Four E analysis and multi-objective optimization of combined cycle power plants integrated with Multi-stage Flash (MSF) desalination unit

Desalination 320 (2013) 105–117

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Four E analysis and multi-objective optimization of combined cycle power plants integrated with Multi-stage Flash (MSF) desalination unit Sepehr Sanaye ⁎, Saeid Asgari Energy System Improvement Laboratory (ESIL), School of Mechanical Engineering, Iran University of Science & Technology (IUST), Iran

H I G H L I G H T S • • • •

Four E modeling and analysis of system were performed. Two objectives in multi-objective genetic algorithm optimization were selected. Effects of gas turbine partial load and ambient temperature were investigated. The sensitivity analysis with change in the fuel cost was implemented.

a r t i c l e

i n f o

Article history: Received 16 January 2013 Received in revised form 15 April 2013 Accepted 17 April 2013 Available online 17 May 2013 Keywords: CHP Desalination 4E analysis Optimization

a b s t r a c t 4E analysis and multi-objective optimization for a combined cycle power generating unit with a Multi-stage Flash (MSF) desalination unit are investigated in this paper. The first objective function was considered as the sum of investment and operational costs as well as penalty for producing NOx emissions. The second objective function was the cycle total amount of exergy destruction. Genetic algorithm optimization technique was applied to obtain the optimum values of design parameters such as Heat Recovery Steam Generator (HRSG) drum pressure, pinch point temperature in HRSG, top brine temperature in MSF, last stage temperature of MSF and number of MSF stages. Also the effects of gas turbine part load, as well as ambient temperature and fuel cost changes on the optimal values of design parameters were analyzed. © 2013 Elsevier B.V. All rights reserved.

1. Introduction As climate changes, population grows, and local water scarcity concerns heighten, desalination of brackish water and seawater is increasingly considered as an option for a source of new water to meet anticipated water supply needs. The combined production of power and water is the most economical way to simultaneously satisfy the demands for electricity and water. Among the potential of thermal power plant schemes, a gas-turbine-based combinedcycle power plant will cogenerate the steam needed for a desalination plant in the most economical manner [1]. Cardona and Piacentino [2] optimized a combined cycle with simultaneous production of electricity and fresh water. Their study involved a combination of reverse osmosis (RO) and Multi-stage Flash (MSF) desalination systems in which exhaust energy from the power cycle entered an MSF section, while electrical power was supplied to the RO section and MSF auxiliary equipment. They were interested in optimal design of such cogeneration ⁎ Corresponding author at: Energy Systems Improvement Laboratory, Mechanical Engineering Department, Iran University of Science and Technology, Narmak, Tehran 16488, Iran. Tel./fax: + 98 21 77240192. E-mail address: [email protected] (S. Sanaye). 0011-9164/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.desal.2013.04.023

plants, based on exergo-economics and on profit maximization. Wade [3] reviewed energy and cost allocation methods of power generating cycle and desalination processes. He studied the combination of gas turbine power plants and combined heat and power cycles with RO and MSF desalination systems. He presented a method of analyzing the energy consumption for power and desalination processes covering both single and dual-purpose schemes in comparison with the efficiency of a reference power cycle. Darwish et al. [4] presented the use of availability (exergy) concept to bring different kinds of energy to a common basis of comparison. Darwish and Najem [1] also proposed using gas turbine with RO and MSF desalination units when there is no enough steam supply to desalting units. Hosseini et al. [5] investigated the effects of equipment reliability in thermoeconomic analysis of a combined power and Multi-stage Flash water desalination plant. Khoshgoftar Manesh and Amidpour [6] studied the application of an evolutionary algorithm to multi-objective thermoeconomic optimization of coupling Multi-stage Flash desalination (MSF) plant with a pressurized water reactor (PWR) nuclear power plant. Johansen et al. [7] evaluated four CHP plants with several desalination processes. They showed, by using a gas-turbine, an HRSG and a back-pressure steam turbine together with a MED-RO desalination process, in which high effective energy utilization can be achieved.

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Nomenclature A C C_ Cp cel cf cNOx cw E_ D E_ D e h hfg M _ m N n n_ P Q_ S S_ T t U _ W X Y z

heat transfer area (m 2) cost ($) annual cost ($/year) specific heat (kJ/kg·°C) price of electricity ($/kWh) price of natural gas ($/GJ) penalty cost factor ($/kg NOx) price of water ($/m 3) exergy rate (kW) exergy destruction rate (kW) specific exergy (kJ/kg) specific enthalpy (kJ/kmol) evaporation enthalpy (kJ/kg) molecular mass (kg/kmol) mass rate (kg/s) number of heat rejection part number of effects molar flow rate pressure (bar) heat transfer rate (kJ/kg) specific entropy (kJ/kmol·K) annual income ($/year) temperature (°C or K) temperature of water (°C) heat transfer coefficient (kW/m 2·K) power (kW) salt concentration (ppm) time of operation (day/year) mole fraction of air component

Subscripts a air ac annual investment cost app approach av average bd blow down cw cooling water cm contingency co construction overhead CV control volume d direct dis distillate el electrical eq equipment f fuel fr freight fw feed water GT gas turbine HB heater brine HJ heat rejection HP high pressure HR heat recovery In investment IP intermediate pressure id indirect l liquid la land loss thermodynamic loss (°C) ms motive steam ow owner p product

pin r ST sw S sd st v

pinch point recirculating water steam turbine sea water isentropic site development stage vapor

