0 # 8X exp ðNTUHBÞexp NTUHS 1 X < 2 2 0 0 c 0 0 1 L1 ¼ 2 ½1 exp ðNTULBÞ 4X1 exp NTUHE2 1 X1 00 : X2 X1 1 X2 1 ðX2 1Þ X1 1 2
00 X1 exp NTULS 1 X100 1 ½X2 exp ðNTULSð1 X2 ÞÞ 1 0
exp ðNTUHBÞ X2 Tw;in ðsh2 þ 1Þ T0 ðs þ 1Þ 0 0 T0 ðs þ 1Þ Tw;in ðsh2 þ 1Þ þ X1 1 X2 1 ðX2 1Þ X100 1
X100 exp NTULS 1 X100 1 ½X2 exp ðNTULSð1 X2 ÞÞ 1 þ X100 exp NTULS 1 X100 1
Tw;in ðss2 þ 1Þ½1 exp ðNTHUBÞ½X2 exp ðNTULSð1 X2 ÞÞ 1 0 X1 1 ðX2 1Þ X100 1 9 X100 exp NTULS 1 X100 1 ½X2 exp ðNTULSð1 X2 ÞÞ 1= 0 ; X1 1 ðX2 1Þ X100 1
þ ðss2 þ 1Þ Tw;in
00 X1 exp NTULS 1 X100 1 ½X2 X2 exp ðNTULSð1 X2 ÞÞ c2 ½1 exp ðNTULBÞ ðsh1 þ 1Þ Tw;in X2 ðX2 1Þ X100 1 X100 X100 exp NTUHEC1 1 X100 0 þ T w;in ðss1 þ 1ÞTw;in 00 X1 1 þ
Similarly, the energy balance across the high pressure evaporator can be written as Eq. (34):
_ w2 L2 ¼ m _ g cpg ðT1 T2 Þ m
(34)
Accordingly, the latent heat of vaporization L2, can be expressed as Eq. (35):
The temperature of the flue gas at the exit of economizer (Tg,out) can be written as Eq. (38):
Tg;out ¼ T0 ðs þ 1Þ X1 ss1 Tw;in þ X2 Tw;in ðss1 þ sh1 Þ 0
0
0
0
0
þ X 1 T w;in X 2 Tw;in ðsh2 þ ss2 Þ
X2 X L 1L c2 1 c0 2
(38)
1
0
c1
½1expðNTUHBÞ 0 X1
0 80 T0 ðs þ1ÞTw;in ðsh2 þ1Þ X exp NTUHS 1X < 2 2 0 : X 2 1 9 0 = X 2 Tw;in ðsh2 þ1ÞT0 ðs þ1Þ s ð þ1Þ ð36Þ þ T s2 w;in 0 ; X 2 1
Energy balance for the entire waste heat recovery unit can be written as Eq. (37):
_ g cpg Tg;in Tg;out ¼ m _ w c1 Tsat1 Tw;in m _ w1 L1 þ c2 Tsup1 Tsat1 þm 0 _ w2 c001 T w;in Tsat1 þm 0 0 þ c1 Tsat2 T w;in þ L2
0 þ c2 Tsup2 Tsat2
0
(35)
L2 is simplified as Eq. (36):
L2 ¼
0
X100 T w;in þ X100 T w;in ðss1 þ 1Þ X 1 ðss2 þ 1Þ Tw;in
0
c1 ½1 exp ðNTUHBÞ T1 Tw;in ðss2 þ 1Þ X1
L2 ¼
(33)
Consequently, by utilizing the above-derived relation, the fth for a dual pressure HRSG, in terms of non-dimensional operating parameters can be expressed as Eq. (39):
Table 1 Cost coefficients. Heat transfer surface cost (US$ per kg)
CEC
CB
CSH
Tubes and fins Joints Welding Bending
4.21 8 2 e
4.21 8 2 e
8 e e 5
Table 2 Initial specification and turbine exhaust gas analysis.
(37)
Item
Unit
Value
Tg,in _g m CO2 H2O N2 O2
542.22 494.87 3.17 7.26 75.76 13.80
C kg/s % % % %
S. Naemi et al. / Applied Thermal Engineering 52 (2013) 371e384
fth
379
0
0 0 80 X 1 X exp ðNTUHBÞ exp NTUHS 1 X exp NTUHE2 1 X < 2 2 1 1 0 0 ¼ X1 ln ðss1 þ 1Þ þ ½1 exp ðNTULBÞ 00 : X 2 1 ðX2 1Þ X1 1 Tw;in ðss1 þ 1Þ X 1 1 00 X1 exp NTULS 1 X100 1 ½X2 exp ðNTULSð1 X2 ÞÞ 1 T0 ðs þ 1Þ Tw;in ðsh2 þ 1Þ
0
0 0 1 X 2 Tw;in ðsh2 þ 1Þ T0 ðs þ 1Þ exp ðNTUHBÞ X 1 exp NTUHE2 1 X 1 0 0 þ X100 exp NTULS 1 X100 1 00 Tw;in ðss1 þ 1Þ X 1 1 X 2 1 ðX2 1Þ X1 1
0 0 1 Tw;in ðss2 þ 1Þ½X2 exp ðNTULSð1 X2 ÞÞ 1 X 1 exp NTUHE2 1 X 1 0 ½X2 exp ðNTULSð1 X2 ÞÞ 1 þ Tw;in ðss1 þ 1Þ X 1 1 ðX2 1Þ X100 1 X100 exp NTULS 1 X100 1 ½1 exp ðNTUHBÞ
0 0 1 Tw;in ðss2 þ 1Þ½X2 exp ðNTULSð1 X2 ÞÞ 1 X 1 exp NTUHE2 1 X 1 0 X100 exp NTULS 1 X100 1 þ 00 Tw;in ðss1 þ 1Þ X 1 1 ðX2 1Þ X1 1 ) 00 Tw;in ðsh1 þ 1Þ X1 exp NTULS 1 X100 1 ½X2 X2 exp ðNTULSð1 X2 ÞÞ X100 X100 exp NTUHE1 1 X100 0 þ þ T w;in 1 ðss1 þ 1ÞðX2 1Þ X100 1 Tw;in ðss1 þ 1Þ X100 1
0 0 80 9 s s s s T X exp NTUHS 1 X ð þ 1Þ T ð þ 1Þ þ X T ð þ 1Þ T ð þ 1Þ < 2 = 2 2 w;in h2 0 0 w;in h2 0 þ ½1 exp ðNTUHBÞ 1 : ; Tw;in ðss2 þ 1Þ X 2 1 2 3 2 3 0 0 0 s ð T T þ 1Þ sh1 þ 1 s þ1 s2 w;in w;in 6 7 5 þ X 1 ln 4 þ X100 ln 4 ln ðs þ 1Þ þ NTU V * þ ðs þ 1Þ þ X2 ln 5 þ X 2 ln h2 0 ss1 þ 1 ss2 þ 1 Tw;in ðss1 þ 1Þ T w;in 0
Tw;in Tw;in T w;in 00 Tw;in 00 Tw;in 0 Tw;in 0 Tw;in 0 X s þ X ðs sh1 Þ X þ X ðs þ 1Þ X ðs þ 1Þ þ X X ðs ss2 Þ 1 T0 1 s1 T0 2 s1 T0 1 T0 1 s1 T0 1 s2 T0 1 T0 2 h2
4. Thermoeconomic optimization
(39)
The results acquired by exergy loss minimization deeply persuade HRSG manufacturers to decrease the pinch point or increase the area of heat transfer surfaces; however, it is not completely approved from economic viewpoint, as initial investment cost should also be taken into account. The economic limitation usually prevents to diminish the exergy losses. For instance, a reduction in temperature difference in heat exchangers can reduce energy losses, but requires the investment for additional heat transfer area. In this regard, a thermoeconomic optimization method is developed here to obtain optimum pinch point, considering thermal efficiency and financial consideration simultaneously. In the present study, the thermoeconomic analysis is presented to minimize the life cycle cost. Due to irreversibilities and exergy waste through the HRSG stack, a substantial proportion of input
exergy inevitably is lost. However, the exergy losses could be converted to useful form of energy in order to improve the income; therefore, the term of the exergy loss should be considered as a cost item. Rosen [21] claimed that a systematic correlation exists between capital cost and internal losses, but not between capital cost and external exergy losses or energy losses. In other words, the installation and operation costs and the exergy losses cost which are playing against each other, should be restricted simultaneously. To achieve this, a thermoeconomic objective function will be defined to minimize total cost. In this regard, both stated terms should be calculated separately over a specific operational time period. Hence, the cost due to exergy losses is computed annually, and the initial investment cost is broken to HRSG’s life time. To obtain the costs related to exergy losses, it should be recasted to HRSG operative costs. For this aim, a proper formula should be presented as Eq. (40):
Table 3 Fixed design parameters of tubes.
Table 4 Fixed design parameters of fins.
Section
Outer diameter (m)
Inner diameter (m)
Transferred pitch (m)
Longitudinal pitch (m)
Section
Number of fins per meter
Height (m)
Thickness (m)
HSH HB HEC2 HEC1 LSH LB LEC
0.051 0.051 0.038 0.038 0.051 0.051 0.038
0.045 0.045 0.032 0.032 0.045 0.045 0.033
0.108 0.108 0.089 0.089 0.108 0.108 0.089
0.135 0.135 0.111 0.111 0.135 0.135 0.111
HSH HB HEC2 HEC1 LSH LB LEC
243.46 251.89 241.77 250.35 199.21 221.46 205.94
0.019 0.019 0.016 0.016 0.019 0.019 0.019
0.001 0.001 0.001 0.001 0.001 0.001 0.001
380
S. Naemi et al. / Applied Thermal Engineering 52 (2013) 371e384
0.8
40 Exergetic efficiency
35
Energetic efficiency 0.78
Gas Pressure Drop (kPa)
Energetic and Exergetic Efficiencies
0.79
0.77 0.76 0.75 0.74 0.73
30 25 20 15
0.72
10
0.71
5
0.7
0
5
10
15
20
25
30
0
Pinch Point (° C)
0
5
Fig. 3. Energetic and exergetic efficiency vs. pinch point (P ¼ 90 bar).
