rb

urkKo

Cost methods

oeca td fon czinma

power (30 MW) and for variable steam mass, and for variable power and steam mass by using the cost

combind corovidealysesles th

sied mainly as thermoeconomic evaluation and optimization,exergetic cost theory, thermoeconomic functional analysis andengineering functional analysis methods.

by Valero, TorresTsatsaronis, Tsat-e exergoeconomicd it to the CGAMcycle) and showed. Iterative exergo-timizing cost and

efciency of a thermal system. Specic costs and average costs arethe two submethods of the iterative exergoeconomic optimizationmethod [10e12].

In the 1990's a group of exergoeconomists (C. Frangopoulos, G.Tsatsaronis, A. Valero, M. von Spakovsky) compared their meth-odologies by solving a predened problem which is known asCGAM problem produced from the initials of their names. The pa-rameters of CGAM system to facilitate the comparisons betweenexergy-costing methodologies presented by Valero et al. [13].

* Corresponding author. Tel.: 90 262 303 34 06; fax: 90 262 303 30 03.E-mail addresses: rabikar@gmail.com (R. Karaali), ilhan@kocaeli.edu.tr

(_I.T. Oztrk).1

Contents lists availab

Ener

journal homepage: www.els

Energy 80 (2015) 474e485Tel.: 90 458 211 1178; fax: 90 458 211 1172.nomic methods [1e3].Thermoeconomic methods are based on algebraic and calculus

methods. The average costs can be obtained by using the algebraicthermoeconomic methods that use cost equations for eachcomponent. The calculus methods that use differential equationsfor each component and stream, allows us to obtain exergetic costsand marginal costs [4e6]. Thermoeconomic methods can be clas-

Exergetic cost theory, which was developedand Lozano uses an average cost approach [9].saronis and Moran [10,11] developed an iterativoptimization method in the 1990's, and applieproblem (air preheated gas turbine cogenerationhow to minimize exergy related costs of a systemeconomic optimization method is based on opeconomically. Exergy destruction, and cost ow in the componentsof the cycles can be traced and understood by using thermoeco-

plications of this method for some other cycles are shown in theirdifferent articles.1. Introduction

Thermoeconomic analysis, whichmethods for analyzing thermal aconvenient methods, because they pthermal cycles. Thermoeconomic anunderstand the behavior of cychttp://dx.doi.org/10.1016/j.energy.2014.12.0040360-5442/ 2014 Elsevier Ltd. All rights reserved.0,0432 $/kWh for simple cycle, 0,0514 $/kWh for inlet air cooling cycle 0,0577 $/kWh for air preheatedcycle and 0,058 $/kWh for air-fuel preheated cycle by using cost equations method.

2014 Elsevier Ltd. All rights reserved.

ne exergy and economicgeneration plants, aredetailed insight aboutare very important toermodynamically and

Rosen [7] has reviewed the methods that combine thermody-namics and economics such as exergoeconomy, thermoeconomy,exergetic costing, etc. He critically reviewed relations betweenexergy and economics and exergy based economic methods. Rosen[7], and Rosen and Dincer [8] have developed a new method calledexergy-cost-energy-mass (EXCEM) analysis. This method is basedon the balance of mass, energy, exergy and cost. In addition, ap-ThermoeconomicOptimization global optimization, the optimum electricity costs which also correspond to minimum are obtained asKeywords:Cogeneration equation method and the effect of size on equipment method. The results obtained by the effect of size

on equipment and by the cost equations methods are very different from each other. For the case ofThermoeconomic optimization of gas tu

Rabi Karaali a, 1, _Ilhan Tekin Oztrk b, *

a Bayburt Univ., Engineering Faculty Mechanical Engineering, 69000 Merkez, Bayburt, Tb Kocaeli Univ., Engineering Faculty Mechanical Engineering, Umuttepe Kamps, 41380

a r t i c l e i n f o

Article history:Received 14 August 2013Received in revised form30 November 2014Accepted 2 December 2014Available online 3 January 2015

a b s t r a c t

In this study, a novel thermcycles is introduced. First,search method is improvemethod to four cogeneratiopreheated cycles for analyconstant power and steamine cogeneration plants

eycaeli, Turkey

onomic optimization method that is simple and efcient, for real complexhermoeconomic analysis method that is called non-linear simplex directr the purposes of this study. The objective of this paper is to apply thisycles that are simple cycle, inlet air cooling cycle, air preheated and air-fuelg and optimizing. The four cycles are thermoeconomically optimized forss (30 MWand 14 kg/s saturated steam ow rate at 2000 kPa), for constant

le at ScienceDirect

gy

evier .com/locate/energy

EnerNomenclature

C compressorC cost ($)_c cost per unit of exergy ($/kJ)CC combustion chamberCOP coefcient of performancee,e specic exergy (kJ/kg), (kJ/kMol)_E exergy ow rate (kW)EQ equipment

h,h specic enthalpy (kJ/kg), (kJ/kMol)IN indexJ generatorLHV lower heating value (kJ/kg)LMTD logarithmic mean temperature difference_m mass ow rate (kg/s)M molecular weight (kg/kmol)P pressure (kPa)_Q heat ow rate (kW)

R ;R universal gas constant (kJ/kmol K), specic gasconstant (kJ/kg K)

r compressor pressure rates,s specic entropy (kJ/kg K), (kJ/kmol K)T temperature (K)_W power (kW)

R. Karaali, _I.T. Oztrk /Erlach et al. [14], demonstrated that the most developed ther-moeconomic optimization and cost accounting methodologies, asall of them employ thermoeconomic models that can easily belinearized, can be dealt with by the mathematical formalism ofstructural theory.

