Simulation and optimization of multi effect

Desalination 285 (2012) 366–376

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Simulation and optimization of multi effect desalination coupled to a gas turbine plant with HRSG consideration Seyed Ehsan Shakib, Majid Amidpour ⁎, Cyrus Aghanajafi Faculty of Mechanical Engineering, K.N. Toosi University of Technology, P.O. Box: 19395–1999, Pardis Str., Mollasadra Ave., Vanak Sq., Tehran 1999 143344, Iran

a r t i c l e

i n f o

Article history: Received 20 July 2011 Received in revised form 27 September 2011 Accepted 19 October 2011 Available online 14 November 2011 Keywords: Multi effect thermal vapor compression desalination Heat recovey steam generator Thermoeconomic analysis Genetic algorithm Particle swarm optimization

a b s t r a c t There are a large number of gas turbine power plants in the south of Iran that could be exploited to produce fresh water and overcome water shortage. In order to combine gas turbine power plant and thermal desalination, heat recovery steam generator (HRSG) is required for producing steam. Few papers in literature have investigated this combination and none of them has considered HRSG in their studies. Thus, in this paper, multi-effect evaporation thermal vapor compression desalination (ME-TVC) is coupled to gas turbine plant through HRSG. After performing a thorough thermoecnomic analysis, an optimization study is done in view of three approaches. The first and second approaches are single objective optimizations, which utilize two heuristic algorithms, namely, genetic algorithm (GA) and particle swarm optimization (PSO). The first approach is a global optimization problem, which completely optimize the combined system. The second one, as an innovative method, is a local optimization approach, which optimize HRSG and ME-TVC in two separate stages while the third approach is a multi objective optimization. Eventually, the results of the first and second approaches show that the minimum amount of objective function achieved by PSO is better, although the third approach presents a system with higher productivity. © 2011 Elsevier B.V. All rights reserved.

1. Introduction There is a huge amount of water on the Earth; but much of it is too salty and only about 2.5% is potable water. From long ago, many technologies have been developed for making drinkable water from brackish and seawater and use of each technology depends on the quantity and quality of fresh water, energy consumption, process efficiency and product cost. Today, distillation and membrane methods are the two main seawater desalination processes. Among these methods, multi-stage flash (MSF), multi-effect evaporation (MEE), vapor compression (VC) and reverse osmosis (RO) are suitable for the large and medium capacity of fresh water production [1]. MSF and MEE seawater desalination systems are suitable for being coupled with power plants because they could utilize the waste heat from power cycle for improving the fuel efficiency of the whole plants. In other words, they usually use the waste energy of flue gas (which exits from gas turbine cycles) and extracted vapor of steam turbines or heat recovery steam generator (HRSG). Compared with the most widely used MSF desalination, MEE and multi-effect evaporation thermal vapor compression (ME-TVC) have the advantages of lower corrosion and scaling rates, lower capital cost, longer operation life and less pumping power consumption [2]. Recently, many researchers have studied thermal desalination from thermodynamic and economic points of view. Alasfour et al. [3],

⁎ Corresponding author. Tel.: + 98 21 84063327; fax: + 98 21 88674748. E-mail address: [email protected] (M. Amidpour). 0011-9164/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2011.10.028

Kahraman and Cengel [4], Karl et al. [5], Shih [6], Ji et al. [7], Kamali et al. [8,9], Ameri et al. [10] and Trostmann [11] studied different aspect of thermal desalination and developed thermodynamic model for investigating the effect of various parameters on systems performance. In all these researches, energy or exergy analysis or heat and mass transfer simulation of thermal system are presented without economic considerations. However, Shakib et al. [12] studied thermodynamic and economic aspects of ME-TVC without performing a complete economical analysis. On the other hand, Nafey et al. Desalination and Water Treatment 37 (2012) 1–13. [13–15], Fiorini and Sciubba [16], Sayyaadi and Saffari [17] presented a methodology of exergy and thermoeconomic analysis for the performance of MSF, ME-TVC and multi-effect evaporation mechanical vapor compression (MEMVC) processes. Since, the required energy for running thermal desalination is widely supplied by power generation cycle in the form of dual-purpose plants, the operating parameters of power cycle and HRSG have impressive effects on the desalination performance. Hence, some researchers have analyzed the whole combined power and water production system. Wang and Lior [2,18] presented a thermodynamic model for integrated ME-TVC and humidified gas turbine cycle. Nevertheless, there is no economic analysis and optimization approach in their research. Chacartegui [19] considered the performance of a cogeneration plant – combined power plant and desalination – with a stationary lumped volume model. Iran has a considerable amount of gas turbine plants that many of them have been located in the south, near seashore region. Because of fresh water shortage in some parts of Iran, these power plants are also