_ g cpg T0 tfth CI ¼ cI m
In above equation, Cost is cost of each heat transfer section. Costs of economizers have been calculated by Eq. (43):
(43)
Costs of evaporators (boilers) have been also calculated with equation similar to economizers, but costs of superheaters have been estimated in different ways by Eq. (44):
(44)
And in above equation Nb can be calculated by Eq. (45):
Nb ¼ Nw ðNd 1Þ
25
Coefficients shown in above equations are extracted by MAPNA Boiler Company [23] as listed in Table 1. Hence, the total cost of HRSG can be written as Eq. (46):
CHRSG ¼ TCI AF
(46)
In which Annuity Factor (AF) stands for the capital recovery factor, which may be found by Eq. (47):
AF ¼
ið1 þ iÞn ð1 þ iÞn 1
(47)
where i is the rate of return (interest rate), and n is the total operating period of the system in years. Finally, thermoeconomic objective function can be defined by Eq. (48):
fEC ¼
CI þ CHRSC _ g cpg T0 m
(48)
5. Results and discussion
(41)
PEC ¼ CostLE þ CostLB þ CostLS þ CostHE1 þ CostHE2 þ CostHB þ CostHS (42)
CostS ¼ CostS;m MS þ CostS;b Nb
20
(40)
where a is normally between 4.12 and 8.09 [22]. In this study, a is assumed 5.2 considering data provided by MAPNA Boiler Company [23]. Purchased equipment cost is defined as Eq. (42):
CostE ¼ CostE;m ME þ CostE;j ME;j þ CostE;w þ LE;w
15 Pinch Point (°C)
Fig. 4. Pressure drop vs. pinch point.
where cI represents the specific cost of exergy losses and t is the annualized number of the operation hours of the unit. To define the specific cost of the exergy loss, (cI) a variety of strategies can be observed. It is not realistic to assume cI as the price of fuel, because the conversion efficiency should be taken into consideration. One approach is to consider the cost of exergy losses equal to the cost of fuel divided for mean efficiency of the power plant (about 50%). Another approach [15] is to consider it as the price of electricity. The total capital investment (TCI) of HRSG consists of different items such as, purchased equipments costs (PEC), piping, instrumentation and controls, electrical equipment and materials, construction costs, civil, structural and architectural work, installation costs, land, service facilities, engineering and supervision, startup cost, licensing, research and development, tax, transportation, etc. Although, these factors directly influence the HRSG cost, it is not possible to have a specific formula to cover them all, since they depend on different parameters. Therefore, all above costs have been considered as a percentage of PEC [22]. Accordingly, total capital investment can be calculated by Eq. (41):
TCI ¼ a PEC
10
(45)
As previously stated, an attempt is made to present optimum thermodynamic and thermoeconomic design of a dual pressure HRSG coupled with a V94.2 Siemens gas turbine, using nondimensional parameters. Table 2 indicates the specifications of Table 5 Non-dimensional parameters at optimum design. HP drum pressure (bar) Optimum pinch point (C) NTUHS NTUHB NTUHE2 NTUHE1 NTULS NTULB NTULE X1 X1ʹ X1ʺ X2 X2ʹ
s sh1 sh2 ss1 ss2
75 2.5 3.692 4.243 3.056 1.964 12.41 2.419 2.461 0.599 0.5824 0.5247 0.05077 0.317 1.83 0.762 1.765 0.5549 0.9563
80 2.2 3.731 4.347 3.122 2.021 12.26 2.478 2.513 0.6006 0.5852 0.5232 0.05268 0.3209 1.83 0.7683 1.766 0.5549 0.9719
85 2.14 3.68 4.351 3.116 2.029 11.86 2.479 2.505 0.6022 0.5874 0.5215 0.05457 0.3253 1.83 0.7714 1.763 0.5549 0.9867
90 2.1 3.627 4.354 3.11 2.037 11.5 2.481 2.498 0.6038 0.5898 0.52 0.05636 0.3298 1.83 0.7741 1.761 0.5549 1
S. Naemi et al. / Applied Thermal Engineering 52 (2013) 371e384 Table 6 Input data for thermoeconomic analysis.
Thermodynamic Objective Function
0.27 P=90 bar P=85 bar P=80 bar P=75 bar
0.26
381
0.25
Parameter
Value
cI,Fuel cI,Electricity t
0.0262 ($/kWh) 0.08 ($/kWh) 7000 (h) 0.48 0.124 30 (years)
hCCPP i n
0.24 0.23
Fig. 4 indicates the gas side pressure drop versus pinch point. It can be clearly seen that, the gas side pressure drop exponentially rises by increasing heat transfer areas in order to obtain lower pinch point temperature. In order to obtain the optimum operation, the effect of operating parameters on the HRSG performance must be known. In this regard, the influence of non-dimensional parameters on thermodynamic objective function is highlighted in this section. Table 5 depicts the value of non-dimensional parameters at optimum design condition for four working pressure of HP drum. Fig. 5 reveals variation of thermodynamic objective function versus the pinch point. As it shows, the optimum pinch point decreases slightly by increasing the pressure of HP drum. Among non-dimensional parameters, NTUHB and NTULB are playing most significant roles, as the evaporator is the main source of exergy destruction. Furthermore, NTULE is another critical parameter, considering the exergy waste of the stack. Fig. 6a and b presents the variation of fth versus NTUHB and NTULB respectively. It is shown that, the fth tends to approach clearly a minimum value at a particular NTUHB and NTULB, and then shows an upward trend. This suggests that for a particular gas flow and water/steam conditions, at a particular NTUHB and NTULB, the temperature profiles (DT) and pressure drop (DP) in the unit are such that, the overall irreversibility is minimum.
0.22 0.21 0.2
0
5
10
15 Pinch Point (°C)
20
25
Fig. 5. Thermodynamic objective function vs. pinch point.
gas turbine exhaust gas at full load. In CCPPs, a preheater using waste heat is usually employed to increase the feed water temperature from condensation temperature, so inlet temperature of water is also assumed 129 C; however, the preheater itself is not considered here. The tube and fins design specifications also are reported in Tables 3 and 4, respectively. Fig. 3 represents the effect of pinch point on the first and second law efficiencies of the HRSG. Accordingly, although the energetic efficiency always has a downward trend by increasing the pinch point, the exergetic efficiency hits a maximum value at approximately 1.5 C. In other words, up to the peak point, the exergy loss due to pressure drop dominates, whereas after that point, the exergy loss of heat transfer process outweighs.
a
0.26
0.32
Thermodynamic Objective Function
Thermodynamic Objective Function
0.34
0.3 0.28 0.26 0.24 0.22 0.2 2.5
3
3.5
4
4.5 5 NTUHB
5.5
6
6.5
7
b
0.25
0.24
0.23
0.22
0.21
0.2 1.5
2
2.5
3
3.5
4
NTULB
c
0.224 Thermodynamic Objective Function
0.222 0.22 0.218 0.216 0.214 0.212 0.21 0.208 0.206 0.204
1
1.5
2
2.5 NTULE
3
3.5
4
Fig. 6. (a) Thermodynamic objective function vs. number of transfer units of high pressure boiler (evaporator) (NTUHB). (b) Thermodynamic objective function vs. number of transfer units of low pressure boiler (evaporator) (NTULB). (c) Thermodynamic objective function vs. number of transfer units of low pressure economizer (NTULE).
S. Naemi et al. / Applied Thermal Engineering 52 (2013) 371e384
a
a
0.2
4.5
Electricity Cost HRSG Cost
0.55 0.324 0.5
0.32 0.316
0.45
0.312
18 20 22 24 26 28
4
0.15
3.5
0.1
0.4 0.35 0.05
0.65
5
10
15 Pinch Point (°C)
20
25
8
10
12
14
16 18 20 22 Optimum Pinch Point (°C)
0.315 0.5
0.31 16 18 20 22 24 26
0.45
0.15
4.5 6
0.32 0.55
3
28
Electricity Cost HRSG Cost Electricity Cost ($ / kWh)
0.6
26
b
0.2
b Based on electricity cost Based on fuel cost
24
HRSG Cost (x 10 $)
0
Thermoeconomic Objective Function
6
Based on electricity cost Based on fuel cost
0.6
Electricity Cost ($ / kWh)
Thermoeconomic Objective Function
0.65
HRSG Cost (x 10 $)
382
0.1
4
0.05
3.5
0.4 5
0.35
0
5
10
15 Pinch Point (°C)
20
25
Fig. 7. (a) Thermoeconomic objective function vs. pinch point (HP ¼ 75 bar). (b) Thermoeconomic objective function vs. pinch point (HP ¼ 90 bar).
Fig. 6c reveals the variation of thermodynamic objective function with NTULE. The results show that, the fth tends to approach clearly a minimum value at a particular NTULE and then shows an exponential upward trend. This suggests that for a particular gas flow and water/steam conditions, there is a particular NTULE, where the overall irreversibilities reach a minimum value. Before the minimum point, more heat is absorbed from the flue gas by increasing NTULE, which causes lower temperature of the flue gas
10
15 20 Optimum Pinch Point (°C)
25
3 30
Fig. 9. (a) Electricity price vs. optimum pinch point (P ¼ 75 bar). (b) Electricity price vs. optimum pinch point (P ¼ 90 bar).
at the exit of HRSG, and consequently lower irreversibilities; however, after that point, the irreversibility of heat transfer outweighs the irreversibility of pressure drop. The aim of thermodynamic optimization is to achieve the maximum output from exergy inflow; hence, more heat transfer surfaces should be employed to minimize the irreversibilities. From thermoeconomic viewpoint, whenever the benefit of increasing heat transfer areas outweighs the cost, it is advised to use larger surfaces, because the target of thermoeconomic optimization is to gain more profit. In other words, the revenue of extra electricity generation by
Fig. 8. HRSG layout under study.