In recent years Kwon et al., Kwak et al. [15,16], Lazzaretto et al.[17,18] and Tsatsaronis et al., and Koch et al. [11,12] have used searchalgorithms (genetic, evolutionary) for exergo-economic analysis.Lazzaretto and Tsatsaronis [18] showed that multi-objective evolu-tionary algorithms are powerful and effective methods to optimizethermal systems. The thermoeconomic functional analysis method,developed by Frangopoulos [19], uses an optimization method thatemploys marginal costs. These methods use a set of linear exergyequations that dene the objective function of each component.

Lazzaretto and Tsatsaronis [18] have introduced SPECO (specicexergy costing) method in which the product and the fuel of acomponent is dened and then its exergy and costs are calculated.Cost balances for each component and auxiliary costing equationsare taken under consideration for exergoeconomic evaluation orLagrangian-based approaches. The basic principle of SpecicExergy Costing method is to evaluate local average costs of exergyof each stream and the variations in cost. Identication of exergystreams, denition of fuel and product and obtaining cost equationsare the main steps of SPECO method. SPECO method also includesSAA (structural analysis approach) , LIFOA (last in rst outapproach), EFA (engineering functional analysis), EEA (exergyeconomics approach), FEA (rst exergoeconomic approach), (ther-moeconomic functional approach) (TFA) and ECT (exergetic costtheory) [6,12e14,18e22].

x mole fraction (kmol/kmol)

Greek lettersh efciency

l constantSubcriptsaph air preheaterC compressorCC combustion chamberch chemicalCI capital investmentD destructionec economizerex exergyexh exhaustev evaporatorf fuelHRSG heat recovery steam generatorhe heat exchangeri i. mixture componenti; ch i. mixture component, chemicalL losslm logarithmic mean temperature differenceOM operating and maintenanceP productph physicalpreh preheatedref referenceR recuperators isentropicst steam

gy 80 (2015) 474e485 475Kim et al. [23], have introduced MOPSA (modied productivestructure analysis) methodwhere an exergy costingmethod is usedwithout ow-stream cost calculations. For the entire system a set ofequations for the unit exergy costs are obtained by assigning a unitexergy cost for the cost balance equation for each component.Kwon et al. [15], compared SPECO andMOPSAmethods by applyingthem to the CGAM problem.

C.Frangopoulos [19] developed a Lagrangian method that iscalled Thermoeconomic Functional Approach (TFA) where thesystem is optimized as a Lagrangian function. This method is notconvenient for increasing number of components unless the systemis decomposed into subsystems.

Valero et al. [9], developed a Lagrangian method named Exer-getic Cost method based on fuel-product-entropy matrixes. In thismethod, the system is decomposed into subsystems and theirLagrangian functions are optimized.

Vieira et al. [24], introduced a new process simulation programbased on the cost equations that were proposed by Lazzaretto andTsatsaronis [18]. Tsatsaronis and Moran [11] have showed that thecost equations cannot provide current cost for purchasing equip-ment of the thermal system.

Hua et al. [25], Munoz and Spakovsky [26] and Lazzaretto et al.[17], have analyzed the decomposition of complicated thermalsystems in exergoeconomic analysis and optimization and appliedit to appropriate examples by nding local and then global optima.

Alvarado and Gherardelli [27], have presented a newLagrangian approach based on the exergetic efciency and theelasticity for the selection of the components of the CGAMproblem.

sys systemT turbinetot totalw equipment item0 environment conditions1 compressor inlet state2 compressor outlet state

adding recuperators and an absorption cooling system in thesample cycle, the four cycles are obtained and analyzed. The rstcycle that is called simple cycle is shown in Fig. 1. In this cycle, thecompressed air of the outlet of the compressor enters the com-bustion chamber and after the combustion, the exhaust gases areexpanded in a gas turbine to obtain work. Some of the thermalenergy of the exhaust gases of the outlet of the gas turbine is usedto obtain steam in a heat exchanger. The second cycle that is calledinlet air cooling cycle, is shown in Fig. 2. In this cycle, the ambientair is taken into an absorption cooling system to cool the air byusing exhaust heat energy. The cooled air is compressed and afterthat, the cycle works as the simple cycle explained above. The thirdcycle that is called air preheated cycle, is shown in Fig. 3. In thiscycle, the compressed air is heated by the hot exhaust gases at the

formation in the exhaust, the outlet temperature of the heat re-covery steam generator is taken as 400 K. It is assumed that the

Energy 80 (2015) 474e485Ahmadi and Dincer [28], developed exergoenvironmentalanalysis and optimization by using MGA (Multimodal Genetic Al-gorithm) for a cogeneration plant. In their study, cost equations ofthe equipment (cost functions) are used, and NOx and CO2 emis-sions are taken into consideration. They found that increasing theturbine inlet temperature, and the isentrophic efciencies of thecompressor and the gas turbine decreases fuel consumption andexergy destruction of the cycle. Agudelo et al. [29], have introduceda new methodology named allocation of waste cost. They haveobtained the denition of the ratios of thewaste cost distribution touse in thermoeconomic analysis. Kim [30], introduced a newthermoeconomic methodology for energy systems. To evaluate theworth of each product, wonergy as a new term is dened, and thegradient search technique is used in his study.

There are two groups of approaches in formulating auxiliarycosting equations and efciencies. The rst one is the Lagrangianbased approaches that aim optimization of the overall system andthe second one is the Exergoeconomic Accounting methods thatuse iterative optimization of the system or components. There is asignicant need for using a clear and efcient thermoeconomicprocedure for optimizing energy systems. Our main goal is todevelop an appropriate thermoeconomic iterative optimizationmethod for the overall system.

Thermoeconomic evaluation has two competing objectives thatareminimizing cost andmaximizing efciency. In the literature, theoptimization of the CGAMproblem is solved by nding local optimafor the constant power and steam mass (30 MW and 14 kg/s steamat 2000 kPa).