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Nomenclature

hf k Km m M N Nr Nw nf L le P PR r2, r3, r4 s ST T tf Ts TBT Q U V vf X Z

Heat transfer area (m 2) Obstruction area (m) Gas side heat transfer surface (m 2) Fluid side heat transfer surface (m 2) Rejected mass flow rate(kg/s) Capital cost ($/s) Cost of water ($/m 3) Cost of steam ($/ton) Specific heat capacity (kJ/kg °C) Tube diameter (mm) Distillated mass flow rate (kg/s) Specific exergy (kJ/kg) Friction coefficient, corrosion coefficient Friction coefficient of two phase fluid Feed mass flow rate of each effect (kg/s) Gas mass velocity (kg/m 2 s) Specific enthalpy (kJ/kg), heat transfer coefficient (kW/kg °C) Fin height (mm) Specific heat capacity ratio Heat transfer coefficient of tube wall (kW/kg °C) Mass flow rate (kg/s) Mass flow rate (kg/s) Number of effects number of rows deep number of rows wide Fin density (fin/m) Latent heat (kJ/jg), length (m) Equivalent length (m) Pressure (kPa) Performance ratio Factors used in two-phase pressure drop calculation Specific entropy (kJ/kg K) transverse pitch (m) Temperature (°C) Fin thickness (mm) Heating steam temperature (°C) Top brine temperature (°C) Heat rate (kW) Heat transfer coefficient (kw/m 2 °C) Velocity (m/s) Specific volume of fluid (m 3/kg) Salinity (ppm) Capital cost, constant coefficient

Greek ρf η ηo ηit ΔPg ΔPa ΔPf ΔPg ΔTmax ΔTmin ΔTLM

Fluid density (kg/m 3) Efficiency Fin efficiency Isentropic efficiency of turbine Flue gas pressure drop (kPa) acceleration loss (kPa) friction loss (kPa) gravity loss (kPa) Maximum terminal differences (°C) Minimum terminal differences (°C) Mean-log temperature difference (°C)

A Ao At Aw B CC Cw Cs Cp d D e f fm F G h

subscripts ap Approach point

atm c e eco eva eff ev ex f F g hs i o m P pp sw t v w

367

Atmosphere Condenser Cvaporator Economizer Evaporator Effect Entrained vapor Exergy Feed water Fuel Flue gas Heating steam Inlet, effect number, Outlet Motive steam Products Pinch point Seawater Turbine inlet Vapor Water

excellent choices for supplying fresh water. In order to integrate a desalination plant with a gas turbine cycle, a selective HRSG is required for producing saturated motive steam. Few papers can be found in literature [20–22] which have investigated combined gas turbine cycle and thermal desalination from thermodynamic and economic points of view and all of them only have considered desalination plants. However, only Rensonnet et al. [20] applied the thermoeconomic method for the economic evaluation of a dual-purpose plant. In fact, because of the interaction between HRSG and ME-TVC desalination, both should be simultaneously included in the simulation and optimization study. This approach causes these two components (HRSG and ME-TVC) to be considered an integrated system that is coupled to the gas turbine cycle; thus, economic optimization of the combined system leads to obtain an optimal design for the fresh water production system. According to these facts and due to the lack of studied in this area, in this paper a potable water production system consisting of HRSG and ME-TVC is added to an available gas turbine power plant which has been located in the south of Iran, near the seashore region, and has a nominal output power of 130 Mw. First, a complete and comprehensive model including thermodynamic, heat transfer and pressure loss calculation is developed for HRSG and ME-TVC. After simulation stage, total revenue requirement method is used (TRR) for predicting annual cost; then, an innovative thermoeconomic analysis is performed and cost balance equation is taken into account. Afterwards, two heuristic optimization algorithms, namely, genetic algorithm (GA) and particle swarm optimization (PSO), are applied and the whole system is optimized. Three approaches are considered for performing the optimization. The first approach is a global optimization, which optimize the whole combined system and minimizes the cost of water (Cw). The second one, as an innovative method, is a local optimization approach, which optimizes the HRSG at first stage and after that, by applying optimum parameters obtained from HRSG optimization, optimizes the ME-TVC in order to achieve the minimum cost of water. Furthermore, in order to investigate thermodynamic and economic characteristics of the system simultaneously, a multi objective optimization is done as the third approach. 2. System description Figs. 1 to 3 show the desalination plant and co-generative cycle, respectively. The flue gas comes into the HRSG, which has an economizer