S. Naemi et al. / Applied Thermal Engineering 52 (2013) 371e384
0.32
3.6
3.5
0.28
3.4
0.26
3.3
0.24
3.2
6
HRSG Cost (x 10 $)
0.3
3
Fuel Price ($ / m )
Fuel Price HRSG Price
0.22 18
19
20
21 22 23 Optimum Pinch Point (°C)
24
3.1 25
383
for the design, clearly where the total irreversibility is low. Additionally, the results present that, thermodynamic objective function reaches a minimum point at a particular NTULE, where the overall irreversibility of heat transfer and pressure drop is at least amount. Obviously, increasing the area of heat transfer surfaces increases the initial investment cost of HRSG, and by contrast decreases the exergy losses. In other words, capital cost and exergy losses cost should be considered simultaneously to find the trade-off pinch point between them. Accordingly a comprehensive thermoeconomic optimization has been proposed to obtain the financially optimum design. In this regard, the exergy loss is converted into cost based on electricity price and also fuel price. Thermoeconomic analysis offers pinch points about 22 C to minimize the HRSG cost, whereas thermodynamic analysis suggests pinch points about just only 2 C to minimize exergy losses. Additionally, as expected the optimum pinch point reduces by increasing the working pressure of HP drum from 75 bar to 90 bar.
Fig. 10. Fuel price vs. optimum pinch point (P ¼ 90 bar).
Appendix A the steam turbine has to compensate the extra expenses of heat transfer materials in order to decrease the pinch point. As previously mentioned, exergy losses should be considered as a cost to perform thermoeconomic analysis. In this regard, two strategies are used to adapt exergy loss to the cost form. In the first strategy, exergy price is considered as the price of fuel divided for exergetic efficiency of the HRSG. As the role of boiler is to convert the fossil fuel energy into steam, the HRSG exergy loss could be used the same as the steam; therefore, it can be a novel and justifiable strategy to cost exergy loss. In the second strategy, exergy loss cost is considered as the multiple of electricity price to CCPP’s energetic efficiency. This strategy is valid because the exergy loss could have been converted to electricity by means of the steam turbine. Table 6 depicts input data which are considered for the thermoeconomic analysis. It should be stated that, the natural gas price is considered 0.25 $/m3 equal to 0.0262 $/kWh. Fig. 7a and b illustrates the variation of thermoeconomic objective function versus HRSG pinch point for 75 bar and 90 bar, regarding both strategies. As can be clearly seen, optimum pinch point is 20.6 C (for 75 bar) and 19.2 C (for 90 bar) based on electricity price, and 25.4 C and 23.7 C based on fuel price. It seems that, the optimum pinch point based on thermoeconomic optimization is more reliable. Fig. 8 reveals the temperature of water/steam side under optimum thermoeconomic condition at electricity price strategy for HRSG at 90 bar. Fig. 9a and b depicts the optimum pinch point design of different electricity prices. HRSG cost for different pinch points is also compared. Additionally, Fig. 10 indicates the optimum design pinch point of different fuel prices.
6. Conclusion Depletion of fossil fuels and global warming accelerate activities to improve design guidelines for thermal power plants. Applying first and second laws of thermodynamics together with economic analysis, make a powerful tool to evaluate thermal systems. This research deals with thermodynamic and thermoeconomic analyses and optimization of a dual pressure HRSG coupled with a heavy duty gas turbine. In this regard, an attempt has been made to highlight how non-dimensional operating parameters can affect proposed thermodynamic objective function. It has been observed that for a particular non-dimensional hot flue gas inlet temperature difference ratio, thermodynamic objective function is minimized at particular NTUHB and NTULB suggesting a possible optimum value
The equations to calculate the heat transfer coefficients and other coefficients that expressed in paper are taken from Ref. [19] which are listed as following: Nusselt number or convective heat transfer coefficient inside the tubes:
Nu ¼ 0:023Re0:8 Pr0:4 where: Re: Reynolds number, Pr: Prandtl number, k: thermal conductivity [W/m K]. Outside convective heat transfer coefficient:
hc ¼ C1 C2 C3
d þ 2h d
0:5 0:25 0:67 Tg k Gcpg mcp;g Ta
where C1, C2, C3 are defined in Ref. [19] and m is viscosity (Pa s). Nonluminous heat transfer coefficient:
hN ¼ sεg
4 Tg4 Tout
!
Tg Tout
The method for calculating εg is reported in Ref. [19].
ho ¼ hc þ hN References [1] Ibrahim Dincer, Marc A. Rosen, Exergy, Energy, Environment and Sustainable Development, Elsevier, 2007. [2] Xiaojun Shi, Defu Che, Thermodynamic analysis of an LNG fuelled combined cycle power plant with waste heat recovery and utilization system, Int. J. Energy Res. 31 (2007) 975e998. [3] Ahmet Cihan, Oktay Hacıhafızoglu, Kamil Kahveci, Energyeexergy analysis and modernization suggestions for a combined-cycle power plant, Int. J. Energy Res. 30 (2006) 115e126. [4] Pouria Ahmadi, Ibrahim Dincer, Marc A. Rosen, Exergy, exergoeconomic and environmental analyses and evolutionary algorithm based multi-objective optimization of combined power plants, J. Energy 36 (2011) 5886e5898. [5] Pouria Ahmadi, Ibrahim Dincer, Thermodynamic analysis and thermoeconomic optimization of a dual pressure combined cycle power plant with a supplementary firing unit, J. Energy Convers. Manage. 52 (2011) 2296e2308. [6] Manuel Valdes, Antonio Rovira, Ma Dolores Duran, Influence of the heat recovery steam generator design parameters on the thermoeconomic performances of combined cycle gas turbine power plants, Int. J. Energy Res. 28 (2004) 1243e1254. [7] P.K. Nag, S. De, Design and operation of a heat recovery steam generator with minimum irreversibility, J. Appl. Therm. Eng. 17 (1997) 385e391. [8] Jong Soo In, Sang Yong Lee, Optimization of heat recovery steam generator through exergy analysis for combined cycle gas turbine power plants, Int. J. Energy Res. 32 (2008) 859e869. [9] C.J. Butcher, B.V. Reddy, Second law analysis of a waste heat recovery based power generation system, J. Heat Mass Transf. 50 (2007) 2355e2363.
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[10] B.V. Reddy, G. Ramkiran, K. Ashok Kumar, P.K. Nag, Second law analysis of a waste heat recovery steam generator, J. Heat Mass Transf. 45 (2002) 1807e1814. [11] Jiangfeng Guo, Mingtian Xu, Lin Cheng, Thermodynamic analysis of waste heat power generation system, J. Energy 35 (2010) 2824e2835. [12] C. Casarosa, A. Franco, Thermodynamic optimization of the operative parameters for the heat recovery in combined power plants, Int. J. Appl. Thermodyn. 4 (2001) 43e52. [13] Alessandro Franco, Nicola Giannini, A general method for the optimum design of heat recovery steam generators, J. Energy 31 (2006) 3342e3361. [14] Alessandro Franco, Alessandro Russo, Combined cycle plant efficiency increase based on the optimization of the heat recovery steam generator operating parameters, Int. J. Therm. Sci. 41 (2002) 843e859. [15] C. Casarosa, F. Donatini, A. Franco, Thermoeconomic optimization of heat recovery steam generators operating parameters for combined plants, J. Energy 29 (2004) 389e414. [16] Hassan Hajabdollahi, Pouria Ahmadi, Ibrahim Dincer, An exergy-based multiobjective optimization of a heat recovery steam generator (HRSG) in
[17] [18]
[19] [20] [21]
[22] [23]
a combined cycle power plant (CCPP) using evolutionary algorithm, Int. J. Green Energy 8 (2011) 44e64. Mapna Turbine Corporation. http://www.mapnaturbine.com/en/Pages/ Default.aspx. R. Karthikeyan, M. Afsarhussain, B.V. Reddy, P.K. Nag, Performance simulation of heat recovery steam generators in a cogeneration system, Int. J. Energy Res. 22 (1998) 399e410. V. Ganapathy, Industrial Boiler and Heat Recovery Steam Generators, Marcel Dekker, Inc., New York, 2003. Adrian Bejan, The thermodynamic design of heat and mass transfer processes and devices, J. Heat Fluid Flow 8 (1987) 258e276. M.A. Rosen, An investigation of the relation between capital costs and selected thermodynamic losses. AES-Vol. 25/HTD-Vol. 191, in: Second Law Analysis e Industrial and Environmental Application, ASME, 1991, pp. 55e62. A. Bejan, G. Tsatsaronis, M. Moran, Thermal Design and Optimization, John Wiley & Sons, New York, 1996. Mapna Boiler Company, R and D Department. http://www.mapnaboiler.com/.