In the literature thermoeconomic optimization of thermal sys-tems is mostly performed for a constant power production. Thismeans that answers to the question What are the optimumworking conditions for a thermal system to produce the constantpower? are sought. However, in order to nd global optimumworking conditions of the system, the question should be set aswhat are the optimumworking conditions for a thermal system toproduce power? It is clear that, the answers of the rst questiondeal with the local optima of the system. However, the answer ofthe second question is about the global optimum. With the infor-mation about the global optimum at hand, we have a better insighton the working conditions of the thermal system that gives themaximum benets.

In this study, the simple cycle, the inlet air cooling cycle usingthe absorption cooling, the air preheated cycle and the air-fuelpreheated cycle are analyzed and optimized thermoeconomicallyby using non-linear simplex direct search method that is improvedby the authors of this study. By taking variable parameters of thesystems that are explained in the literature for CGAM (air pre-heated) cycle [31], iterative optimization process is performed forthe four cycles that are explained below. In our analyses, enthalpiesand entrophies are taken as functions of temperature and pressure,which are non-linear equations, and then themathematical modelsas a function of temperature of the four cycles are obtained. Thesemodels have been simulated with computer programs generatedby the authors using FORTRAN codes. All working conditions, suchas compression rates, excess air rates, recuperator outlet temper-atures, isentropic efciencies of the compressors and the turbinesand the capacities of the devices of the systems are taken intoconsideration and the performance characteristics obtained.

2. Description of the cycles

The four cycles are gas turbine cogeneration cycles withdifferent designs, and are obtained by adding different componentsto them. Adding any component into a cycle affects all the working

R. Karaali, _I.T. Oztrk /476conditions and the characteristics of the cycle. In this study bypressure drops in the combustion chamber is 5%; in the HRSG (heatrecovery steam generator) is 5%; in the air pre-heater air side is 5%and in the air pre-heater gas side, 3%. The environmental conditionsare taken to be xed with the following values: T0 T1 298.15 Kand P0 101.3 kPa. The mass ow rate for the air compressors andfor the saturated steam at 2000 kPa for the HRSG, are _m1 91.4 kg/s, _mst 14 kg/s respectively. The electricity power production of theturbine is 30MWand the mass ow rate of methane as combustionchamber fuel is _mf 1.64 kg/s.recuperator and then enters into the combustion chamber. The hotgases, which exit from the combustion chamber, expand in the gasturbine. After that, they are further cooled down by providing theirheat content at the recuperator and the heat recovery steamgenerator. The fourth cycle that is called air-fuel preheated cycle isshown in Fig. 4. In this cycle, the compressed air and the fuel isheated by the hot exhaust gases at the recuperator and then entersinto the combustion chamber. After that, the cycle works as the airpreheated cycle that is explained above [31e33].

3. Analysis of the cycles

3.1. Thermodynamic analyses of the cycles

In this section, thermodynamic analyses of each component ofthe cycles introduced in the previous section are performed and themathematical models used in these analyses are explained. Theworking uid is assumed to be an ideal gas; the cogenerationsystems operate at steady state; natural gas is taken as methane,the combustion is complete and N2 is inert and heat losses from thecombustion chamber are 2% of the fuel's LHV and all other com-ponents operate without heat loss [31,32,34]. Kinetic and potentialenergy effects are ignored. In order to avoid corrosive sulfuric acidFig. 1. Simple cycle.

h2 h2s h1hs;C

h1 (7)

T2 can be found from h2 by solving equation (1). The work of thecompressor can be found as follows.

_WC _m1h2 h1 (8)The exergy balance equation can be written as

_ED;C _E1 _E2 W:

C (9)

Exergetic efciency of the air compressor is,

hex;C _E2 _E1

_WC(10)

R. Karaali, _I.T. Oztrk / Energy 80 (2015) 474e485 477The compressor and the turbine operate adiabatically. Theisentropic temperature of the gas turbine, the compressor outlet,the combustion chamber outlet, the recuperator exhaust side outletand the heat recovery steam generator inlet exhaust side arecalculated by inserting specic entropy expressions for N2, O2, CO2and H2O taken from Ref. [31]. In addition, the entropies of thestreams are calculated from the same reference. The thermody-namical model and optimization procedure is applied step by stepfor the CGAM cycle (air preheated cycle) as follows.

Specic enthalpies and specic entropies are calculated for eachstream from the equations that are given in Ref. [31] and Table 1.

hi f Ti; Pi (1)

si f Ti; Pi (2)

_E _Eph _Ech (3)

_Eph _mh h0 T0s s0 (4)

_Ech _mM

Xxiei;ch RT0

Xxi ln xi

(5)

- Compressor

T2s can be found from the s1 by solving equation (2) taken fromRef. [31].

Fig. 2. Inlet air cooling cycle.S1 S2 (6)

h2s is calculated from equation (1). Then h2 can be found.

Fig. 3. Air preheated cycle.- Recuperator

h3 and s3 can be found from equations (1) and (2) respectively,for a given T3 which is the inlet temperature of the recuperator. Theenergy balance of the recuperator is,

_m5h6 h5 _m2h2 h3 (11)The exergy balance equation can be written as,

_ED;R _E2 _E3 _E5 _E6 (12)Then the exergetic efciency of the recuperator is,

hex;R _E3 _E2_E5 _E6

(13)

- Combustion chamber

The chemical reaction in the combustion chamber can bewritten as follows [29].

lCH4 0:7748N2 0:2059O2 0:0003CO2 0:019H2O/

1 lxN2N2 xO2O2 xCO2CO2 xH2OH2O

(14)

xN2 0:77481 l (15)Fig. 4. Air-fuel preheated cycle.

stan

EnerxCO2 0:0003 l

1 l (16)

xH2O 0:019 2l

1 l (17)

xO2 0:2059 2l

1 l (18)

The mass balance of the combustion chamber is,

_m3 _m10 _m4 (19)

Table 1Variation of specic enthalpy and entropy with temperature at 1 bar for various sub

SubstanceM(kg/mol)