368

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Fig. 1. A six-effect thermal vapor compression desalination (METVC).

and evaporator, and produces the required saturated steam for running the desalination plant. In order to produce fresh water, a multi-effect evaporation thermal vapor compression (ME-TVC) is selected. The plant is parallel-cross feed and includes evaporators, flashing boxes, steam jet ejector and end condenser. For all parts of the system, energy and exergy equations are developed and applied to evaluate the performance of the combined system.

temperature profiles. Especially, the pinch point is more important in order to quantify the operating parameters. Representing the minimum difference between the gas temperature leaving the evaporator and the saturation temperature, the pinch point implicitly considers both thermodynamic and economic points of view. So, both pinch point and approach point are included in the modeling. T ap ¼ T sat −T v2

ð1Þ

′

ð2Þ

3. System modeling T pp ¼ T

g1 −T v3

3.1. Heat recovery steam generator The heat recovery steam generator (HRSG) which is applied for producing the required motive steam of ME-TVC, includes an economizer and an evaporator. In fact, the required motive steam is assumed to be saturated and thus the boiler does not need any superheater section. The HRSG design in the actual technology is based on the concepts of pinch point and approach point, which govern the gas and steam

For the economizer and evaporator, energy and mass balance equations could be written as follows: Evaporator:
 mg C p;g T g1 −T ′g1 ¼ mms C p;w ðT v4 −T v3 Þ

ð3Þ

Economizer:
 mg C p;g T ′g1 −T g2 ¼ mms C p;w ðT v2 −T v1 Þ

ð4Þ

In addition to the thermodynamic model of HRSG, the model proposed by Ganapathy [23] is applied for heat transfer and pressure loss calculation that presented in Appendix A. Therefore, the model of HRSG is comprehensive enough for predicting the behavior of a real case and can simulate thermal performance as well as geometrical characteristics. One of the most noticeable aspects of integrating HRSG with gas turbine cycle is power generation loss due to pressure drop of flue gas passing through HRSG that could be calculated by the following relation [24]: "   k−1=k # P atm þ ΔP g k−1=k P − atm Pt Pt

W loss ¼ M g C pg ηit ðT t Þ

ð5Þ

Thus, according to the developed model for HRSG, it would be possible to optimize both thermodynamic and geometrical parameters. 3.2. ME-TVC modeling For evaluation of thermal performance and needed heat transfer area of system, a mathematical model is developed by applying mass and energy conservation laws to the evaporators, steam ejector, flash boxes and condenser. The following assumptions are considered for desalination system:

Fig. 2. Heat recovery steam generator.

- Vapor formed in each effect is free of salt. - Thermal loss from desalination to environmental is negligible. - Final reject salinity is assumed 70000 ppm.

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369

Fig. 3. Combined gas turbine cycle and METVC desalination.

- Heat transfer area of evaporators 2 to N is the same. - Initially, it was supposed that the temperature difference of all effects is the same which T1 and TN are first and last effect temperature, respectively: ΔT ¼

T 1 T N N1

The cooling water flow rate is obtained from following equation: Mcw ¼

ðDN þ D′N M ev ÞLs
 Mf C p T f Tcw

ð16Þ

ð6Þ

T 1 ¼ T s ΔT Tiþ1 ¼ Ti ΔTi ¼ 2…N

ð7Þ

Heat load of evaporator and condenser can calculate by blew equations: A1 ¼

ð17Þ

It should be noted that the Eq. 8 is an initial assumption and in the end of calculation, the temperature differences of all effects would be different. Water and salt mass balance for the first effect and the effects 2 to N is as follow:

Ms Ls U e1 ðT s T1 Þ

Ai ¼

ðDi1 þ D′i1 ÞLi1 i ¼ 2; ::; N U ei ΔT

ð18Þ

B1 ¼ FD1

ð8Þ

Ac ¼

ðDN þ D′N ÞLN U c LMTDe

ð19Þ

Bi ¼ F þ Bi1 Di i ¼ 2; ::; N

ð9Þ

x1 ¼

F x B1 f

ð10Þ

xi ¼

F B x þ i1 xi1 i ¼ 2; ::; N Bi f Bi

ð11Þ

The motive steam of first effect is supplied by heat recovery steam generator. So, energy balance equation of first effect can be written as:
i 1h D1 ¼ M s Ls FC p T 1 T f L1

ð12Þ

T f ¼ T N ΔTcond

ð13Þ

On the other hand, vapor is produced by two mechanisms in the effect 2 to N: boiling and flashing. In these effects, brine reject of each effect inters to next effect and because of decreasing pressure, a small amount of vapor is formed. Another small quantity of vapor is formed in the flash box due to the flashing of distillate condensed in previous effect. The mass flow rate of vapor formed in the flash box obtains by following equation [25]. D′i ¼ Di1 C p

T vi1 T′i Li

ð14Þ

So, energy balance equation of the effects 2 to N can be written as: Di ¼


 i 1h ðDi1 þ D′i1 ÞLi1 FC p T i  T f Bi1 C p ΔT Li

ð15Þ

For steam jet ejector, the model developed by reference [26] is used to calculate entertainment ratio as a function of compression ratio (Cr) and expansion ratio (Er): Cr ¼

P hs P ev

ð20Þ

Er ¼

Pm Pev

ð21Þ

The specific heat transfer area, total product and brine of ME-TVC is defined as: N P

a¼

i¼1

Md ¼

Ai þ Ac Dtot

N X Di i¼1

ð22Þ

ð23Þ

M b ¼ BðnÞ One of the most important characteristics of thermal desalination is gain output ratio (GOR), the ratio between the mass of produced fresh water to that of the consumed motive steam: GOR ¼

Md Mm

ð24Þ

370

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3.3. Exergy analysis The specific exergy of a stream can be written as: ph

e¼e

ch

pt

kn

þe þe þe

ð25Þ

Physical exergy can be defined as: ph

e

¼ ðh−ho Þ−T o ðs−so Þ

ð26Þ

In order to calculating seawater exergy, the specific entropy and enthalpy of a component per unit mole in an ideal solution at a specified temperature T and pressure P is written as [4]: s ¼ mf s ss þ mf w ss

ð27Þ

h ¼ mf s hs þ mf w hs

ð28Þ

Seawater can be considered to be an “ideal solution” with negligible error [4]. Therefore, the entropy of a component per unit mole in an ideal solution at a specified temperature T and pressure P is: si ¼ sðP; T Þi;pure Ru lnxi

ð29Þ

With above equation chemical exergy of seawater is calculated by: ch

e

¼ −Nm RT o ½ðxw lnxw þ xs lnxs Þ

ð30Þ

Eventually, exergy efficiency of combined system including HRSG and ME-TVC could be presented as: ηex ¼

M d ed þ M b eb þ Mcw ecw −M f ef Mg eg

ð31Þ

4. Thermoeconomic analysis Thermoeconomic analysis is applied to calculate the expenditure cost and the unit product cost and also to point out the unit that needs more improvement. Thermoeconomic analysis requires solving energy, exergy and cost balance equations of the considered different components of HRSG as well as ME-TVC plant. The governing equation of thermoeconomic model for the cost balancing of an energy system is written as: CF þ Z ¼ CP

4.1.1. Levelized costs The series of annual costs associated with carrying charges CCj and expenses (FCj and OMCj) for the jth year of plant operation is not uniform. A levelized value TRRL for the total annual revenue requirement can be computed by applying a discounting factor and the capitalrecovery factor CRF: TRRL ¼ CRF