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Optimum design of dual pressure heat recovery steam generator using non-dimensional parameters based on thermodynamic and thermoeconomic approaches Sanaz Naemi a, Majid Saffar-Avval a, *, Sahand Behboodi Kalhori b, Zohreh Mansoori c a b c
Mechanical Engineering Department, Amirkabir University of Technology, Hafez Ave., P.O. Box 15875-4413, Tehran, Iran Lab. for Alternative Energy Conversion, Mechatronic Systems Engineering, School of Engineering Science, Simon Faser University, Canada Energy research center, Amirkabir University of Technology, Iran
h i g h l i g h t s < Presenting thermodynamic and thermoeconomic optimization of a heat recovery steam generator. < Defining an objective function consists of exergy waste and exergy destruction. < Defining an objective function including capital cost and cost of irreversibilities. < Obtaining the optimized operating parameters of a dual pressure heat recovery boiler. < Computing the optimum pinch point using non-dimensional operating parameters.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 May 2012 Accepted 6 December 2012 Available online 21 December 2012
The thermodynamic and thermoeconomic analyses are investigated to achieve the optimum operating parameters of a dual pressure heat recovery steam generator (HRSG), coupled with a heavy duty gas turbine. In this regard, the thermodynamic objective function including the exergy waste and the exergy destruction, is defined in such a way to find the optimum pinch point, and consequently to minimize the objective function by using non-dimensional operating parameters. The results indicated that, the optimum pinch point from thermodynamic viewpoint is 2.5 C and 2.1 C for HRSGs with live steam at 75 bar and 90 bar respectively. Since thermodynamic analysis is not able to consider economic factors, another objective function including annualized installation cost and annual cost of irreversibilities is proposed. To find the irreversibility cost, electricity price and also fuel price are considered independently. The optimum pinch point from thermoeconomic viewpoint on basis of electricity price is 20.6 C (75 bar) and 19.2 C (90 bar), whereas according to the fuel price it is 25.4 C and 23.7 C. Finally, an extensive sensitivity analysis is performed to compare optimum pinch point for different electricity and fuel prices. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Heat recovery steam generator Exergy analysis Optimum pinch point temperature Thermoeconomic analysis
1. Introduction Due to global energy crisis, an increasingly attitude to efficient energy conversion technologies especially Combined Cycle Power Plants (CCPPs) have seen in recent decades, in which gas turbine operating in open cycle is integrated with a steam cycle by means of a Heat Recovery Steam Generator (HRSG). Hereupon, HRSG provides the critical connection between the gas turbine topping cycle and * Corresponding author. Tel.: þ98 21 66405844; þ98 21 66419736. E-mail addresses: [email protected] (S. Naemi), [email protected] (M. SaffarAvval), [email protected] (S. Behboodi Kalhori), [email protected] (Z. Mansoori). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.12.004
the steam turbine bottoming cycle. Undoubtedly, the optimum design of HRSG has a particular interest to improve the performance of heat recovery for maximizing the power generated by steam cycle. Besides, it reduces the environmental impacts of pollutant emissions. In the design of HRSGs, the method to obtain the optimum design usually is a combination of the thermodynamic and economic point of views. The exergy method, which uses the conservation of mass and energy principles together with the second law of the thermodynamics, is a useful tool to identify the locations, types and magnitudes of losses. In the past decade, coupled energy and exergy analyses of different thermal systems have been carried out. Dincer and Rosen
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Nomenclature A Af At Ai Ao Aw B b cI cp Cost CostE,j CostE,m CostE,w CostS,b CostS,m c1 c1 c001 c2 c2 d di f ffi ffo fEC fth G h hc hi ho hN km L LEC,w LMTD _ m ME ME,j MS Nb Nd Nw n NTU P0 Q
heat transfer area (m2) fin surface areas (m2/m) total surface area (m2/m) inside surface area (m2/m) obstruction surface area (m2/m) area of tube wall (m2/m) factor used in Grinson’s correlation fin thickness (m) specific cost of exergy loss (US $/kWh) specific heat (kJ kg1 k1) cost of each heat transfer section (US $) cost of economizer joints (US $/kg) cost of tubes and fins (economizer) (US $/kg) cost of welding (economizer) (US $/kg) cost of bending (superheater) (US $/kg) cost of tubes and fins (superheater) (US $/kg) specific heat of water in low pressure economizer (kJ kg1 K1) specific heat of water in high pressure economizer1 (kJ kg1 K1) specific heat of water in high pressure economizer2 (kJ kg1 K1) specific heat of steam in low pressure superheater (kJ kg1 K1) specific heat of steam in high pressure superheater (kJ kg1 K1) tube outer diameter (m) tube inner diameter (m) friction factor inside fouling factors (m2 s K kJ1) outside fouling factors (m2 s K kJ1) thermoeconomic objective function thermodynamic objective function gas mass velocity (kg m2 s1) fin height (m) convection heat transfer coefficient (W m2 K1) inside heat transfer coefficient of tubes (W m2 K1) outside heat transfer coefficient of tubes (W m2 K1) nonluminous heat transfer coefficient (W m2 K1) metal thermal conductivity (W m K1) latent heat of vaporization (kJ/kg) length of welding (m) logarithmic mean temperature difference (for evaporator) (K) mass flow rate (kg s1) mass of tube and fins (economizer) (kg) joint mass for economizer (kg) mass of tube and fins (superheater) (kg) number of bending in superheater number of tubes per row number of tube rows number of fins per meter number of transfer units ambient pressure (kPa) heat transferred (kW)
[1] reviewed application of exergy approach, to analyze and design a wide range of energy conversion systems. Shi and Che [2] conducted energy and exergy analyses of an improved liquefied natural gas fuelled CCPP with a waste heat recovery, considering mass, energy and exergy balances for each component. Cihan et al. [3]
SL ST St S_ gen Tg T0 Tout Tsat1 Tsat2 Tsup1 Tsup2 Tw 0 Tw;in Uo V V* X1 X1ʹ X1ʺ X2 X2ʹ
longitudinal pitch (m) transferred pitch (m) Stanton number rate of entropy generation (kW/K) temperature of flue gas at the considered location (K) ambient temperature (K) flue gas temperature at the economiser outlet (K) saturation temperature of water or steam (low pressure boiler) (K) saturation temperature of water or steam (high pressure boiler) (K) temperature of superheated steam (low pressure superheater) (K) temperature of superheated steam (high pressure superheater) (K) temperature of water at the considered location (K) temperature of water at the entrance of high pressure economizer2 (K) overall heat transfer coefficient (W m2 K1) flue gas velocity (m/s) non-dimensional gas velocity ratio of heat capacities of water and gas stream (LE) ratio of heat capacities of water and gas stream (HE2) ratio of heat capacities of water and gas stream (HE1) ratio of heat capacities of steam and gas stream (LS) ratio of heat capacities of steam and gas stream (HS)
Greek symbols DPg pressure drop (kPa) h fins efficiency s non-dimensional hot flue gas inlet temperature difference ratio ss1 non-dimensional water saturation temperature (LP drum) difference ratio ss2 non-dimensional water saturation temperature (HP drum) difference ratio sh1 non-dimensional HP superheated steam temperature difference ratio sh2 non-dimensional LP superheated steam temperature difference ratio Subscripts g gas HB high pressure boiler (evaporator) HE1 high pressure economizer1 HE2 high pressure economizer2 HS high pressure superheater HRSG heat recovery steam generator I irreversibility in inflow LB low pressure evaporator LE low pressure economizer LS low pressure superheat out outflow w water water in low pressure economizer w1 water in high pressure economizer w2
preformed energy and exergy analyses of a CCPP investigating the potential for improving system efficiency. They indicated that, while the greatest energy loss takes place at the stack, the greatest exergy loss takes place in the combustion chamber of gas turbine and HRSG.
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Many researchers have recommended that costs are better distributed among the outputs, if cost accounting is based on the exergy quantity. Ahmadi et al. [4] optimized a CCPP based on exergy, exergoeconomic and environmental impact point of the views; they investigated the influence of supplementary firing on the performance of bottoming cycle and CO2 emissions. Then, they carried out a multiobjective optimization to determine the best design parameters, maximizing the exergy efficiency using a genetic algorithm. Additionally, Ahmadi and Dincer [5] introduced an objective function in terms of dollar per second, including the sum of the operating and maintenance, and capital investment costs. They obtained the optimum key variables by minimizing the objective function using a generic algorithm. They summarized that, by increasing the fuel price, the optimized decision variables in the thermoeconomic design tend to those of the thermodynamic optimum design. Valdes et al. [6] presented a methodology to identify the most relevant design parameters that impact on the thermal efficiency and the economic results of CCPP focusing on the HRSG design. They proposed two different thermoeconomic models aimed to determine whether an increase in the investment is worthy from the economic viewpoint. There are many researches done regarding HRSG systems for minimizing the losses. Nag and De [7] employed thermodynamic analysis to optimize the design and operation of a waste heat recovery boiler without superheater. Authors introduced entropy generation number function of design and operating parameters, and estimated the effect of these parameters on the operation during generation of saturated steam for a steam power cycle. They concluded that, there is an optimum evaporation temperature for minimizing irreversibilities of an HRSG. Moreover, operating the HRSG at full load reduces entropy generation, and also increases the number of transfer units of evaporator and economizer beyond certain cut-off values will have marginal benefit with respect to entropy generation. In and Lee [8] optimized design parameters of HRSGs by minimizing the sum of the destroyed and the lost exergies. They chose a single pressure HRSG system and obtained the optimum evaporation temperature corresponding to maximum useful work for the given condition of inlet water and gas temperatures; Also it is shown the dependency of number of transfer unit (NTU) on the saturation temperature, which is another important factor for determining the optimum conditions, when the construction cost is taken into account besides the operating cost. Butcher and Reddy [9] investigated the impact of different operating conditions such as gas composition, specific heat, pinch point, and gas inlet temperature on the performance of an HRSG. They indicated that, the energetic and exergetic efficiencies of the power plant deeply depend on the exhaust gas composition, specific heat and pinch point. Reddy et al. [10] studied the effects of various non-dimensional operating parameters on the entropy generation number for a single pressure HRSG. They claimed that, the entropy generation number increases with increase in non-dimensional hot flue gas inlet temperature difference ratio. They showed that, the temperature difference between hot gases and water has dominating effect on the entropy generation rate, whereas heat loss to the surroundings, ambient temperature and frictional pressure drop in the unit are not considered as the temperature difference. Guo et al. [11] analyzed waste heat power generation system on the basis of the first law, second law efficiencies and entropy generation. They tried to highlight how some operating parameters, such as the turbine exergy efficiency and pump performance could affect the unit’s performance; however, they did not consider the exergy waste to atmosphere. They concluded that, the optimal
373
operation condition should be achieved at the trade-off between the heat/exergy input and the heatework conversion ability of the unit. Casarosa and Franco [12] investigated different configurations of HRSG systems to minimize exergy losses, taking into account only the irreversibility due to the temperature difference between the hot and cold streams (pressure drop not accounting). Authors optimized the operating parameters for the HRSG on the basis of thermodynamic analysis. All the solutions lead to the zero pinch point and infinite heat transfer surface. They also developed thermoeconomic optimization; depending on the HRSG operating costs, evidently, the pinch point temperature difference in this case is obtained the values different from zero. Franco and Giannini [13] outlined a method to achieve optimum design of convective HRSGs for combined cycles. They obtained the main operating parameters of the HRSG and a detailed design of the components concerning the geometric variables of the heat transfer sections, in order to minimize the pressure drop of the elements of the HRSG. Franco and Russo [14] preformed the thermodynamic and thermoeconomic optimizations; the purpose of thermodynamic optimization was to diminish energy losses, expressed on exergy basis, while the aim of the thermoeconomic optimization was to minimize a cost function; sum of the cost of exergy inefficiencies and the cost of HRSG. In their method, the cost of every section is considered proportional to the heat transfer area, and exergy losses are computed as the selling price of the desired plant output, i.e., the electrical energy is estimated about three times of the cost of fuel per unit of energy. Similarly, Casarosa et al. [15] developed another HRSG design optimization methodology to meet both thermodynamic and economic objectives simultaneously. Hajabdollahi et al. [16] modeled an HRSG with a typical geometry and a number of pressure levels used at CCPPs, and developed a thermodynamic model and thermoeconomic optimization. They conducted exergoeconomic analysis and multi-optimization of an HRSG through energy and exergy, and compared their results with data provided from a power plant situated near the Caspian Sea in Iran. They introduced a new objective function (the total cost per unit of steam produced exergy). Then, optimum design parameters are selected when objective function is minimized while HRSG exergy efficiency is maximized. Authors summarized that an increase in high and low pressure drums increases exergy efficiency, while an increase in pinch point decreases exergy efficiency. Additionally, an increase in the HRSG inlet gas enthalpy results in an increase of the exergy efficiency. In the present work, as the first step, the thermodynamic model of a dual pressure HRSG coupled with a heavy duty gas turbine [17] was developed, and exergy waste and exergy destruction were computed for different pinch points of four pressure levels. In the second step, a thermodynamic objective function was proposed to minimize the exergy losses of dual pressure HRSGs to obtain the optimum design. In this regards, the effects of non-dimensional parameters on the HRSG performance were discussed. As expected, an increase in the efficiency of an HRSG can be achieved by reducing exergy losses through the heat recovery process. In the next step, optimum design of HRSG regarding financial considerations was investigated. A proper trade-off between the efficiency and the capital cost of equipment requires that some additional losses of exergy must be tolerated in order to reduce the capital cost. Therefore, the cost of exergy losses recast to operating cost of HRSG, and combined with the HRSG installation costs. To convert the exergy losses into cost, two strategies were employed; one based on electricity tariff, another based on fuel price. Finally, a sensitivity analysis was carried out to see how electricity tariff and fuel price affect on the optimum value of pinch point.