ForTmax>T>T0(K)

CH4 16,043 298,15-2000

CO2 44,01 298,15-3000

H2O (g) 18,015 298,15-2000

H2O (l) 18,015 298,15-500

N2 28,013 298,15-3000

O2 31,999 298,15-3000

R. Karaali, _I.T. Oztrk /478and the heat loss can be written as,

_QL;CC 0:02 _mfuelLHVCH4 (20)The energy balance equation of the combustion chamber is,

_m3h3 _m10h10 _m3 _m10h4 _QL;CC (21)

where T4 can be calculated from hexh h4 by using equation (1) andthen s4 can be found from equation (2) taken from Ref. [31]. Theexergy balance equation can be written as,

_ED:CC _E3 _E10 _E4 (22)

and the exergetic efciency of the combustion chamber is,

hex;CC _E4

_E3 _E10(23)

- Gas turbine

T5s can be found from s4 by solving equation (2) taken fromRef. [31].s4 s5s (24)

h5s is calculated from equation (1). Then h5 can be found from;

h5 h4 hs;Th4 h5s

(25)

T5 can be found from h5 by solving equation (1). The net workobtained from the gas turbine is,

_Wnet;T _m4h5 h4 _WC (26)

By neglecting heat transfer to ambient, the energy and theexergy balance equations of the gas turbine are;

ces that taken from reference [31].

h0 (kJ/kmol), s0 (kJ/kmol K)y10-3T , (T (K))

h0 103 81;242 11;933y 77;647 y220;142 y1 18;414 y

3

3

s0 96;731 11;933 lnT 77;647 y 0;142 y22 18;414 y2

2

h0 103 413;886 51;128y 4;368 y22 1;469y1

s0 87;078 51;128 lnT 4;368 y 1;469 y22h0 103

253;871 34;376y 7;841 y22 0;423 y1

s0 11;750 34;376 lnT 7;841y 0;423 y22h0 103

289;932 20;355y 109;198 y22 2;033y1

s0 67;147 20;355 lnT 109;198y 2;033 y22h0 103

9;982 30;418y 2; 544 y22 0;238 y1

s0 16;203 0;418 lnT 2;544y 0;238 y22h0 103

9;589 29;154y 6; 477 y22 0;184 y1 1;017 y

3

3

s0 36;116 29;154 lnT 6;477y 0; 184 y22 1;017 y2

2

gy 80 (2015) 474e485_m4h4 _m5h5 _WC _Wnet;T (27)

_ED;T : _E4 _E5 _WC _WT (28)

And the exergetic efciency of the gas turbine is,

hex;T _Wnet;T _WC

_E4 _E5(29)

For the recuperator h5 is known and h6 can be calculated fromequation (11). T6 can be found from equation (1).

- Heat recovery steam generator (HRSG)

T7, T8 and T9 are known, so h7, h8, h9, s7, s8 and s9 can becalculated by using equations (1) and (2). The energy balanceequation of the HRSG is,

_m8h9 h8 _m6h6 h7 (30)

The exergy balance equation can be written as,

_ED:HRSG: _E6 _E7 _E8 _E9 (31)

The exergetic efciency of the HRSG is,

ket input parameters for the cost calculation, the third one is total

EnerCref :;year Cref _Enet= _Eref (37)

arevenue requirement calculation and the fourth one is levelizedproduct cost calculation [31]. Estimation of total capital investmentis a one-time cost, and includes xed capital investment that hasdirect and indirect costs elements. The direct costs are the costs of allmaterials, equipment and other resources and the indirect costs arethe expenses needed to complete the project, such as workingcapital, start up costs, research and development costs. Threemethods are used for cost estimating of purchased equipment:estimating charts, calculation effect of size on equipment cost andcost indices. In our analysis, the cost is based on the effect of size onequipment cost named costing method A and, the cost equations ofthe equipment named costing method B that are given below[31,35e38]. The values are taken from CEPCI cost index that is takenfrom the web site of Chemical Engineering Plant Cost Index [39].

CEQ Cref 2012 CEPCI EQ : IN:=1994 CEPCI EQ : IN: (36)The effect of size on equipment cost method named costing

method A, can be calculated from:hex;HRSG _E9 _E8_E6 _E7

(32)

- Absorption cycle

For this component, LiBr-water is used as working pair and COP(coefcient of performance) is taken as,

COP 0,70 (33)

- Overall balance equations for the cycles

The overall energy balance of the system is,

m1h1 _m10LHVCH4 _QL;CC _m7h7 Wnet;T _m8h8 h9 0(34)

The exergetic efciency of the cycles is,

hex _Wnet;T

_E9 _E8

_E10

(35)

3.2. Thermoeconomic analysis of the cycles

Thermoeconomy uses exergy and economic analysis methodsthat are called exergetic cost minimization methods. Effects of theinefciencies and the destruction of exergy on the cost of eachcomponent can be analyzed with the thermoeconomic methods.For the design of thermal systems, thermoeconomic analysis is veryimportant. Thermoeconomic analysis considers each product cost,entropy generation and exergy streams costs, optimization vari-ables of each component and optimization variables of overallsystem. In our analysis, the Cost Levelization Approach is used todetermine the cost variation with time [1].

The revenue requirement method is applied for economic anal-ysis and for main product cost calculation of the thermal systems.The main four steps of the revenue requirement method are asfollows: the rst one is estimating the total capital investment, thesecond one is determining economic, operating, nancial and mar-

R. Karaali, _I.T. Oztrk /The superscript a in the above equation is a scaling exponent.Details of the calculations of the revenue requirement method forCC CC1 _mair=CC2 hs r ln r (42)The cost equation for the combustion chamber:

CCC CCC1 _mair=CCC2 p4=p3 1 expCCC3:T4 CCC4(43)

The cost equation for the gas turbine:

CT CT1 _mg

CT2 hs

lnp4

p51 expCT3 T4 CT4

(44)

The cost equation for the recuperator:

CR CR1

_mgh5 h6

=U DTlm;aph

0:6(45)

The cost equation for the heat exchanger:

Che Che1

_Qec=DTlm;ec0:8 _Qev=DTlm;ev

0:8

Che2 _mwater C53 _m1:2g(46)

Details of the calculations of the cost equation method which isnamed costing method B for the air preheated cycle, are given byBejan et al. [31].