Superscripts CH chemical KN kinetic PH physical PT potential

Greek symbols β coefficient of M&O η efficiency (%) λ molar fuel–air ratio Δh specific enthalpy difference (kJ/kmol) ΔT temperature difference (°C)

Abbreviations CRF capital recovery factor LHV lower heating value (kJ/kg) LMTD logarithmic mean temperature difference M&O maintenance & operational PR performance ratio TAC total annual cost ($/year) TDU thermal desalination unit TBT top brine temperature TTD terminal temperature difference (°C)

In this paper, an integrated gas-turbine combined-cycle power plant with Multi-stage Flash (MSF) desalination unit was modeled, analyzed and optimized using multi-objective genetic algorithm method. It covers 4-E (energy, exergy, economic and environmental) system analysis to estimate the optimal design parameters. The following are the contributions of this paper into the subject: ∙ Four E (energy, exergy, economic and environmental) modeling and analysis of system was performed. ∙ Two objective functions (total annual cost and exergy destruction) in multi-objective genetic algorithm optimization were selected. Total annual cost included the annual investment cost, annual maintenance and operational cost (M&O) and the penalty cost for NOx production in gas turbine combustion chamber. ∙ Effects of gas turbine partial load and variations of ambient temperature on optimum values of design parameters as well as operational parameters such as net power output and fresh water production, were investigated. ∙ The sensitivity analysis of optimum values of design parameters with change in the fuel cost (in gas turbine nominal load) was implemented. 2. The system configuration The studied plant in this paper consists of two gas turbines, two double-pressure Heat recovery steam generators (HRSGs) and one back pressure steam turbine. The collected high and moderate pressure

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steam from two HRSGs entered the back pressure steam turbine. Then the outlet steam from turbine was sent to MSF desalination units. The steam was condensed in desalination units and returned into HRSG as feed water. Therefore desalination unit not only was for producing fresh water but it was a condenser for the combined cycle as well. The schematic view of the studied system is shown in Fig. 1. 3. Energy analysis

And by substituting λ n_ a ¼ n_ f : _f ¼λ m

n_ f ¼λ n_ a n_ p ¼1þλ n_ a

ð1Þ

0¼−

 Mf _a m Ma

0 ¼ Q_ CC þ n_ f h f þ n_ a h a −n_ p h p

ð3Þ


 Q_ CC ¼ −0:02n_ f LHV ¼ n_ a −0:02λLHV

ð4Þ


 0 ¼ −0:02λLHV þ h a þ λh f − 1 þ λ h p

ð5Þ

relations for compressor and turbine. Finally the inlet air and outlet combustion gas mass flow rates were obtained from following relations:

h 1 −h 2



_ Ma W CV  
 þ 1 þ λ h 3 −h 4

ð10Þ

1) Computing T4s by try and error method from a non-linear equation in terms of T4s based on relation: s 4s −s 3 ¼ 0

ð6Þ

ð9Þ

The following is the procedure of computing the turbine exhaust gas temperature:

ð11Þ

using the definition of molar entropy for perfect gas mixture (N2, O2, CO2, H2O): s ðT; P Þ ¼ s∘ ðT Þ−R ln

zN2 Δh N2 þ zO2 Δh O2 þ zCO2 Δh CO2 þ zH2 O Δh H2 O   : h f −0:02LHV − −2h O2 þ h CO2 þ 2h H2 O ðT product Þ

ð8Þ

    where h 1 −h 2 and h 3 −h 4 were obtained from isentropic efficiency

_ aþm _ f: _p¼m m

where n_ f , n_ a and n_ p are mole rates of fuel, air and combustion products, respectively. From the energy balance for combustion chamber, λ can be obtained as follows:

λ¼

ð7Þ

 
 _  W net þ h 1 −h 2 þ 1 þ λ h 3 −h 4 n_ a

_a¼ m ð2Þ



where Mf and Ma are molecular weight of fuel and air. Furthermore from energy conservation equation for the whole gas turbine:

3.1. Gas turbine cycle The exhaust gas mass flow rate and temperature are the interested parameters which should be estimated from gas turbine modeling. Considering λ as the fuel to air ratio in the gas turbine combustion chamber:

107

p pref

and computing s∘ ðT Þ in terms of (T) from relations for various gas components provided in Reference [16].

Fig. 1. Schematic of the investigated system.

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Fig. 2. A double pressure HRSG.

2) Estimating h 3 and h 4s from relations in terms of (T3) and (T4s) respectively for various gas components provided in Reference [16] and with using a known value for ηT. Then computing h 4 from Eq. (12) and its corresponding temperature (i.e., the turbine exhaust gas temperature T4) from relations h(T). ηT ¼

h 3 −h 4 h 3 −h 4s

:

ð12Þ

3.2. Heat Recovery Steam Generator A double pressure HRSG includes three economizers, two evaporators and two superheaters. Fig. 2 shows a schematic of studied HRSG in which steam is delivered to back pressure steam turbine. Energy balance in HP evaporator and HP superheater: _ p Cpp ðT in −T b Þ ¼ m _ HP Cpv ðT 13 −T 12 Þ þ m _ HP hfg : m

ð13Þ

Energy balance in HP economizer and IP evaporator and IP superheater: _ HP Cpl ðT 9 −T 4 Þ þ m _ IP Cpv ðT 8 −T 7 Þ þ m _ IP hfg : _ p Cpp ðT b −T e Þ ¼ m m