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2. Thermodynamic simulation
_ g cpg Tg;in Tg;out Q ¼ m
(1)
_ w cpw Tw;out Tw;in Q ¼ m
(2)
Fig. 1 reveals the schematic diagram of a dual pressure HRSG which will be simulated to find the optimum design. According to Fig. 1, gas turbine exhaust gases meet high pressure superheater (HS), high pressure boiler (HB), high pressure economizer2 (HE2), low pressure superheater (LS), high pressure economizer1 (HE1), low pressure boiler (LB) and low pressure economizer (LE) through the HRSG from left to right (hot side to cold side). Important operating parameters of HRSG are pinch point, approach point and gas side pressure drop through the HRSG. Fig. 2 describes the sketch of temperature profile for a dual pressure HRSG. As can be clearly seen, pinch point is the difference between the gas temperature leaving the evaporator and the saturation temperature corresponding to the steam pressure at drum, and approach temperature is the difference between the saturation temperature and temperature of drum inlet water. Karthikeyan et al. [18] investigated the performance simulation of an HRSG to see how pinch point and approach point affect the mass of steam generation and also temperature profiles across the HRSG. They concluded that, low pinch point increases steam production rate. On the other hand, although pinch point reduction leads to improvement of HRSG’s first law efficiency, it increases evaporating area causing greater expense for the heat transfer material.
Detailed formulations used to compute each resistance can be found in Appendix A and [19]. The characteristics of exhaust gases and physical properties of HRSG tubes and fins are given in the beginning of Results and discussion section.
2.1. Energy balance
2.2. Gas side pressure drop
The first step to simulate the HRSG is to balance the mass and energy on different heat transfer sections. In this study, the logarithmic means temperature difference (LMTD) method is used to size the heat transfer area. Additionally, some of the main assumptions to derive the mathematical modeling are listed below:
Undoubtedly, when the flue gas is passing through the HRSG, the pressure inevitably drops; therefore, exhaust gas should leave the turbine with a pressure more than the ambient to compensate this drop, this reduces the electricity generation; hence, the reduction of the gas side pressure drop is essential and plays important role as designing and operating parameters of HRSGs. Eq. (6) is used to estimate the pressure drop of each heat transfer section [19].
The system is assumed to be steady state. The exhaust gas mass flow rate, temperature and chemical composition are known. The staggered pitch tubes with solid fins are considered. The natural circulation is assumed for evaporator. The pressure drop of the flue gas across the HRSG is taken into account, whereas the pressure drop in water side is negligible. There is no external heat loss except the outflow of the exhaust gas which enters the stack. Energy balance in all heat transfer surfaces between the hot and cold streams (gas side and water/steam side) can be expressed as Eqs. (1) and (2):
The designing method is based on logarithmic means temperature difference, therefore the heat transfer areas are obtained by Eq. (3):
Q ¼ Uo A LMTD
(3)
where Uo is total heat transfer coefficient and LMTD is logarithmic mean temperature difference as Eqs. (4) and (5):
1 At At At d d 1 ¼ þ f fi þ f fo þ ln þ hi Ai Ai Aw 24km Uo di hho LMTD ¼
DPg ¼
Tg;in Tw;out Tg;out Tw;in " # Tg;in Tw;out ln Tg;out Tw;in
fg þ a G2 NL 500rg
(4)
(5)
(6)
Calculations of fg and a are reported in Ref. [19]. 3. Thermodynamic optimization Minimization of exergy losses ensures that the HRSG will operate efficiently. The exergy losses of HRSG were chosen as the objective function, that can successfully measure both the quality
Fig. 1. Schematic diagram of a dual pressure HRSG.
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375
Fig. 2. Gas and steam temperature profile of dual pressure HRSG.
and quantity of energy flow in the HRSG. Although this approach is not acceptable financially, it proposes a rough design criterion to define operating parameters of the HRSG. Exergy losses consist of two terms: exergy destruction and exergy out flow waste. First term is due to the irreversibility of the heat transfer process and pressure drops which leads to destruction of a substantial proportion of the input exergy through the HRSG. Second term is because of the hot gas outflow leaving the stack which is referred as exergy waste. Exergy destruction is expressed as Eq. (7):
E_ Destruction ¼ T0 S_ LEC þ S_ LB þ S_ LS þ S_ HE1 þ S_ HE2 þ S_ HB þ S_ HS
_ g cpg ln E_ waste ¼ T0 m
fth ¼
Hence, the total exergy destruction rate can be expressed as Eq. (9):
2 6_ E_ destruction ¼ T0 S_ gen;destruction ¼ T0 4m w c1 ln
Tsat1 Tw;in
! þ
_ w1 L1 m Tsat1
00 1 Tsup1 T _ w2 c001 ln @ w;in A _ w1 c2 ln þm þm Tsat1 Tsat1 0 1 _ L Tsup2 m BT C _ w2 _ w2 þm c1 ln @ 0 sat2 A þ w2 2 þ m c2 ln Tsat2 Tsat2 T w;in 3 ! Tg;out P0 þ DP 7 _ g cpg ln _ g Rln þm þm (9) 5 P0 Tg;in
Additionally, the exergy waste due to the external irreversibility can be obtained by Eq. (10) [8]:
! _ w1 L1 m Tsat1 þ _ g cpg Tsat1 m Tw;in 00 1 _ w2 c001 _ w1 c2 Tsup1 T w;in m m A þ þ ln ln @ _ g cpg _ g cpg m m Tsat1 Tsat1 0 1 _ w2 _ w2 L2 _ w2 Tsup2 m c1 B Tsat2 C m m c2 ln @ 0 þ ln þ þ A _ g cpg _ g cpg Tsat2 m _ g cpg m m Tsat2 T w;in Tg;out T0 T R P0 þ DP þ þ ln 0 þ ln (11) Tg;in cpg T0 P0
_ w c1 m E_ destruction þ E_ waste ¼ ln _ g cpg T0 _ g cpg m m
(7)
(8)
(10)
Accordingly, the thermodynamic objective function (fth) of HRSG can be formulated as Eq. (11):
where entropy generation in a counter flow heat exchanger is calculated by Eq. (8) [20]:
T T P _ p 1 ln 1;out þ mc _ p 2 ln 2;out ðmRÞ _ 1 ln 1;out S_ gen ¼ mc T1 T2 P1 P2;out _ 2 ln ðmRÞ P2
T0 _ g cpg Tg;out T0 þm Tg;out
The fth depends on different variables; thus, non-dimensional parameters are defined to study the impact of these variables on the fth. Those non-dimensional parameters are: nondimensional hot flue gas inlet temperature difference ratio (s), non-dimensional water saturation temperature difference ratio (sS), non-dimensional superheated steam temperature difference ratio (sh), ratio of heat capacities of water and gas stream (X1), ratio of heat capacities of steam and gas steam (X2), NTUHS, NTUHB, NTUHE1, NTUHE2, NTULE, NTULB, NTULS and nondimensional gas velocity (V*), which are defined by Eqs. (12)e (24).
s¼
Tg;in T0 T0
(12)
ss1 ¼
Tsat1 Tw;in Tw;in
(13)
ss2 ¼
Tsat2 Tw;in Tw;in
(14)
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sh1 ¼
Tsup1 Tw;in Tw;in
(15)
sh2 ¼
Tsup2 Tw;in Tw;in
(16)
where s is non-dimensional hot flue gas inlet temperature difference ratio and ss is non-dimensional water saturation temperature difference ratio.