3.3. Thermoeconomic optimization of the cycles

In an optimization study, the rst step is to clearly dene theboundaries of the system, which can be the entire system or asubsystem. The second step is to select the optimization criteriawhich can be technological (efciency, production rate, etc.), eco-nomic (cost, net prot, etc.) or environmental (rate of pollutants).An optimization process might have multiple criteria such asmaximum efciency and minimum cost. After these steps, inde-pendent variables and parameter selection are considered. Thenthe mathematical model, the objective function which is to bemaximized or minimized, and constrains represented by equalitiesand/or inequalities are set. In this study the objective function is,

Minimize _CP;tot _Cf ;tot _ZCItot _Z

OMtot (47)

where: _Cf ;tot ; _ZCItot ;

_ZOMtot are the variables that are functions of the

decision variables. The equality and inequality constraints arethe cycles, which are used in our analysis, are given by Bejan et al.[31]. The cost balance for the overall system operating at steadystate is given as follows.

_CP;tot _Cf ;tot _ZCItot _Z

OMtot (38)

Stream costing for entering and exiting exergy and the costassociated with each stream can be determined from:

_Ci ci: _Ei ci$ _mi$ei (39)

_Co co: _Eo co: _mo:eo (40)

_CW cW : _W (41)The cost equation of each component of the air preheated cycle

is given below.The cost equation for the compressor:

gy 80 (2015) 474e485 479provided by the material and energy balance equations (maximum

4. Optimization results of the cycles

Thermoeconomic optimization of different cogeneration cycles(minimum electricity cost) in the literature is mostly done by usingcost equations named costing method B and the effect of size onequipment cost named costing method A in our study. In the costequations of compressors and gas turbines, isentropic efciencieshave very important effect on the cost although only the power iseffective on the effect of size on equipment cost. These twomethods are applied on the simple, the preheating air, the pre-heating air and fuel, the inlet air-cooling cogeneration systems.

Some of our studies have been carried out in order to under-stand the variations of the global optima of the systems withrecuperator outlet temperatures and with the isentropic ef-ciencies of the compressors and the turbines. Analyses are per-formed using the costing method A and the costing method B.Some of the results are given in Figs. 6e8 where power and steammass rates are not constrained.

Fig. 6 shows the variations of electricity production costs withthe excess air rate by using the costing method A, and with thedifferent recuperator outlet temperatures. In these analyses thefollowing values are used: r 6, hs,C 0,88 and hs,T 0,90. In order

R. Karaali, _I.T. Oztrk / Energy 80 (2015) 474e485480Fig. 5. The ow-chart of the iterative process of the computer programs written inFORTRAN code.or minimum values of temperatures, pressures etc.). For complexthermal systems suboptimization methods can be applied [31,36].

In this work by using a non-linear simplex direct search methodthat is improved by thermoeconomic analysis, the simple cycle, theinlet air cooling cycle, the air preheated and the air-fuel preheatedcycles are analyzed and optimized thermoeconomically. In Fig. 5,the ow-chart of the iterative process of the computer programswritten in FORTRAN code is given.

Fig. 6. Variation of the electricity production costs with the excess air rate by using the chsT 0,90 and unconstraint outlet temperature of the combustion chamber).to see the variations in the full range, the constraints on the outlettemperatures of the combustion chambers are removed. The opti-mum values of electricity production costs are obtained at lowoutlet temperatures of the recuperator. In addition, the optimumvalues of the electricity production costs are obtained at a ratebetween 1.8 and 2.4 of the excess air. As can be seen in Fig. 6 theminimum costs are obtained with the air preheated cycle.

Fig. 7 shows the variations of the electricity production costswith the excess air rate by using the costing method B and, withdifferent recuperator outlet temperatures. In these analyses thefollowing values are used: r 6, hs,C 0,86 and hs,T 0,86. To beable to see the variations, the constraints on the outlet tempera-tures of the combustion chambers are not taken into consideration.Optimum values of the electricity costs are obtained at a minimumrecuperator outlet temperature and at a rate between 2.1 and 3.0 ofthe excess air.

For each cycle, there is a minimum cost value of the air-fuel ratiohowever the air preheated cycle has the best value among othercycles.osting method A for different recuperator outlet temperatures (r 6, hsC 0,88 and

he c

R. Karaali, _I.T. Oztrk / Energy 80 (2015) 474e485 481The variations of the electricity production costs with the excessair rate by using the costing method B, andwith different isentropicefciencies of the compressors and turbines are given in Fig. 8. Inthese analyses r 6 is taken and to see the variations of the pro-

Fig. 7. Variation of the electricity production costs with the excess air rate by using thsT 0,86 and unconstraint outlet temperature of the combustion chamber).duction costs, the constraints on the outlet temperatures of thecombustion chambers are not taken into consideration. As can beseen, by decreasing the isentropic efciencies of the compressorsand the turbines, the production costs of electricity decreases, butat the same time, the efciencies of the systems decrease. Thereason for the decreasing production costs is that, increasingisentropic efciencies of the compressors and the turbines in-creases the cost of these equipment.

Fig. 8. Variation of the electricity production costs with the excess air rate by using the costiand unconstraint outlet temperature of the combustion chamber).As can be concluded from the Figs. 6 and 7 that decreasing theoutlet temperature of the recuperator decreases the electricity costfor the two costing methods, each gas turbine cogeneration cyclehas an optimum excess air rate value that gives the minimum

osting method B for different recuperator outlet temperatures (r 6, hsC 0,86 andelectricity cost. Additionally, the results of the costing method Bshow that decreasing the compression rate and decreasing theisentropic efciencies of the compressor and the turbine results inreduced electricity cost.