ð33Þ

The above relations are global cost balance equation, which should be applied for different component. Here, for each component of combined system, cost balance equation is taken into account. 4.1. Economic analysis In order to perform the economic analysis; first, the purchase cost of equipments must be determined. The purchase cost of the equipments are determined by some correlations that proposed by El-sayed [27]. It is worth mentioning that these correlations have been used by ElNahsar [28] and Nafey et al. [13–14]. After calculating the purchase cost of all equipments, for calculation of capital investment and operating and maintenance of each component, an economic method, namely, TRR (total revenue requirement) is applied that has been proposed by Bejan et al. [29]. The annual

BL X 1

TRRj
j 1 þ ieff

ð34Þ

where TRRj is the total revenue requirement in the jth year of plant operation, ieff is the average annual effective discount rate (cost of money) and it is about 12%, and BL denotes the plant economic life (book life) expressed in years. In Eq. (34), it is assumed that each money transaction occurs at the end of each year. Therefore, the capital-recovery factor CRF is given by:
BL ieff 1 þ ieff n CRF ¼
1 þ ieff −1

ð35Þ

Finally, the levelized carrying charges CCL are obtained from:

ð32Þ

By defining exergy cost of each stream, c, Eq. (32) could be changed to cF E F þ Z ¼ cP E p

Total Revenue Requirement (TRR) for a system is the revenue that must be collected in a given year through the sale of all products to compensate the system operating company for all expenditures incurred in the same year and to ensure sound economic system operation [29]. It involves two parts: a) carrying charges that are a general designation for charges that are related to the capital investment, whereas b) expenses that are used to define costs associated with the operation of a system [29]. Carrying charges include the total capital recovery and return on investment for preferred stock [29]. The annual total revenue requirement (total product cost) for a system is the revenue that must be collected in a given year through the sale of all products to compensate the system operating company for all expenditures incurred in the same year and to ensure sound economic plant operation [3]. It consists of two parts: carrying charges and expenses. Carrying charges are a general designation for charges that are related to capital investment, whereas expenses are used to define costs associated with the operation of a plant. All annual carrying charges and expenses have to be estimated for each year over the entire economic life of a plant.

CC L ¼ TRRL −FC L −OMC L

ð36Þ

The major difference between a conventional economic analysis and an economic analysis conducted as part of a thermoeconomic analysis is that the latter is done at the plant component level. The annual carrying charges (Z CI) and operating and maintenance costs (Z OMC) of the total plant can be apportioned among the system components according to the contribution of the kth component to the purchased equipment cost for the overall system: CI

Zk ¼

OMC

Zk

CC L PEC k τ ∑k PEC k ¼ CI

OMC L PEC k τ ∑k PEC k OMC

Zk ¼ Zk þ Zk

ð37Þ

ð38Þ ð39Þ

Zk = ZkCI + ZkOMCτ and Zk denote the purchased-equipment cost of the kth plant component, the total annual time (in hours) of system

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operation at full load, and the cost rate associated with the capital investment and the operating and maintenance expenses, respectively.

371

Table 2 Specifications of the base case combined system. Parameter

5. Optimization approach In order to achieve the optimal parameters, an optimization algorithm tool can be used. Although gradient descent methods are the most elegant and precise numerical methods to solve optimization problems, however, they have the possibility of being trapped at local optimum depending on the initial guess of solution. In order to achieve a good result, these methods require very good initial guesses for parameters. Stochastic optimization methods such as genetic algorithm (GA) and Particle Swarm Optimization (PSO) that have been applied for this study seem to be promising alternative for solving this problem. In general, they are robust search and optimization techniques, able to cope with ill-defined problem domain such as multimodality, discontinuity and time-variance. GA is a population based optimization technique that searches the best solution of a given problem based on the concepts of natural selection, genetics and evolution [30]. PSO is a heuristic population based optimization algorithm simulating the movement and flocking of birds [31]. In addition to these sigle objective algorithms, in this paper multi objective genetic algorithm (MOGA) was applied for finding optimal solution. 6. Results and discussion Table 1 shows the operating parameters of gas turbine plant. After modeling and simulating the combined system, many results were obtained and the effects of main parameters on performance of the system were studied. The initial values of design parameters are mentioned in Table 2. For verification, the models proposed by references [21] and [23] were selected for ME-TVC and HRSG, respectively. Tables 3 and 4 show the verification of HRSG and ME-TVC models, respectively. 6.1. Results of simulation and thermoeconomic analysis In this section, the results of simulation and thermoeconomic evaluation are presented in the form of several figures that some of them are shown as three-dimensional graphs for better explanation. The first figure, Fig. 4, describes exergy destruction of different parts of the combined system. As can be observed, the main part of exrgy destruction is related to the evaporator of HRSG and, after that, steam jet ejector has the highest amount of exergy destruction. Naturally, steam jet ejector is a low efficient device although it has a strong effect on productivity. The ME-TVC effects have the lowest amount of exergy destruction. On the other hand, HRSG has more than 50% of exergy destruction of the combined system. 6.1.1. Effect of ejector compression ratio Fig. 5 shows the effect of ejector compression ratio on the cost of water. Compression ratio is one of the most important parameter of ME-TVC system that has a significant effect on the mass flow rate of heating steam and thus productivity. When compression ratio increases, the mass flow rate of entrainment vapor sucked by ejector goes down and, thus, the mass flow rate of heating steam and