_ w c1 m _ g cpg m
(17)
X1 ¼
_ w2 m c1 _ g cpg m
(18)
X100 ¼
_ w2 c001 m _ g cpg m
(19)
X1 ¼ 0
T1 ¼
V V * ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 St U0 P0 cpg f h0 r R
(23)
NTU ¼ NTUHS þ NTUHB þ NTUHE1 þ NTUHE2 þ NTULS þ NTULB þ NTULE
(24)
By considering a small element length dx for each heat transfer surface, and by making energy balance for the element and integrating between the limits (inlet and outlet flue gas temperature in each heat transfer surface), and by further simplification, the temperature of the flue gas at the exit of each heat transfer section can be expressed in term of other operating parameters as Eqs. (25)e(30). Gas temperature at entrance of high pressure (boiler) evaporator:
0 0 0 X2 exp NTUHS 1 þ X 2 T0 ðs þ 1Þ Tw;in ðsh2 þ 1Þ X 2 Tw;in ðsh2 þ 1Þ T0 ðs þ 1Þ (25)
0
X2 1
Gas temperature at entrance of high pressure economizer2:
_ c m X2 ¼ w1 2 _ g cpg m
(20)
_ w2 m c2 _ g cpg m
(21)
0
X2 ¼
where X1 is ratio of heat capacities of water and gas stream and X2 is ratio of heat capacities of steam and gas steam. NTUHS, NTUHB, NTUHE1, NTUHE2, NTULE, NTULB, NTULS and non-dimensional gas velocity:
R ln Cpg
1þ
DPg
P0
¼
R DPg ¼ ðNTUÞV * Cpg P0
(22)
T2 ¼exp ðNTUHBÞ
0 8 0
0 8 0
T0 ðs þ 1Þ Tw;in ðsh2 þ 1Þ X exp ðNTUHBÞexp NTUHS 1 X < 2 2 0 0 0 0 1 T3 ¼ X1 exp NTUHE2 1 X1 : X1 1 X2 1 0
9 exp ðNTUHBÞ X 2 Tw;in ðsh2 þ 1Þ T0 ðs þ 1Þ Tw;in ðss2 þ 1Þ½1 exp ðNTUHBÞ= 0 0 0 þ þ ; X1 1 X2 1 X1 1
0 0 0 Tw;in ðss2 þ 1Þ X 1 X 1 exp NTUHE2 1 X 1 0 þ X1 1
(27)
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377
Gas temperature at entrance of high pressure economizer2:
8 < T4 ¼ ½X2 exp ðNTULS2ð1 X2 ÞÞ 1 T ðs þ 1Þ Tw;in ðsh2 þ 1Þ : 0 0
0 0 0 X 1 exp NTUHE2 1 X 1 1 X 2 exp ðNTUHBÞexp NTUHS 1 X 2 0 0 X1 1 X 2 1 ðX2 1Þ
0
0
0 0 0 1 X 2 Tw;in ðsh2 þ 1Þ T0 ðs þ 1Þ X 1 exp NTUHE2 1 X 1 1 exp ðNTUHBÞ X 1 exp NTUHE2 1 X 1 0 0 0 þ þ X 1 1 ðX2 1Þ X1 1 X 2 1 ðX2 1Þ
0 0 0 9 Tw;in ðss2 þ 1Þ X 1 X 1 exp NTUHE2 1 X 1 = 0 Tw;in ðss2 þ 1Þ ½1 exp ðNTUHBÞ þ ; X 1 1 ðX2 1Þ þ Tw;in ðsh1 þ 1Þ
X2 X2 exp ½NTULSð1 X2 Þ ðX2 1Þ (28)
Gas temperature at entrance of low pressure boiler (evaporate):
0
0 0 80 X 1 X exp ðNTUHBÞ exp NTUHS 1 X exp NTUHS 1 X < 2 2 1 1 0 0 T5 ¼ X100 exp NTULS 1 X100 1 00 : X1 1 X 2 1 ðX2 1Þ X1 1 ½X2 exp ðNTULSð1 X2 ÞÞ 1 T0 ðs þ 1Þ Tw;in ðsh2 þ 1Þ
0 0
0 1 X 2 Tw;in ðsh2 þ 1Þ T0 ðs þ 1Þ exp ðNTUHBÞ X 1 exp NTUHE2 1 X 1 0 0 þ ½X2 exp ðNTULSð1 X2 ÞÞ 1 X1 1 X 2 1 ðX2 1Þ X100 1
0 0 1 ½X2 exp ðNTULSð1 X2 ÞÞ 1 X 1 exp NTUHE 1 X 1 0 Tw;in ðs þ 1Þ½1 exp ðNTUHBÞ þ X 1 1 ðX2 1Þ X100 1
0 0 ½X2 exp ðNTULSð1 X2 ÞÞ 1 X 1 exp NTUHE2 1 X 1 1 0 þ Tw;in ðss2 þ 1Þ X 1 1 ðX2 1Þ X100 1 0 X 00 X200 exp NTUHE1 1 X100 ½X X2 exp ðNTULSð1 X2 ÞÞ 00 00 þ Tw;in ðsh1 þ 1Þ 2 þ T w;in 1 X1 1 ðX2 1Þ X1 1
Gas temperature at entrance of low pressure economizer:
T6 ¼ T5 exp ðNTULBÞ þ Tw;in ðss1 þ 1Þ½1 exp ðNTULBÞ
(30)
The energy balance across the low pressure evaporator can be written as Eq. (31):
_ w1 L1 ¼ m _ g cpg ðT5 T6 Þ m
(31)
(29)
Therefore, the latent heat of vaporization (L1), can be expressed as Eq. (32):
L1 ¼
C2 ½1 exp ðNTULBÞ T5 Tw;in ðss1 þ 1Þ X2
L1 is simplified as Eq. (33):
(32)
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0 0 # 8X exp ðNTUHBÞexp NTUHS 1 X < 2 2 0 0 c 0 0 1 L1 ¼ 2 ½1 exp ðNTULBÞ 4X1 exp NTUHE2 1 X1 00 : X2 X1 1 X2 1 ðX2 1Þ X1 1 2
00 X1 exp NTULS 1 X100 1 ½X2 exp ðNTULSð1 X2 ÞÞ 1 0
exp ðNTUHBÞ X2 Tw;in ðsh2 þ 1Þ T0 ðs þ 1Þ 0 0 T0 ðs þ 1Þ Tw;in ðsh2 þ 1Þ þ X1 1 X2 1 ðX2 1Þ X100 1
X100 exp NTULS 1 X100 1 ½X2 exp ðNTULSð1 X2 ÞÞ 1 þ X100 exp NTULS 1 X100 1
Tw;in ðss2 þ 1Þ½1 exp ðNTHUBÞ½X2 exp ðNTULSð1 X2 ÞÞ 1 0 X1 1 ðX2 1Þ X100 1 9 X100 exp NTULS 1 X100 1 ½X2 exp ðNTULSð1 X2 ÞÞ 1= 0 ; X1 1 ðX2 1Þ X100 1
þ ðss2 þ 1Þ Tw;in
00 X1 exp NTULS 1 X100 1 ½X2 X2 exp ðNTULSð1 X2 ÞÞ c2 ½1 exp ðNTULBÞ ðsh1 þ 1Þ Tw;in X2 ðX2 1Þ X100 1 X100 X100 exp NTUHEC1 1 X100 0 þ T w;in ðss1 þ 1ÞTw;in 00 X1 1 þ
Similarly, the energy balance across the high pressure evaporator can be written as Eq. (34):
_ w2 L2 ¼ m _ g cpg ðT1 T2 Þ m
(34)
Accordingly, the latent heat of vaporization L2, can be expressed as Eq. (35):
The temperature of the flue gas at the exit of economizer (Tg,out) can be written as Eq. (38):
Tg;out ¼ T0 ðs þ 1Þ X1 ss1 Tw;in þ X2 Tw;in ðss1 þ sh1 Þ 0
0
0
0
0
þ X 1 T w;in X 2 Tw;in ðsh2 þ ss2 Þ
X2 X L 1L c2 1 c0 2
(38)
1
0
c1
½1expðNTUHBÞ 0 X1
0 80 T0 ðs þ1ÞTw;in ðsh2 þ1Þ X exp NTUHS 1X < 2 2 0 : X 2 1 9 0 = X 2 Tw;in ðsh2 þ1ÞT0 ðs þ1Þ s ð þ1Þ ð36Þ þ T s2 w;in 0 ; X 2 1
Energy balance for the entire waste heat recovery unit can be written as Eq. (37):
_ g cpg Tg;in Tg;out ¼ m _ w c1 Tsat1 Tw;in m _ w1 L1 þ c2 Tsup1 Tsat1 þm 0 _ w2 c001 T w;in Tsat1 þm 0 0 þ c1 Tsat2 T w;in þ L2
0 þ c2 Tsup2 Tsat2
0
(35)
L2 is simplified as Eq. (36):
L2 ¼
0
X100 T w;in þ X100 T w;in ðss1 þ 1Þ X 1 ðss2 þ 1Þ Tw;in
0
c1 ½1 exp ðNTUHBÞ T1 Tw;in ðss2 þ 1Þ X1
L2 ¼
(33)
Consequently, by utilizing the above-derived relation, the fth for a dual pressure HRSG, in terms of non-dimensional operating parameters can be expressed as Eq. (39):
Table 1 Cost coefficients. Heat transfer surface cost (US$ per kg)
CEC
CB
CSH
Tubes and fins Joints Welding Bending
4.21 8 2 e
4.21 8 2 e
8 e e 5
Table 2 Initial specification and turbine exhaust gas analysis.