ð14Þ

Energy balance in HP and IP economizers: _ HP Cpl ðT 4 −T 2 Þ þ m _ IP Cpl ðT 3 −T 1 Þ: _ p Cpp ðT e −T out Þ ¼ m m

ð15Þ

Pinch point and approach temperatures are defined as: T pin ¼ T e −T 5 ¼ T b −T 10

ð16Þ

T app ¼ T 5 −T 3 ¼ T 10 −T 9 :

ð17Þ

3.3. Back pressure steam turbine The back pressure steam turbine included high pressure (HP) and intermediate pressure (IP) sections. The power output of HP and IP steam turbine sections was obtained from following relations (subscripts 1, 2, 3 and 4 are HP inlet section, HP outlet section, IP inlet section and IP outlet section respectively): _ _ W HP ¼ m HP ðh1 −h2 Þ

ð18Þ

_ ¼ ðm _ HP þ m _ IP Þðh3 −h4 Þ: W IP

ð19Þ

3.4. Multi-stage Flash desalination Multi-stage Flash desalination process involves the use of distillation through several (multi-stage) chambers. In the MSF process, each successive stage of the plant operates at progressively lower pressures. The feed water is first heated under high pressure, and is led into the first ‘flash chamber’, where the pressure is released, causing the water to boil rapidly resulting in sudden evaporation or ‘flashing’. This

Fig. 3. A Multi-stage Flash (MSF) desalination with brine recirculation flow.

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109

Fig. 4. Single stage flashing unit and temperature profiles.

‘flashing’ feed continues in each successive stage, because the pressure at each stage is lower than that in the previous stage. The vapor generated by the flashing is converted into fresh water by being condensed on heat exchanger tubes in each stage. The tubes are cooled by the incoming cooler feed water [8–10]. Many Multi-stage Flash plant arrangements and operational techniques are available [11]. Each evaporator is usually described by defining the three main plant characteristics: the flashing flow system, the chemical treatment and the tube configuration. The MSF plant studied here [Fig. 3] is a brine recirculation flow, and cross tube configuration, the most typical of the MSF plant types. The following assumptions are used for modeling [9,11–15]: ∙ All processes are steady state and steady flow and effects of kinetic and potential energy are negligible ∙ The product leaving any stage is salt free ∙ Steam at the brine heater inlet is assumed to be saturated vapor ∙ The maximum achievable concentration of the rejected brine is 70,000 ppm. The total mass and salt balance equations are: _ fw ¼ m _ bd þ m _ dis m

ð20Þ

_ bd X bd : _ fw X fw ¼ m m

ð21Þ

ΔT st ¼ ðTBT−T n Þ=n:

ð23Þ

As shown in Fig. 4, (TBT − t1) is equal to the sum of the stage temperature drop, the stage terminal temperature difference and the thermodynamic losses: ðTBT−t 1 Þ ¼ ΔT st þ ΔT loss þ TTD:

ð24Þ

The thermodynamic loss, ΔTloss, is difference between the brine temperature which leaves the stage and condensing vapor temperature. This loss is caused by the boiling point elevation, the nonequilibrium allowance, and the temperature drop corresponding to the pressure drop in the demister and during condensation. The condenser terminal temperature difference is difference between condensing vapor temperature and feed water temperature which leaves the condenser. The value of condenser terminal temperature difference plays a very important role in the design of the MSF system, and its value ranges between 3 and 5 °C [11] (Fig. 5). Energy balance in brine heater is: _ ms hfg;ms ¼ m _ r Cpl ðTBT−t 1 Þ: m

ð25Þ

Net energy balance for stages is:

The stage temperature drop, ΔTst, is equal to: ðTBT−T 1 Þ ¼ ΔT st :

To achieve the optimum operating condition, temperature drop in all stages was assumed to be equal [13], therefore:

ð22Þ

Fig. 4 shows the temperature profile in a single stage flashing unit.

_ dis h fg;v _ r Cpl ðTBT−T n Þ ¼ m m

ð26Þ

where h fg;v is the average latent heat of vapor condensation which was estimated at: Tav = (TBT + Tn)/2.

Fig. 5. Inlet and outlet flow exergy rates for MSF desalination unit.

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Table 1 Tuning parameters in applying genetic algorithm. 1. Number of generation 2. Size of population 3. Selection function 4. Tournament size 5. Mutation function 6. Crossover function 7. Crossover fraction 8. Migration direction 9. Migration fraction 10. Pareto front population fraction

1200 100 Tournament 2 Randomly Scattered 0.8 Forward 0.2 0.35

The salt concentration in the recycled stream is obtained by using salt balance equation for the heat rejection section: _ bd X bd ¼ m _ fw X fw þ ðm _ r −m _ dis ÞX bd : _ r Xr þ m m

ð27Þ

The cooling water mass flow rate is obtained by using overall energy balance for the MSF system:

Table 3 Comparison of results of gas turbine modeling with Thermo-flow software [TF] output for verification.         kg kg kg kg _ air sec _ air sec _ fuel sec _ fuel sec m Ambient m Difference m m Difference Temperature [TF] (%) [TF] modeling modeling (%) (°C) 0 15 30

519.96 494.99 465.43

527.66 497.93 467.05

+1.48 +0.59 +0.35

9.54 8.92 8.31

9.81 9.09 8.45

+2.83 +1.90 +1.68

Where ΔtHJ is: Δt HJ ¼ ðT n −T cw Þ=N:

ð33Þ

Finally the heat transfer surface area for MSF desalination unit was obtained from the following relation: A ¼ AHB þ ðn−NÞAHR þ NAHJ :

ð34Þ

4. Exergy analysis _ cw m

h

i. _ ms hfg;ms −m _ fw Cpl ðT n −T cw Þ ½Cpl ðT n −T cw Þ: ¼ m

ð28Þ

Furthermore seawater mass flow rate will be: _ sw ¼ m _ cw þ m _ fw : m

ð29Þ

At the steady state condition, the exergy rate balance for a control volume is [16,17]: ! T0 _ _ þ ∑m _ i ei −∑ m _ e ei −E_ D : 0 ¼ ∑ 1− Q j −W j Tj e j i

The specific exergy (e) includes: Physical exergy, kinetic exergy, potential exergy, and chemical exergy:

Heat transfer surface area for the brine heater is:  . _ ms hfg⋅ms U HB ðLMTDÞHB : AHB ¼ m

ð30Þ PH

e¼e The heat transfer surface area for heat recovery and heat rejection sections is: AHR

 _ r Cpl ðΔT st Þ= U HR ðLMTDÞHR ¼ ½m

AHJ

   .h i _ fw þ m _ cw Cpl Δt HJ U HJ ðLMTDÞHJ ¼ m

ð35Þ

þe

KN

PT

þe

CH

þe :

ð36Þ

Chemical exergy for multi-component mixture is obtained by:

ð31Þ e

CH

CH

¼ ∑xk e k þ RT 0 ∑xk lnxk :

ð37Þ

ð32Þ Therefore the total exergy destruction will be:

Table 2 Properties of system and input parameters for modeling and optimization. Parameter

Symbol

Value

Turbine inlet temperature (°C) Pressure ratio Pressure drop in combustion chamber (%) Fuel Lower heating value of fuel (kJ/kg) Ambient pressure (bar) Isentropic efficiency of compressor and turbine (%) Isentropic efficiency of steam turbine (%) Temperature of seawater (°C) Salt concentration of seawater (ppm) Salt concentration of blow down (ppm) Temperature of motive steam (°C) Specific heat capacity of water (kJ/kg·°C) Reference temperature (°C) Interest rate (%) Plant life (year) Price of fuel ($/GJ) Price of selling electricity ($/kWh) Price of selling water ($/m3) Unit damage cost for NOx ($/kg NOx) Time of operation (day/year) Coefficient of M&O cost

TIT Pr dP – LHV Pa ηC, ηT ηHP, ηIP Tsw Xsw Xn Cpl Cpl T0 i q cf cw cw cNOx Y β

1060 11 5 CH4 50,035 1.03 88 90 30 42,000 70,000 TBT + 10 4.186 25 10 20 2.53 0.07 1.5 6.85 330 0.06

E_ D;tot ¼ E_ D;MSF þ E_ D;GT þ E_ D;HRSG þ E_ D;ST :

ð38Þ

5. Economic and environmental analysis The total annual cost was considered as one of two objective functions which included the annual investment cost, annual maintenance and operational costs and the cost of penalty for producing NOX emissions. Total Annual Cost ðTAC Þ ¼ C_ ac þ C_ M&O þ C_ NOx :

ð39Þ

Table 4 Comparison of results of MSF desalination unit modeling with those reported at [11] for verification. TBT (°C)

90

95

100

105

110

PR [11] PR (modeling) Difference (%)

8.48 8.47 −0.11

8.93 8.95 +0.22

9.32 9.38 +0.64

9.72 9.78 +0.61

10.13 10.15 +0.19

S. Sanaye, S. Asgari / Desalination 320 (2013) 105–117

111

Table 5 The estimated values of system operating parameters at the optimal design point and various ambient temperature values for gas turbine running at nominal load. Parameter

_ p ðkg=sÞ m _ f ðkg=sÞ m Tout,GT(°C) E_ D;GT ðMWÞ _ v;HP ðkg=sÞ m _ v;IP ðkg=sÞ m Tv,HP(°C) Tv,IP(°C) Tout,HRSG(°C) E_ D;HRSG ðMWÞ _ ST ðMWÞ W E_ D;ST ðMWÞ PR
 _ dis m3 =day m _ m sw ðkg=sÞ _ bd ðkg=sÞ m E_ D;MSF ðMWÞ

Ambient temperature (°C) 15

20

25

30

35

40

45

1011.66 18.80 545.7 390.96 140.13 29.88 525.6 250.5 152.3 9.51 122.26 8.82 8.00 117,618 5323.0 2041.9 63.38

990.84 18.44 545.8 381.21 137.44 29.25 525.8 250.5 152.3 9.31 119.98 8.62 8.00 115,318 5218.9 2002.1 62.14

969.66 18.08 546.2 370.86 134.78 28.60 526.2 250.4 152.2 9.11 117.75 8.40 8.00 113,011 5115.2 1962.2 60.91

947.90 17.72 546.7 359.71 132.15 27.92 526.7 250.3 152.2 8.90 115.59 8.17 8.00 110,740 5011.7 1922.6 59.67

925.26 17.34 547.5 347.56 129.51 27.21 527.5 250.2 152.1 8.68 113.46 7.92 8.00 108,426 4907.0 1882.4 58.43

901.48 16.94 548.4 334.16 126.86 26.46 528.4 249.9 151.9 8.45 111.37 7.64 8.00 106,070 4800.4 1841.5 57.16