The optimum results of the thermoeconomic optimization byusing cost equations are obtained for the four cycles are shown inTable 2 for constant power (30 MW) and steam mass ow rate(14 kg/s). In addition, only for constant power (30 MW), and for

ng method B for different isentropic efciencies of the compressors and turbines (r 6

production costs. Because the isentropic efciencies of the com-pressors and the turbines are not effective on the costing method Acost calculation, isentropic efciencies are taken as hs,C 0,88 andhs,T 0,90. The costing method A gives the minimum electricityproduction costs in small interval than the costing method B forthe four cycles for constant electricity production and steam massow rate.

For the four cycles by using the costing method A (Eq. (37)), theoptimum values are obtained at the compression rates of r 16. Inthe air and the air-fuel preheated cycles, adding recuperators to thecycles increases the costs. However, adding an absorption unit inthe simple cycle decreases the cost of electricity production. Thesimple cycle is not appropriate for constant electricity productionand steam mass ow rate according to the costing method A.

The thermoeconomic optimization results for the constantelectricity production (30 MW) by using the costing method B toobtain local minimum of the production costs for the four cycles aregiven in Table 4. It can be seen that production costs decrease withincreased air-fuel mass ow rates. As can be seen in Table 4 theminimum production costs of the simple cycle are found to bebetter than the others.

The thermoeconomic optimization results for constant elec-tricity production (30MW) by using the costingmethod A (Eq. (37))to obtain local minimum of the electricity production costs for thefour cycles are given in Table 5.

As can be seen in Table 5 the local minimum of the production

Energy 80 (2015) 474e485variable power and steam mass ow rate, the minimum electricitycosts have been analyzed and the results have been compared witheach other. The thermoeconomic optimization has been done forthe four different cycles and six different working conditions. Ascan be seen in Table 2, the local minimum electricity costs are ob-tained for the air-fuel preheated gas turbine cycle.

Minimum electricity costs for the simple and the absorptioncycles are higher than the preheated cycles because these two cy-

Table 2Thermoeconomic optimization results for local optimum electricity costs for thefour cycles by using the costing method B for constant power (30 MW) and steammass ow (14 kg/s).

Cycle Simplecycle

Inlet aircoolingcycle

Air preheatedcyclea

Air-fuelpreheatedcycleb

Air mass ow (kg/s) 95,5 78,5 121,7 118,9Fuel mass ow (kg/s) 1,62 1,62 1,65 1,65Recuperator outlet (K)

e e900 900

Combustion chamberoutlet temperature (K)

1331 1423 1412 1444

Compressor pressure rate (r) 16 16 6 6Combustion chamber

exergy efciency0,76 0,76 0,81 0,82

Recuperatorexergy efciency e e

0,86 0,86

Fuel recuperatorexergy efciency

0,49

Turbine exergy efciency 0,91 0,91 0,91 0,91Compressor exergy efciency 0,95 0,95 0,90 0,90HRSG exergy efciency 0,70 0,68 0,75 0,76Compressor - turbine

isentropic efciency0,89 0,89 0,83e0,84 0,83e0,84

System exergy efciency 0,513 0,5105 0,5 0,5013Excess air rate % 265 218 330 323Electricity cost $/kWh 0,3400 0,2900 0,0957 0,0901

a Air R. LMTD 130.4 K HRSG LMTD 139.4 K.b Air R. LMTD 136.7 K Fuel R. LMTD 362.8 K.

R. Karaali, _I.T. Oztrk /482cles are not appropriate cycles for constant power and steam owrate. In fact, the simple and the absorption cycles are appropriatefor the power plants where steam production is the primary aimand electricity production is the secondary aim. Also for the vari-ations of electricity and heat productionwhere production dependson heat or electricity demands, the simple and the absorption cy-cles are not appropriate. The preheated cycles have better workingconditions for variable demand of electricity and steam production.For the four cycles, the local minimum production costs and theexergy efciencies are slightly different. The gas turbine exergyefciencies for the four cycles are almost the same, but the com-pressors exergy efciencies of the simple and the absorption cyclesare higher than the air and the air-fuel preheated cycles, because ofthe higher air mass rates. The efciencies of the combustionchambers of the simple and the absorption cycles are lower thanthe air and the air-fuel preheated cycles because in the latter airenters at higher temperature into the combustion chamber becauseof the recuperation. Design differences of the cycles are veryeffective on production cost as can be seen in the results obtainedwith the costing method B. Production costs, for the four differentcycles are given in Figs. 7 and 8.

Table 3 shows the costing method A (Eq. (37)) in the thermoe-conomic optimization of the four cycles for constant electricityproduction and steam mass ow rate (30 MW and 14 kg/s steam).The costing method A gives almost the same minimum electricityproduction cost (0,12 $/kWh) for the four cycles. For the absorption,the air and the air-fuel preheated cycles the air mass ow rate aremore or less the same, but for the simple cycle is different andhigher air mass ow rate values are obtained at minimumcosts of electricity for the four cycles obtained around 0,10 $/kWh.Isentropic efciencies are not effective in the costing method A sothat isentropic efciencies of the compressors and the turbines aretaken as hs,C 0,88 and hs,T 0,9, respectively. It is observed thatadding new equipment increases production costs, so addingrecuperators in the cycles increases exergy efciency but also in-creases production costs.

The thermoeconomic optimization results obtained by using thecosting method B to obtain global minimum production costs forthe four cycles are given in Table 6. These results agree with thevariations of the production costs with respect to the excess air rate

Table 3Thermoeconomic optimization results for constant electricity production and steammass ow rate (30 MWand 14 kg/s steam) by using the costing method A (Eq. (37))for the four cycles.