(37)
Item
Unit
Value
Tg,in _g m CO2 H2O N2 O2
542.22 494.87 3.17 7.26 75.76 13.80
C kg/s % % % %
S. Naemi et al. / Applied Thermal Engineering 52 (2013) 371e384
fth
379
0
0 0 80 X 1 X exp ðNTUHBÞ exp NTUHS 1 X exp NTUHE2 1 X < 2 2 1 1 0 0 ¼ X1 ln ðss1 þ 1Þ þ ½1 exp ðNTULBÞ 00 : X 2 1 ðX2 1Þ X1 1 Tw;in ðss1 þ 1Þ X 1 1 00 X1 exp NTULS 1 X100 1 ½X2 exp ðNTULSð1 X2 ÞÞ 1 T0 ðs þ 1Þ Tw;in ðsh2 þ 1Þ
0
0 0 1 X 2 Tw;in ðsh2 þ 1Þ T0 ðs þ 1Þ exp ðNTUHBÞ X 1 exp NTUHE2 1 X 1 0 0 þ X100 exp NTULS 1 X100 1 00 Tw;in ðss1 þ 1Þ X 1 1 X 2 1 ðX2 1Þ X1 1
0 0 1 Tw;in ðss2 þ 1Þ½X2 exp ðNTULSð1 X2 ÞÞ 1 X 1 exp NTUHE2 1 X 1 0 ½X2 exp ðNTULSð1 X2 ÞÞ 1 þ Tw;in ðss1 þ 1Þ X 1 1 ðX2 1Þ X100 1 X100 exp NTULS 1 X100 1 ½1 exp ðNTUHBÞ
0 0 1 Tw;in ðss2 þ 1Þ½X2 exp ðNTULSð1 X2 ÞÞ 1 X 1 exp NTUHE2 1 X 1 0 X100 exp NTULS 1 X100 1 þ 00 Tw;in ðss1 þ 1Þ X 1 1 ðX2 1Þ X1 1 ) 00 Tw;in ðsh1 þ 1Þ X1 exp NTULS 1 X100 1 ½X2 X2 exp ðNTULSð1 X2 ÞÞ X100 X100 exp NTUHE1 1 X100 0 þ þ T w;in 1 ðss1 þ 1ÞðX2 1Þ X100 1 Tw;in ðss1 þ 1Þ X100 1
0 0 80 9 s s s s T X exp NTUHS 1 X ð þ 1Þ T ð þ 1Þ þ X T ð þ 1Þ T ð þ 1Þ < 2 = 2 2 w;in h2 0 0 w;in h2 0 þ ½1 exp ðNTUHBÞ 1 : ; Tw;in ðss2 þ 1Þ X 2 1 2 3 2 3 0 0 0 s ð T T þ 1Þ sh1 þ 1 s þ1 s2 w;in w;in 6 7 5 þ X 1 ln 4 þ X100 ln 4 ln ðs þ 1Þ þ NTU V * þ ðs þ 1Þ þ X2 ln 5 þ X 2 ln h2 0 ss1 þ 1 ss2 þ 1 Tw;in ðss1 þ 1Þ T w;in 0
Tw;in Tw;in T w;in 00 Tw;in 00 Tw;in 0 Tw;in 0 Tw;in 0 X s þ X ðs sh1 Þ X þ X ðs þ 1Þ X ðs þ 1Þ þ X X ðs ss2 Þ 1 T0 1 s1 T0 2 s1 T0 1 T0 1 s1 T0 1 s2 T0 1 T0 2 h2
4. Thermoeconomic optimization
(39)
The results acquired by exergy loss minimization deeply persuade HRSG manufacturers to decrease the pinch point or increase the area of heat transfer surfaces; however, it is not completely approved from economic viewpoint, as initial investment cost should also be taken into account. The economic limitation usually prevents to diminish the exergy losses. For instance, a reduction in temperature difference in heat exchangers can reduce energy losses, but requires the investment for additional heat transfer area. In this regard, a thermoeconomic optimization method is developed here to obtain optimum pinch point, considering thermal efficiency and financial consideration simultaneously. In the present study, the thermoeconomic analysis is presented to minimize the life cycle cost. Due to irreversibilities and exergy waste through the HRSG stack, a substantial proportion of input
exergy inevitably is lost. However, the exergy losses could be converted to useful form of energy in order to improve the income; therefore, the term of the exergy loss should be considered as a cost item. Rosen [21] claimed that a systematic correlation exists between capital cost and internal losses, but not between capital cost and external exergy losses or energy losses. In other words, the installation and operation costs and the exergy losses cost which are playing against each other, should be restricted simultaneously. To achieve this, a thermoeconomic objective function will be defined to minimize total cost. In this regard, both stated terms should be calculated separately over a specific operational time period. Hence, the cost due to exergy losses is computed annually, and the initial investment cost is broken to HRSG’s life time. To obtain the costs related to exergy losses, it should be recasted to HRSG operative costs. For this aim, a proper formula should be presented as Eq. (40):
Table 3 Fixed design parameters of tubes.
Table 4 Fixed design parameters of fins.
Section
Outer diameter (m)
Inner diameter (m)
Transferred pitch (m)
Longitudinal pitch (m)
Section
Number of fins per meter
Height (m)
Thickness (m)
HSH HB HEC2 HEC1 LSH LB LEC
0.051 0.051 0.038 0.038 0.051 0.051 0.038
0.045 0.045 0.032 0.032 0.045 0.045 0.033
0.108 0.108 0.089 0.089 0.108 0.108 0.089
0.135 0.135 0.111 0.111 0.135 0.135 0.111
HSH HB HEC2 HEC1 LSH LB LEC
243.46 251.89 241.77 250.35 199.21 221.46 205.94
0.019 0.019 0.016 0.016 0.019 0.019 0.019
0.001 0.001 0.001 0.001 0.001 0.001 0.001
380
S. Naemi et al. / Applied Thermal Engineering 52 (2013) 371e384
0.8
40 Exergetic efficiency
35
Energetic efficiency 0.78
Gas Pressure Drop (kPa)
Energetic and Exergetic Efficiencies
0.79
0.77 0.76 0.75 0.74 0.73
30 25 20 15
0.72
10
0.71
5
0.7
0
5
10
15
20
25
30
0
Pinch Point (° C)
0
5
Fig. 3. Energetic and exergetic efficiency vs. pinch point (P ¼ 90 bar).
_ g cpg T0 tfth CI ¼ cI m
In above equation, Cost is cost of each heat transfer section. Costs of economizers have been calculated by Eq. (43):
(43)
Costs of evaporators (boilers) have been also calculated with equation similar to economizers, but costs of superheaters have been estimated in different ways by Eq. (44):
(44)
And in above equation Nb can be calculated by Eq. (45):
Nb ¼ Nw ðNd 1Þ
25
Coefficients shown in above equations are extracted by MAPNA Boiler Company [23] as listed in Table 1. Hence, the total cost of HRSG can be written as Eq. (46):
CHRSG ¼ TCI AF
(46)
In which Annuity Factor (AF) stands for the capital recovery factor, which may be found by Eq. (47):
AF ¼
ið1 þ iÞn ð1 þ iÞn 1
(47)
where i is the rate of return (interest rate), and n is the total operating period of the system in years. Finally, thermoeconomic objective function can be defined by Eq. (48):
fEC ¼
CI þ CHRSC _ g cpg T0 m
(48)
5. Results and discussion
(41)
PEC ¼ CostLE þ CostLB þ CostLS þ CostHE1 þ CostHE2 þ CostHB þ CostHS (42)
CostS ¼ CostS;m MS þ CostS;b Nb
20
(40)
where a is normally between 4.12 and 8.09 [22]. In this study, a is assumed 5.2 considering data provided by MAPNA Boiler Company [23]. Purchased equipment cost is defined as Eq. (42):
CostE ¼ CostE;m ME þ CostE;j ME;j þ CostE;w þ LE;w
15 Pinch Point (°C)
Fig. 4. Pressure drop vs. pinch point.
where cI represents the specific cost of exergy losses and t is the annualized number of the operation hours of the unit. To define the specific cost of the exergy loss, (cI) a variety of strategies can be observed. It is not realistic to assume cI as the price of fuel, because the conversion efficiency should be taken into consideration. One approach is to consider the cost of exergy losses equal to the cost of fuel divided for mean efficiency of the power plant (about 50%). Another approach [15] is to consider it as the price of electricity. The total capital investment (TCI) of HRSG consists of different items such as, purchased equipments costs (PEC), piping, instrumentation and controls, electrical equipment and materials, construction costs, civil, structural and architectural work, installation costs, land, service facilities, engineering and supervision, startup cost, licensing, research and development, tax, transportation, etc. Although, these factors directly influence the HRSG cost, it is not possible to have a specific formula to cover them all, since they depend on different parameters. Therefore, all above costs have been considered as a percentage of PEC [22]. Accordingly, total capital investment can be calculated by Eq. (41):
TCI ¼ a PEC
10
(45)
As previously stated, an attempt is made to present optimum thermodynamic and thermoeconomic design of a dual pressure HRSG coupled with a V94.2 Siemens gas turbine, using nondimensional parameters. Table 2 indicates the specifications of Table 5 Non-dimensional parameters at optimum design. HP drum pressure (bar) Optimum pinch point (C) NTUHS NTUHB NTUHE2 NTUHE1 NTULS NTULB NTULE X1 X1ʹ X1ʺ X2 X2ʹ
s sh1 sh2 ss1 ss2
75 2.5 3.692 4.243 3.056 1.964 12.41 2.419 2.461 0.599 0.5824 0.5247 0.05077 0.317 1.83 0.762 1.765 0.5549 0.9563
80 2.2 3.731 4.347 3.122 2.021 12.26 2.478 2.513 0.6006 0.5852 0.5232 0.05268 0.3209 1.83 0.7683 1.766 0.5549 0.9719
85 2.14 3.68 4.351 3.116 2.029 11.86 2.479 2.505 0.6022 0.5874 0.5215 0.05457 0.3253 1.83 0.7714 1.763 0.5549 0.9867
90 2.1 3.627 4.354 3.11 2.037 11.5 2.481 2.498 0.6038 0.5898 0.52 0.05636 0.3298 1.83 0.7741 1.761 0.5549 1
S. Naemi et al. / Applied Thermal Engineering 52 (2013) 371e384 Table 6 Input data for thermoeconomic analysis.
Thermodynamic Objective Function
0.27 P=90 bar P=85 bar P=80 bar P=75 bar
0.26
381
0.25
Parameter
Value
cI,Fuel cI,Electricity t
0.0262 ($/kWh) 0.08 ($/kWh) 7000 (h) 0.48 0.124 30 (years)
hCCPP i n
0.24 0.23
Fig. 4 indicates the gas side pressure drop versus pinch point. It can be clearly seen that, the gas side pressure drop exponentially rises by increasing heat transfer areas in order to obtain lower pinch point temperature. In order to obtain the optimum operation, the effect of operating parameters on the HRSG performance must be known. In this regard, the influence of non-dimensional parameters on thermodynamic objective function is highlighted in this section. Table 5 depicts the value of non-dimensional parameters at optimum design condition for four working pressure of HP drum. Fig. 5 reveals variation of thermodynamic objective function versus the pinch point. As it shows, the optimum pinch point decreases slightly by increasing the pressure of HP drum. Among non-dimensional parameters, NTUHB and NTULB are playing most significant roles, as the evaporator is the main source of exergy destruction. Furthermore, NTULE is another critical parameter, considering the exergy waste of the stack. Fig. 6a and b presents the variation of fth versus NTUHB and NTULB respectively. It is shown that, the fth tends to approach clearly a minimum value at a particular NTUHB and NTULB, and then shows an upward trend. This suggests that for a particular gas flow and water/steam conditions, at a particular NTUHB and NTULB, the temperature profiles (DT) and pressure drop (DP) in the unit are such that, the overall irreversibility is minimum.