876.28 16.54 549.7 319.24 124.17 25.65 529.6 249.7 151.8 8.21 108.91 7.34 8.00 103,656 4691.1 1799.6 55.85

Table 6 The estimated values of system operating parameters at the optimal design point for gas turbine running at nominal (100%) and various partial loads and ISO ambient conditions. Parameter

_ p ðkg=sÞ m _ f ðkg=sÞ m Tout,GT(°C) E_ D;GT ðMW Þ _ v;HP ðkg=sÞ m _ v;IP ðkg=sÞ m Tv,HP(°C) Tv,IP(°C) Tout,HRSG(°C) E_ D;HRSG ðMWÞ _ ST ðMWÞ W E_ D;ST ðMWÞ PR
 _ dis m3 =day m _ sw ðkg=sÞ m _ bd ðkg=sÞ m E_ D;MSF ðMWÞ

Partial load (%) 100

90

80

70

60

50

1011.66 18.80 545.7 390.36 140.13 29.88 525.7 250.5 152.3 9.51 122.26 8.82 8.00 117,618 5323.0 2041.9 63.38

910.50 16.92 545.7 329.83 126.16 26.88 525.7 250.5 152.3 8.56 110.09 7.93 8.00 105,878 4791.7 1838.2 57.05

809.32 15.04 545.7 293.18 112.69 24.01 525.7 250.5 152.3 7.64 98.34 7.08 8.00 94,578 4280.2 1641.9 50.96

708.16 13.16 545.7 256.54 98.12 20.91 525.7 250.5 152.3 6.66 85.63 6.17 8.00 82,349 3726.8 1429.7 44.37

607.00 11.28 545.7 219.88 84.11 17.92 525.7 250.5 152.3 5.71 73.39 5.28 8.00 70,585 3194.4 1225.4 38.03

505.84 9.40 545.7 183.24 70.09 14.93 525.7 250.5 152.3 4.75 61.16 4.40 8.00 58,822 2662.1 1021.2 31.69

  5.1. Annual investment cost C_ ac

The indirect investment cost includes freight cost, construction overhead cost, owner's cost and contingency cost [17,18].

The investment cost refers to all associated terms correlated to building a plant and setup. This cost can be classified as direct and indirect costs [18,19]. C In ¼ C d þ C id :

ð41Þ

Equipment cost includes processing equipment such as gas turbine (compressor, combustion chamber and turbine), HRSG, back pressure steam turbine, MSF desalination unit (heater brine, evaporators, condensers, heat exchanger) and pumps. These costs are computed by cost functions listed in References [20–22]. Site development cost is estimated as: C sd ¼ 0:2  C eq :

ð43Þ

ð40Þ

Direct investment costs include the major and auxiliary equipment, site development and land (because of land availability, this cost is assumed to be zero in this paper) costs. C d ¼ C eq þ C sd þ C la :

C id ¼ C fr þ C co þ C ow þ C cm :

ð42Þ

Table 7 The system investment and operational costs at the optimal design point for gas turbine running at nominal load and 15 °C of ambient temperature. Parameter

Nominal load & Tamb = 15 °C

CGT(m$) CHRSG(m$) CST(m$) CMSF(m$) C_ In;GT ðm$=yearÞ C_ In;HRSG ðm$=yearÞ C_ In;ST ðm$=yearÞ C_ In;MSF ðm$=yearÞ C_ M&O;GT ðm$=yearÞ C_ M&O;HRSG ðm$=yearÞ C_ M&O;ST ðm$=yearÞ C_ M&O;MSF ðm$=yearÞ C_ fuel ðm$=yearÞ C_ NOx ðm$=yearÞ

156.46 30.03 19.58 240.6 29.95 5.75 3.75 46.06 1.79 0.35 0.23 6.58 72.55 29.60

m = million.

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Table 8 Variation of the fuel operating cost, NOx emission penalty cost, income and payback period with variation for gas turbine running at nominal load and various ambient temperatures. Parameter

Ambient temperature (°C)

C_ fuel ð$= secÞ C_ NOx ð$= secÞ S_ ð$= secÞ Payback period (year)

15

20

25

30

35

40

45

2.544 1.038 10.53 4.25

2.502 1.018 10.22 4.44

2.456 0.997 9.93 4.63

2.402 0.974 9.63 4.83

2.356 0.951 9.35 5.06

2.301 0.926 9.07 5.29

2.247 0.901 8.78 5.55

5.3. Annual penalty cost for producing NOx emissions The annual penalty cost for producing NOx emissions was estimated based on considering milligram of NOx in 1 kg of combustion product [23,24] _ product  150  10−6  Y  24  3600 C_ NOx ¼ cNOx  m

ð49Þ

where cNOx is penalty cost factor for NOx emission. 5.4. Payback period

The investment cost should be amortized to compute the annual cost by using the capital recovery factor which was computed from the following relation:  q q CRF ¼ iði þ 1Þ =ði þ 1Þ −1

ð44Þ

where i and q are the amount of interest rate and plant life cycle, respectively. So the annual investment cost was computed as the following:

The payback period can be computed for both Net Present Worth (NPW) and Net Future Worth (NFW) methods as follows [25]:



 ð1 þ iÞpp −1 ð1 þ iÞpp −1 NPW ¼ −C In −C_ M&O þ S_ pp pp ið1 þ iÞ ið1 þ iÞ

NFW ¼ −C In ð1 þ iÞ −C_ M&O pp

C_ ac ¼ CRF  C In :