Cycle Simplecycle

Inlet aircoolingcycle

Air preheatedcyclea

Air-fuelpreheatedcycleb

Air mass ow (kg/s) 94,9 75,8 75,0 76,8Fuel mass ow (kg/s) 1,6 1,61 1553 1,56Recuperator outlet

temperature (K) e e780 735,0

Combustion chamberoutlet temperature(K)

1332 1447 1550 1517

Compressor pressure rate (r) 16 16 16 16Compressor-turbine

isentropic efciency0,88e0,9 0,88e0,9 0,88e0,9 0,88e0,9

Combustion chamberexergy efciency

0,76 0,76 0,8 0,78

Recuperator exergyefciency e e

0,82 0,73

Fuel recuperatorexergy efciency

0,57

Turbine exergy efciency 0,93 0,92 0,94 0,93Compressor exergy efciency 0,95 0,94 0,93 0,95HRSG exergy efciency 0,70 0,67 0,71 0,68System exergy efciency 0,5166 0,5133 0,5313 0,5297Excess air rate % 266 211 217 221Electricity cost $/kWh 0,1248 0,1202 0,1200 0,1209

a Air R. LMTD 141 K HRSG LMTD 198 K.b Air R. LMTD 139 K Fuel R. LMTD 317 K.

that are given in Figs. 6e8. Increasing air mass ow rates decreasesproduction costs. From the results obtained by using the costingmethod B, the minimum production costs are half of the resultsobtained by using the costing method A for the four cycles.

preheated cycles by using the costing method B are lowerthan the local optima of the constant power (30 MW).

Table 6Thermoeconomic optimization results by using the costing method B for the fourcycles.

Cycle Simplecycle

Inlet aircoolingcycle

Air preheatedcyclea

Air-fuelpreheatedcycleb

Air mass ow (kg/s) 90,95 103,9 102 108,25Fuel mass ow (kg/s) 2,2 2,59 2,32 2,41Steam mass ow (kg/s) 27,98 31,37 28,85 29,68Combustion chamber

outlet temperature (K)1462 1460 1467 1464

Recuperator outlettemperature (K) e e

600 600

Compressor pressure rate (r) 6 6 6 6Excess air rate % 185,6 180,15 197,44 201,71Electricity power (kWh) 22,017 26,967 24,345 25,828Compressor-turbine

isentropic efciency0,8 0,8 0,8 0,8

System exergy efciency 0,4182 0,4153 0,4226 0,4248Electricity cost $/kWh 0,0432 0,0514 0,0577 0,0580

a Air R. LMTD 490 K.b

Table 4Thermoeconomic optimization results for constant electricity production (30 MW)by using the costing method B for the four cycles.

Cycle Simplecycle

Inlet aircoolingcycle

Air preheatedcycle

Air-fuelpreheatedcycle

Air mass ow (kg/s) 124,03 115,6 121 117,8Fuel mass ow (kg/s) 2,99 2,88 1,82 1,82Steam mass ow (kg/s) 38 34,88 17,0 17,13Recuperator outlet

temperature (K) e e897,5 897,5

Combustion chamberoutlet temperature (K)

1460 1459 1462 1498

Compressor pressure rate (r) 6 6 6 6Compressor-turbine

isentropic efciency0,8 0,8 0,8e0,84 0,8e0,84

System exergy efciency 0,4184 0,4153 0,4837 0,484Excess air rate % 186,28 180,25 298,56 290,66Electricity cost $/kWh 0,0440 0,0516 0,0871 0,0871

R. Karaali, _I.T. Oztrk / Energy 80 (2015) 474e485 483The thermoeconomic optimization results obtained by using thecosting method A (Eq. (37)) to achieve global minimum productioncosts for the four cycles are given in Table 7. These results t withthe variations of the production costs with the excess air ow ratethat are given in Figs. 6e8. In the thermoeconomic optimizationanalyses r 6, hs,C 0,88, hs,T 0,90 are taken. However, the massow rate used is approximately 115 kg/s. Increasing the air massow rate decreases global minimum of the production costs for thefour cycles. Besides the minimum production cost is obtained forthe simple cycle among the four cycles.

A comparison of the results of the thermoeconomic optimiza-tion are presented in Table 8. These results can be summarized asfollows;

a. For each cycle and for both of the costing methods, by usingglobal optimization research method, optimum production costis decreasing. That means that the global optimization search

Table 5Thermoeconomic optimization results for constant electricity production (30 MW)by using the costing method A (Eq. (37)) for the four cycles.Cycle Simplecycle

Inlet aircoolingcycle

Air preheatedcycle

Air-fuelpreheatedcycle

Air mass ow (kg/s) 89,45 85,45 90,5 90,34Fuel mass ow (kg/s) 2,45 2,41 2288 2242Steam mass ow (kg/s) 29,59 27,94 26,63 25,80Recuperator outlet

temperature (K) e e600 600

Combustion chamberoutlet temperature (K)

1550 1550 1550 1550

Compressor pressure rate (r) 6 6 6 6Combustion chamber

exergy efciency0,70 0,70 0,72 0,73

Air recuperatorexergy efciency e e

0,55 0,55

Fuel recuperatorexergy efciency e e e

0,54

Turbine exergy efciency 0,91 0,91 0,94 0,94Compressor exergy efciency 0,93 0,93 0,93 0,93HRSG exergy efciency 0,58 0,58 0,60 0,60System exergy efciency 0,45 0,4455 0,459 0,46,195Excess air rate % 163,96 159,23 177,63 180,95Electricity cost $/kWh 0,0986 0,1034 0,1043 0,1063method is better than the local optimization one. Especially, thiscan be seen very clearly for the simple cycle.

b. The thermoeconomic optimization results of the global mini-mums of the production costs for the simple (0,04 kW/$) and forthe absorption (0,05 kW/$) cycles by using the costing method Bare almost the same as the results of the local optima for theconstant power (30 MW), as can be seen in Table 8. That meansthe costing method B gives the same local and global optimi-zation results for the two cycles.