0.22 0.21 0.2
0
5
10
15 Pinch Point (°C)
20
25
Fig. 5. Thermodynamic objective function vs. pinch point.
gas turbine exhaust gas at full load. In CCPPs, a preheater using waste heat is usually employed to increase the feed water temperature from condensation temperature, so inlet temperature of water is also assumed 129 C; however, the preheater itself is not considered here. The tube and fins design specifications also are reported in Tables 3 and 4, respectively. Fig. 3 represents the effect of pinch point on the first and second law efficiencies of the HRSG. Accordingly, although the energetic efficiency always has a downward trend by increasing the pinch point, the exergetic efficiency hits a maximum value at approximately 1.5 C. In other words, up to the peak point, the exergy loss due to pressure drop dominates, whereas after that point, the exergy loss of heat transfer process outweighs.
a
0.26
0.32
Thermodynamic Objective Function
Thermodynamic Objective Function
0.34
0.3 0.28 0.26 0.24 0.22 0.2 2.5
3
3.5
4
4.5 5 NTUHB
5.5
6
6.5
7
b
0.25
0.24
0.23
0.22
0.21
0.2 1.5
2
2.5
3
3.5
4
NTULB
c
0.224 Thermodynamic Objective Function
0.222 0.22 0.218 0.216 0.214 0.212 0.21 0.208 0.206 0.204
1
1.5
2
2.5 NTULE
3
3.5
4
Fig. 6. (a) Thermodynamic objective function vs. number of transfer units of high pressure boiler (evaporator) (NTUHB). (b) Thermodynamic objective function vs. number of transfer units of low pressure boiler (evaporator) (NTULB). (c) Thermodynamic objective function vs. number of transfer units of low pressure economizer (NTULE).
S. Naemi et al. / Applied Thermal Engineering 52 (2013) 371e384
a
a
0.2
4.5
Electricity Cost HRSG Cost
0.55 0.324 0.5
0.32 0.316
0.45
0.312
18 20 22 24 26 28
4
0.15
3.5
0.1
0.4 0.35 0.05
0.65
5
10
15 Pinch Point (°C)
20
25
8
10
12
14
16 18 20 22 Optimum Pinch Point (°C)
0.315 0.5
0.31 16 18 20 22 24 26
0.45
0.15
4.5 6
0.32 0.55
3
28
Electricity Cost HRSG Cost Electricity Cost ($ / kWh)
0.6
26
b
0.2
b Based on electricity cost Based on fuel cost
24
HRSG Cost (x 10 $)
0
Thermoeconomic Objective Function
6
Based on electricity cost Based on fuel cost
0.6
Electricity Cost ($ / kWh)
Thermoeconomic Objective Function
0.65
HRSG Cost (x 10 $)
382
0.1
4
0.05
3.5
0.4 5
0.35
0
5
10
15 Pinch Point (°C)
20
25
Fig. 7. (a) Thermoeconomic objective function vs. pinch point (HP ¼ 75 bar). (b) Thermoeconomic objective function vs. pinch point (HP ¼ 90 bar).
Fig. 6c reveals the variation of thermodynamic objective function with NTULE. The results show that, the fth tends to approach clearly a minimum value at a particular NTULE and then shows an exponential upward trend. This suggests that for a particular gas flow and water/steam conditions, there is a particular NTULE, where the overall irreversibilities reach a minimum value. Before the minimum point, more heat is absorbed from the flue gas by increasing NTULE, which causes lower temperature of the flue gas
10
15 20 Optimum Pinch Point (°C)
25
3 30
Fig. 9. (a) Electricity price vs. optimum pinch point (P ¼ 75 bar). (b) Electricity price vs. optimum pinch point (P ¼ 90 bar).
at the exit of HRSG, and consequently lower irreversibilities; however, after that point, the irreversibility of heat transfer outweighs the irreversibility of pressure drop. The aim of thermodynamic optimization is to achieve the maximum output from exergy inflow; hence, more heat transfer surfaces should be employed to minimize the irreversibilities. From thermoeconomic viewpoint, whenever the benefit of increasing heat transfer areas outweighs the cost, it is advised to use larger surfaces, because the target of thermoeconomic optimization is to gain more profit. In other words, the revenue of extra electricity generation by
Fig. 8. HRSG layout under study.
S. Naemi et al. / Applied Thermal Engineering 52 (2013) 371e384
0.32
3.6
3.5
0.28
3.4
0.26
3.3
0.24
3.2
6
HRSG Cost (x 10 $)
0.3
3
Fuel Price ($ / m )
Fuel Price HRSG Price
0.22 18
19
20
21 22 23 Optimum Pinch Point (°C)
24
3.1 25
383
for the design, clearly where the total irreversibility is low. Additionally, the results present that, thermodynamic objective function reaches a minimum point at a particular NTULE, where the overall irreversibility of heat transfer and pressure drop is at least amount. Obviously, increasing the area of heat transfer surfaces increases the initial investment cost of HRSG, and by contrast decreases the exergy losses. In other words, capital cost and exergy losses cost should be considered simultaneously to find the trade-off pinch point between them. Accordingly a comprehensive thermoeconomic optimization has been proposed to obtain the financially optimum design. In this regard, the exergy loss is converted into cost based on electricity price and also fuel price. Thermoeconomic analysis offers pinch points about 22 C to minimize the HRSG cost, whereas thermodynamic analysis suggests pinch points about just only 2 C to minimize exergy losses. Additionally, as expected the optimum pinch point reduces by increasing the working pressure of HP drum from 75 bar to 90 bar.
Fig. 10. Fuel price vs. optimum pinch point (P ¼ 90 bar).
Appendix A the steam turbine has to compensate the extra expenses of heat transfer materials in order to decrease the pinch point. As previously mentioned, exergy losses should be considered as a cost to perform thermoeconomic analysis. In this regard, two strategies are used to adapt exergy loss to the cost form. In the first strategy, exergy price is considered as the price of fuel divided for exergetic efficiency of the HRSG. As the role of boiler is to convert the fossil fuel energy into steam, the HRSG exergy loss could be used the same as the steam; therefore, it can be a novel and justifiable strategy to cost exergy loss. In the second strategy, exergy loss cost is considered as the multiple of electricity price to CCPP’s energetic efficiency. This strategy is valid because the exergy loss could have been converted to electricity by means of the steam turbine. Table 6 depicts input data which are considered for the thermoeconomic analysis. It should be stated that, the natural gas price is considered 0.25 $/m3 equal to 0.0262 $/kWh. Fig. 7a and b illustrates the variation of thermoeconomic objective function versus HRSG pinch point for 75 bar and 90 bar, regarding both strategies. As can be clearly seen, optimum pinch point is 20.6 C (for 75 bar) and 19.2 C (for 90 bar) based on electricity price, and 25.4 C and 23.7 C based on fuel price. It seems that, the optimum pinch point based on thermoeconomic optimization is more reliable. Fig. 8 reveals the temperature of water/steam side under optimum thermoeconomic condition at electricity price strategy for HRSG at 90 bar. Fig. 9a and b depicts the optimum pinch point design of different electricity prices. HRSG cost for different pinch points is also compared. Additionally, Fig. 10 indicates the optimum design pinch point of different fuel prices.
6. Conclusion Depletion of fossil fuels and global warming accelerate activities to improve design guidelines for thermal power plants. Applying first and second laws of thermodynamics together with economic analysis, make a powerful tool to evaluate thermal systems. This research deals with thermodynamic and thermoeconomic analyses and optimization of a dual pressure HRSG coupled with a heavy duty gas turbine. In this regard, an attempt has been made to highlight how non-dimensional operating parameters can affect proposed thermodynamic objective function. It has been observed that for a particular non-dimensional hot flue gas inlet temperature difference ratio, thermodynamic objective function is minimized at particular NTUHB and NTULB suggesting a possible optimum value
The equations to calculate the heat transfer coefficients and other coefficients that expressed in paper are taken from Ref. [19] which are listed as following: Nusselt number or convective heat transfer coefficient inside the tubes:
Nu ¼ 0:023Re0:8 Pr0:4 where: Re: Reynolds number, Pr: Prandtl number, k: thermal conductivity [W/m K]. Outside convective heat transfer coefficient:
hc ¼ C1 C2 C3
d þ 2h d
0:5 0:25 0:67 Tg k Gcpg mcp;g Ta
where C1, C2, C3 are defined in Ref. [19] and m is viscosity (Pa s). Nonluminous heat transfer coefficient:
hN ¼ sεg
4 Tg4 Tout
!
Tg Tout
The method for calculating εg is reported in Ref. [19].
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