ð45Þ

  5.2. Annual maintenance and operational cost C_ M&O Annual maintenance and operational costs are those expenditures acquired after plant commissioning and during actual operation. The maintenance cost is considered as a percent of annual investment cost. The operational costs include fuel (natural gas) cost in gas turbine and electricity cost needed for HRSG and MSF feed water pumping. C_ M&O ¼ C_ f þ β  C_ ac þ C_ pump

ð46Þ

_ f  Y  106  24  3600 C_ f ¼ cf  LHV  m

ð47Þ

_ C_ pump ¼ cel  W pump  Y  24:

ð48Þ



 pp pp ð1 þ iÞ −1 ð1 þ iÞ −1 þ S_ : i i

ð50Þ

ð51Þ

In relations (50) and (51), S_ is annual income received from selling the fresh water and electricity. Where i is the interest rate and pp is the payback period. By considering NPW and NFW equal to zero and computing pp from Eqs. (50) and (51), the payback period was estimated. Annual income is obtained by:   _ _ S_ ¼ W GT&ST  Y  cel  24 þ ðm dis  Y  cw  24  3:6Þ:

ð52Þ

6. Optimization 6.1. Objective functions Multi-objective optimization is the process of simultaneously optimizing two or more conflicting objectives subject to a list of

Fig. 6. Variations of distillate and steam turbine output power at the optimum design point with variations of ambient temperature.

S. Sanaye, S. Asgari / Desalination 320 (2013) 105–117

113

Fig. 7. Variations of distillate and steam turbine output power at the optimum design point for various gas turbine partial loads at 15 °C ambient temperature.

constraints [26,27]. In mathematical terms, the multi-objective problem can be written as: min ½ μ 1 ðxÞ; μ 2 ðxÞ; …; μ n ðxÞT |ffl{zffl} x

g ðxÞ ≤ 0 hðxÞ ¼ 0 xl ≤ x ≤ xu where μj is the i-th objective function, g and h are the inequality and equality constraints, respectively, and x is the vector of optimization or decision variables. The solution to the above problem is a set of Pareto points. Thus, instead of being a unique solution to the problem, the solution to a multi-objective problem is a possibly infinite set of Pareto points. In multi-objective optimization a process of decisionmaking for the selection of the final optimal solution from available solutions is required. There are several decision-making methods for the selection of a final optimal solution from the Pareto frontier [26]. The two objective functions of our multi-objective optimization problem are the total exergy destruction and the total annual cost

rate (including the annual investment, maintenance & operational cost as well as the corresponding cost due to NOx emission). The first objective function ¼ E_ D;total

ð53Þ

The second objective function ¼ TAC ¼ C_ ac þ C_ M&O þ C_ NOx :

ð54Þ

6.2. Design parameters and constraints Design parameters which their optimum values are sought and their ranges of variations were considered as: 1 2 3 4 5 6

Pressure of high pressure drum in HRSG Pressure of moderate pressure drum in HRSG Pinch point temperature of both drums in HRSG The last stage temperature of MSF Top brine temperature of MSF Number of stages in MSF

4 bar ≤ PIP ≤ 12 bar 20 bar ≤ PHP ≤ 100 bar 10 K ≤ Tpinch ≤ 25 K 40 °C ≤ Tn ≤ 50 °C 80 °C ≤ TBT ≤ 110 °C 15 ≤ n ≤ 23

Fig. 8. Variations of exergy destruction in system components at the optimum design point with variations of ambient temperature.

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Fig. 9. Variations of exergy destruction in system components at the optimum design point, for various gas turbine partial loads at 15 °C ambient temperature.

Also the following constraints were applied in optimization procedure: ∙ To avoid water vapor condensation and corrosive acid formation in the stack, temperature of exhaust gas in HRSG must be greater than 400 K ∙ Performance ratio (PR) is ratio of desalted water to motive steam entered to MSF unit. This parameter is one of the most important parameters in desalination unit that gives performance of it. For having a desirable unit this parameter must be greater than 8 ∙ For maximum using of exhaust heat loss of gas turbine, production of fresh water in gas turbine nominal load in each MSF unit must m3 be greater than 55; 000 day . 6.3. Genetic algorithm A genetic algorithm (GA) is a search heuristic that mimics the process of natural evolution. This heuristic is routinely used to generate useful solutions to optimization and search problems. Genetic algorithms belong to the larger class of evolutionary algorithms (EA), which generate solutions to optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover [26]. Properties which were used for tuning up the genetic algorithm optimization method are shown in Table 1.

7. Case study Two 157 MW gas turbine was used in the proposed CHP plant design for which Table 2 shows their operating parameters. To show the results of the present modeling and optimization, the system described in Fig. 1 was modeled and optimized. The values of input parameters in this case study are shown in Table 2). 8. Results and verification 8.1. Modeling verification and results To verify the gas turbine modeling results, the simulation output was compared with the results obtained from Thermo-flow software. Thermo-flow is a software for heat and mass balance analysis and equipment selection of thermal power plants including steam plant gas turbine, and combined cycles. The comparison of our modeling results and the corresponding values from Thermo-flow software, for the same input values is shown in Table 3. Furthermore to verify the MSF desalination modeling results, the MSF simulation output was compared with the reported results given in Ref. [11]. The comparison of above modeling results for the same input values is shown in Table 4.

Fig. 10. Variations of fuel cost and penalty cost for producing NOx emission at the optimum design point with variations of ambient temperature.

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Fig. 11. Variations of income and payback period at the optimum design point with variations of ambient temperature.