c. In the global optimization method according to the equipmentcost equationmodel, the global optimum production cost valuesof the simple and the air-fuel preheated cycles are 87,3% and35,6% lower than the local optimum values (for 30 MW powerand 14 kg/s steam ow rate), respectively.

d. In the global optimization method according to the costingmethod A, the global optimum production cost values of thesimple and the air-fuel preheated cycles are 24,3% and 16,3%lower than the local optimum values (for 30 MW power and14 kg/s steam ow rate), respectively.

e. The thermoeconomic optimization results of the global mini-mums of the production costs for the air and for the air-fuel

Air R. LMTD 472 K, Fuel R. LMTD 614,9 K.Table 7Thermoeconomic optimization results by using the costing method A (Eq. (37)) forthe four cycles.

Cycle Simplecycle

Inlet aircoolingcycle

Air preheatedcyclea

Air-fuelpreheatedcycleb

Air mass ow (kg/s) 114,5 97,54 113,8 115,8Fuel mass ow (kg/s) 3125 2,75 2875 2875Steam mass ow (kg/s) 37,68 31,88 33,44 33,09Combustion chamber

outlet temperature (K)1547 1550 1550 1550

Recuperator outlettemperature (K) e e

600 600

Compressor pressure rate (r) 6 6 6 6Electricity power (kWh) 38,386 34,253 37,718 38456System exergy efciency 0,4504 0,4455 0,4591 0,4619Excess air rate % 164,54 159,28 177,76 180,88Electricity cost $/kWh 0,0945 0,1009 0,0998 0,1012

a Air R. LMTD 527,5 K.b Air R. LMTD 510,8 K, Fuel R. LMTD 653,3 K.

method should be used with caution since in some workingconditions, it gives non-realistic results [31,36].

steam mass ow rate. The costing method B and the costing

calculus procedures. ASME J Energy Resour Technol 1989;111.

Sim

0,34

0,040,040,12

0,090,09

Energ. In case of variable power and steam mass ow rate, in globaloptimization for the minimum costs are (0,0432 $/kWh) for thesimple cycle, (0,0514 $/kWh) for the inlet air cooling cycle,(0,0577 $/kWh) for the air preheated cycle and (0.058 $/kWh)for the air-fuel preheated cycle by using the costing method B.

h. The prices of the equipment, labor and fuels change every yeareven every day and this makes it impossible to make a com-parison with the published works of the past years. However, inthis study, the analyses are done by taking the data from theliterature [31] for the prices of the equipment and labor, andthese values are updated. For updating process CEPCI equip-ment cost index, taken from the web site of Chemical Engi-neering Plant Cost Index [39] are used in Equation (36). Theupdated values are compared with the market prices. The fuelprices are not updated, and were taken from the year 2012market values.

i. The aim of this study is to show that, for the same data theglobal optimization introduced above and the local optimizationprocesses, costing method A and B, and different designs givevery different results. The advantages and the disadvantages ofthe optimization processes, costing methods and different de-signs are shown by using the thermoeconomic method.

j. A comparison of the thermoeconomic global optimization pro-cess with results available in the literature would not be realisticbecause this study is the rst in this eld. However, thermo-dynamic global optimization process by using decomposition ofenergy systems is discussed in literature especially by Hua et al.[25] and Lazzaretto et al. [17].

5. Conclusion

In this study, a new iterative optimization method is applied tof. The costing method A and the costing method B give verydifferent results for the electricity production costs. The resultsof costing method B agree with the literature. However, this

Table 8Electricity costs results for local and global optimization of the four cycles.

Case

Costingmethod B(Cost equations method)

Constant electricity production andsteam ow rate (30 MW and 14 kg/s)Constant power (30 MW)Unconstrained power and steam mass

Costingmethod A(Costing method of the effect of

size on equipment)

Constant electricity production andsteam mass ow (30 MW and 14 kg/s steam)Constant power (30 MW)Unconstrained power and steam ow rate

R. Karaali, _I.T. Oztrk /484determine the local and the global optima of four cycles; they arecompared with each other and it is seen that the performancecharacteristics values are found to be in good agreement with eachother and with the literature. In order to nd the global optimum,all working conditions of a thermal system should be taken intoaccount and the power should be considered variable. In thestudies available in the literature, thermoeconomic optimization ofthermal systems is performed for constant power production. It isclear that with the information about the global optimum, wewould have a better insight of the working conditions of the ther-mal system that results in maximum benets. Finding the globaloptimum is very important at design stages and in working con-ditions. Global optima might be obtained at low compression ratesas can be seen in the optimization results of the air and the air-fuelmethod A give very different optimum costs results. The results ofthe costing method B are in good agreement with the reality, butwith different excess air rates unrealistic results are obtainedbecause of its structure as is indicated in the literature. For thatreason, the costing method B should be used carefully in thethermoeconomic optimization processes. As the results of the an-alyses of the global optimization indicate the optimum costs ob-tained for the simple cycle 0,0432 $/kWh; for the inlet air coolingcycle 0,0514 $/kWh; for the air preheated cycle 0,0577 $/kWh; andfor the air-fuel preheated cycle 0,058 $/kWh, by using the costingmethod B. However, in the case of the variable demands for elec-tricity and steam mass production, the air and the air-fuel pre-heated cycles give the best solutions.

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R. Karaali, _I.T. Oztrk / Energy 80 (2015) 474e485 485

Thermoeconomic optimization of gas turbine cogeneration plants1. Introduction2. Description of the cycles3. Analysis of the cycles3.1. Thermodynamic analyses of the cycles3.2. Thermoeconomic analysis of the cycles3.3. Thermoeconomic optimization of the cycles

4. Optimization results of the cycles5. ConclusionReferences