Table 1 Operating parameters of gas turbine plant. Parameter

Value

Compression ratio Turbine inlet temperature (°C) Net power output (Mw) Isentropic efficiency of compressor Isentropic efficiency of turbine

12.5 1100 130 0.85 0.9

Value

HRSG Inlet water temperature (°C) Pinch point temperature (°C) Approach point temperature (°C) Produced steam pressure (kPa) Minimum stack temperature (°C) Maximum pressure drop of gas side (kPa) Inlet tube diameter (mm) Fin density (fin/m) Fin height (mm) Fin thickness (mm) Tube length (m) METVC Heating steam temperature (°C) Top brine temperature (°C) Inlet condenser temperature of seawater (°C) Outlet condenser temperature of seawater (°C) Number of effects $jector compression ratio Reject salinity of last effect (ppm) Feed seawater salinity (ppm) Tube diameter (mm) Tube length (m)

35 45 5 1000 130 3 135 51 19.7 2.3 10 70 67 30 5 °C lower than Tn 6 3 70000 36000 19.05 5

produced fresh water decrease. On the other hand, increasing the compression ratio leads to the decrease in the last effect temperature. Therefore, as Fig. 6 illustrates, for a specified TBT, the required heat transfer area, productivity and specific heat transfer area reduce. Although, decreasing heat transfer area decreases the required capital investment, the cost of water increases because of the decrease in productivity. As a result, higher compression ratio implies higher cost for the product but lower capital investment. Another issue that could be extracted from Fig. 5 is that by increasing the number of effects and productivity, the cost of water goes down. 6.1.2. Effect of heating steam temperature and TBT Since both Ts and TBT are introduced as model inputs (Table 1), the influence of these two parameters on performance characteristics of the system could be studied. For a specified TBT, when Ts increases, specific heat transfer area also increases and eventually reaches a maximum value. In fact, an increase in Ts increases the temperature of last effect (Tn) since, in this case, when Ts goes up from 70 °C to 80 °C; Tn increases from 41.53 °C to 50.03 °C. At the same time, by increasing TBT, the temperature difference between the effects increases and specific heat transfer area dramatically goes down. The highest amount of specific heat transfer area is related to the highest Ts and lowest TBT. Consequently, more difference between Ts and TBT implies higher specific heat transfer area. Since, the main parameter that determines the purchase cost of ME-TVC is heat transfer area, by increasing heat transfer area, capital investment of ME-TVC also increases. On the other hand, based on Fig. 7, increasing Ts and TBT

Table 3 Verification of HRSG model. Parameter

Ref. [22]

Present model

mg (kg/s) T1(°C) P (bar) di (m) hf (m) L (m) T2(°C)a U (w/m2K)a ΔPg (pa)a Q (Mw)a

28.98 838.706 14.84 0.045 0.01905 3.353 480.928 42.019 846.879 11.606

28.98 838.706 14.84 0.045 0.01905 3.353 476.213 40 1032.623 11.394

a

Model output

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3.6

Table 4 Verification of METVC model.