The numerical values of system operating parameters at the optimal design point with variations of ambient temperature and the gas turbine partial load are listed in Tables 5 and 6 respectively. The system investment and annual costs at the optimal design point are also listed in Table 7. The fuel cost, penalty cost for producing NOx emissions, income and payback period with variation of ambient temperature are also listed in Table 8. Increasing the ambient temperature decreases the air density and inlet air mass flow rate to the compressor which results in reduction in fuel consumption mass flow rate as well as the gas turbine power output. Furthermore the gas turbine exhaust temperature decreases as well which these both decrease the steam production in HRSG as well as decrease in steam turbine power output. Moreover at gas turbine partial load the air mass flow rate passing through compressor and its corresponding fuel consumption decreased [Eqs. (7) and (9)]. These reductions resulted in decrease in mass flow rates in the whole system (such as steam production in HRSG [Eqs. (13), (14) and (15)]). Results showed that the reduction of produced steam in HRSG causes to both decrease the steam turbine power output and distillate mass flow rates in MSF. Figs. 6 and 7 show the variation of steam turbine output power and distillate mass flow rates as a function of ambient temperature and gas turbine partial loads respectively. Increase of ambient temperature from 15 to 45 °C decreases both steam turbine output power and distillate mass flow rates for about 10.9 and 11.8% respectively. Furthermore as shown in Fig. 7 when gas turbine was running at 50% of its nominal load, the amount of steam turbine power output and distillate production decreased for about 50% of their values at nominal load. Due to the reduction of air fuel and motive steam with increasing the ambient temperature or gas turbine partial load, the exergy destruction in system components decreased (Eq. (35)). The impact of ambient temperature on the exergy destruction of system components is shown in Fig. 8. Increasing the ambient temperature from 15 to 45 °C provides 18.3, 13.6, 16.8 and 11.9% decrease in the exergy

Table 9 The optimum values of design parameters and objective functions for gas turbine running at nominal load and 15 °C of ambient temperature (selected by LINMAP method). Design parameters PIP (kPa) Nominal load ISO conditions

PHP (kPa)

Tpin (°C)

TBT (°C)

Tn (°C)

n

TAC ED (m$/y) (MW)

1067.2 8138.1 21.59 109.9 46.81 18 195.69

475.03

destruction of gas turbine, HRSG, back pressure steam turbine and MSF respectively. Fig. 9 shows the variation of exergy destruction in system components in gas turbine partial loads. Fig. 10 shows the variation of fuel consumption cost and penalty cost for producing NOx emissions as a function of ambient temperature. Increasing the ambient temperature from 15 to 45 °C decreased [Eqs. (47) and (49)] the fuel cost and emission penalty cost for producing NOx for about 11.6 and 13.2% respectively. Finally increasing the ambient temperature from 15 to 45 °C caused 16.6% decrease in income and 30.6% increase in payback period (Fig. 11). 8.2. Optimization results The results of system optimization are listed in Tables 9 to 11. The optimum values of design parameters with their corresponding objective functions for gas turbine running at base load and at 15 °C ambient temperature are shown in Table 9. Table 10 illustrates the variation of design parameters and objective functions with variation of ambient temperature. Also for implementing the sensitivity analysis, the results of change in the optimal values of design parameters and objective functions with 25 and 50% increase and decrease in the fuel cost are listed in Table 11. The Pareto optimal front curve for gas turbine running at base load and 15 °C ambient temperature is shown in Fig. 12. Each point on Pareto curve is an optimum solution which corresponds to specific values for six design parameters. Points A and B correspond to the lowest total annual cost (TAC) and the lowest exergy destruction (ED), respectively. These points are an optimum design point when TAC or ED was one single objective function. There are several Table 10 Variations of optimum values of design parameters and objective functions with variations of ambient temperature for gas turbine running at nominal load. Design parameters

PIP (kPa) PHP (kPa) Tpin (°C) TBT (°C) Tn (°C) n TAC (m$/year) ED (MW)

Ambient temperature (°C) 20

25

30

35

40

45

1042.4 8045.7 22.58 109.96 46.98 18 176.76 392.15

966.8 7373.9 24.95 109.99 47.01 18 192.50 464.24

1133.4 8738.0 23.59 109.93 46.85 18 190.38 449.25

971.8 7101.1 24.68 109.99 46.99 18 185.97 438.93

1128.2 8722.6 21.66 109.99 47.01 18 184.28 422.39

938.2 7119.0 21.87 109.98 46.84 18 179.87 410.78

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Table 11 Variations of optimum values of design parameters and objective functions with variations of fuel cost in ISO condition. Design parameters

PIP (kPa) PHP (kPa) Tpin (°C) TBT (°C) Tn (°C) n TAC (m$/year) ED (MW)

Optimum values of design parameters

Change in fuel cost (%) +50

+25

−25

−50

1067.2 8138.1 21.59 109.90 46.81 18 195.69 475.03

+7.75 −3.29 +8.71 +0.82 +0.36 0.00 +17.93 +0.02

+1.98 −4.18 +3.05 −0.14 +6.00 +5.55 +10.11 −0.39

−8.77 −5.04 +15.37 0.00 +6.15 +5.55 −8.49 −0.15

−7.66 −12.89 +12.78 +0.073 +0.34 0.00 −19.19 +0.57

methods for decision-making process in multi-objective optimization problems which can be employed for selection of a final optimal solution from the Pareto frontier. In our problem due to the dimensions of objectives are different, therefore, before any decision, all objectives should be non-dimensionalized. There are some methods of nondimensionalization utilized in decision making which Euclidian nondimensionalization method was employed here. Details of this method can be found in [28,29]. In this paper LINMAP and TOPSIS methods were used to select one point from Pareto optimal front [28,29]. In LINMAP method, the solution with a minimum distance from the ideal point on the Pareto frontier was selected as an optimal solution. An ideal point is the point in which each objective was optimized regardless to the satisfaction of other objectives. In TOPSIS method the solution with a minimum distance from the ideal point and a maximum distance from the non-ideal point on the Pareto frontier was selected as a best optimal solution. A non-ideal point is the ordinate in the objectives space in which each objective has its worst value. Details of these methods can be found in. The selected point by LINMAP method was considered as the final optimal design point in this paper.

8.2.1. Drum pressures in HRSG (PIP,PHP) Increasing the HRSG drum pressures (PIP and PHP) affects the temperature distribution in HRSG and raises both outlet temperature of steam and hot gasses from intermediate drum. Furthermore increasing HRSG pressure decreased the exergy destruction as well as HRSG investment cost. To give an example by increasing the intermediate pressure from 400 kPa to 800 kPa and increasing the high pressure from 4000 kPa to 8000 kPa, the exergy destruction of HRSG decreased

from 11.9 MW to 4.2 MW (about 65% decrease) and its cost increased from $14.2 million to $16.3 million (about 14% increase). Moreover the optimum values of PIP and PHP were close to their maximum allowable values. Increasing the ambient temperature caused a reduction in air density and mass flow rate as well as fuel consumption and power output in gas turbine. This reduced the sizes of HRSG, back pressure steam turbine and MSF as well as values of objective functions. 8.2.2. Pinch point temperature difference (Tpin) Increasing the pinch point temperature decreases the mass flow rate of high pressure steam while mass flow rate of intermediate pressure steam approximately remains constant. Therefore the output flow exergy rate decreases and the exergy destruction increases. Furthermore an increase in pinch point temperature decreases the HRSG investment cost due to decreasing its heat transfer surface area. To give an example increasing the pinch point temperature for about 10 to 25 °C increased the exergy destruction of each HRSG from 3.25 MW to 5.92 MW (about 45% rise), and decreased its cost from $18.02 million to $14.14 million (about 22% fall). 8.2.3. Top brine temperature (TBT) and last stage temperature (Tn) Increasing the top brine temperature and the last stage temperature in MSF caused an increase in temperature difference among existing stages in heat recovery and heat rejection section. This caused an increase in the temperature driving force and smaller heat transfer surface area and cost. By increasing the TBT and Tn, temperature of distillate, brine blow down and cooling water increased and the exergy destruction decreased. As an example by increasing of top brine temperature from 100 to 110 °C, and increasing last stage temperature from 40 to 50 °C, the exergy destruction of each MSF unit decreased from 20.2 MW to 17.7 MW (about 14% decreasing) and its cost from $83.9 million to $79.3 million (about 6%). 8.2.4. Number of stages (n) Decreasing the number of stages in MSF, cause a reduction in both exergy destruction and cost of MSF unit (both objective functions decrease). Therefore optimum value of this parameter should be selected around its minimum allowable values. However, specific number of stages should work to provide the required fresh water. 8.2.5. Sensitivity analysis Table 11 shows the variations of optimum values of design parameters and objective functions with variations of fuel cost for running

Fig. 12. The Pareto front and the optimum design points selected by LINMAP and TOPSIS methods at 15 °C ambient and gas turbine nominal load.

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the gas turbine in nominal load and at 15 °C ambient temperature. Based on Eqs. (39), (46), and (47), with variation of fuel cost the total annual cost (TAC) changed. The optimum values of design parameters had negligible variation with fuel cost variation. 9. Conclusions Four E (energy, exergy, economic and environmental) analysis and multi-objective optimization of a combined cycle power generating unit with a Multi-stage Flash (MSF) desalination unit were performed in this paper. Energy analysis was performed based on mass and energy conservation equations. Exergy analysis was performed based on system equipment exergy destruction. The total annual cost (TAC) was estimated for all system components in economic analysis which included annual investment and maintenance as well as operational costs. Some part of TAC was related to the penalty cost for producing NOx emission in combustion chamber (environmental analysis). In this study genetic algorithm method in optimization process has been used due to large number of design parameters (decision variables). Results showed that the variation of ambient temperature affects the power output and distillate production as well as income and payback period. Results also showed that the optimum value of design parameters was not dependent on the ambient temperature and change in ambient temperature just varied TAC and ED values. References [1] M.A. Darwish, N.A. Najem, Co-generation power desalting plants: new outlook with gas turbines, Desalination 161 (2004) 1–12. [2] E. Cardona, A. Piacentino, Optimal design of cogeneration plants for seawater desalination, Desalination 166 (2004) 411–426. [3] N.M. Wade, Energy and cost allocation in dual-purpose power and desalination plants, Desalination 123 (1999) 115–125. [4] M.A. Darwish, Fouad A. Yousef, N.M. Al-Najem, Energy consumption and costs with a multi-stage flashing (MSF) desalting system, Desalination 109 (1997) 285–302. [5] S.R. Hosseini, M. Amidpour, A. Behbahaninia, Thermoeconomic analysis with reliability consideration of a combined power and multi stage flash desalination plant, Desalination 278 (2011) 424–433.

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