D (kg/s) msw(kg/s) Atot (m2) GOR

n=4

3.4 n=5

n=6, Cw

n=8, Cw

n=4,CC

n=6, CC

n=8,CC

1.4 1.3

n=6

Ref. [20]

present model

Ref. [20]

present model

Ref. [20]

present model

0.7 4.81 222 6.14

0.7 5.03 219 6.05

0.88 5.02 283 7.72

0.89 5.23 279 7.80

1.08 5.52 355 9.21

1.10 5.65 361 9.61

3.2

Cost of water ($/m3)

Parameter

n=4, Cw

difference leads to the increase in PR; however, the cost of water goes up (Fig. 8). 6.1.3. Effect of motive steam pressure and pinch point Motive steam pressure is one of those parameters that simultaneously effects on the design and performance of both HRSG and ME-TVC plant. Hence, studying its influence on performance of the system is so important and useful. Fig. 9 shows the effect of motive steam on the cost of water. The figure was plotted for several pinch point temperature (Tpp). As can be observed in Fig. 10, when motive steam pressure (Pm) increases, productivity decreases. In contrast to what might be thought, by increasing Pm, the cost of water does not decrease steadily; in fact, in higher Tpp there is a minimum value for the cost of water. According to a similar study conducted for the cost of steam, the same figure was obtained. Whereas, steam is considered fuel of ME-TVC, the cost of water follows the same trend. Consequently, as Fig. 9 shows at an optimum pressure, the cost of water is minimized and by decreasing Tpp, the minimum cost of water occurs in higher Pm. Pm also has a significant impact on the capital investment of HRSG and ME-TVC. This impact is represented in Fig. 11. Based on the figure, the capital investment of HRSG reduces dramatically while, for METVC, reduction rate is much slighter. Decrease in the capital investment of HRSG is related to the change in heat load of economizer and evaporator. Whereas, the pinch point is assumed constant, by increasing Pm, temperature of flue gas exiting from HRSG increases and, consequently, the amount of heat absorbed by fluid, reduces. As a result, heat transfer area and capital cost of HRSG decreases. On the other hand, by reducing the mass of steam, productivity and capital cost of ME-TVC goes down. Fig. 11 also illustrates the influence of pinch point temperature (Tpp) on cost and productivity. From the thermodynamic point of view, pinch point is a challenging parameter and has a strong effect on the capital investment of HRSG and steam cost. Since steam is considered the fuel consumed by ME-TVC, its cost directly affects the cost of fresh water. Fig. 12 describes the effect of pinch point variation on the capital investment of HRSG and ME-TVC. As was expected, by increasing Tpp, the required heat transfer area of HRSG and its capital investment reduces. Similarly, because of the reduction in water

1.2

3 1.1 2.8 1 2.6 0.9 2.4

capital cost ($/s)

372

0.8

2.2

0.7

2 1.8

0.6 1.8

2.2

2.6

3

3.4

3.8

4.2

4.6

5

Cr Fig. 5. Influence of ejector compression ratio on capital cost and cost of water.

production, the required capital investment of ME-TVC reduces in a slighter trend. 6.2. Optimization In order to perform an optimization approach, those operating parameters that affect the performance of the combined system are considered. Decision parameters of the optimization study are selected from input parameters that can be observed in Table 5. In addition, lower and upper bands of decision variables can be observed in Table 5. From the thermodynamic point of view, these parameters play an important role in performance of the combined cycle. Furthermore, the linear and nonlinear constraints of optimization problem that are related to both HRSG and ME-TVC are introduced below. Linear constraint: o

T s TBT≥3 C Nonlinear constraint: T 1 −T N > 3 o C T f  T cw > 3o C xn ≤70000ppm T g2 ≤130o C In order to demonstrate the effect of operating parameters of HRSG on the optimal design of ME-TVC, three approaches are considered for 1.8 1.6

water production

Normalized values

heat transfer area

1.4

a

1.2 1 0.8 0.6 0.4 2

2.4

2.8

3.2

3.6

4

4.4

4.8

5.2

Cr Fig. 4. Exergy destruction percentage of different parts of combined system.

Fig. 6. Effect of ejector compression ratio on water production and heat transfer area.

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373

2.02 Tpp=45

2

8.7

1.98

Cost of water ($/m3)

8.75

GOR

8.65 8.6 8.55

Tpp=35 Tpp=30

1.96

Tpp=25

1.94 1.92 1.9

8.5 8.45 78

Tpp=40

1.88 77

76

75

Ts(oC)

74

73

72

69

68

67

66

65 1.86

TBT (oC)

5

10

15

20

25

30

35

40

45

50

Pm(bar)

Fig. 7. Effect of heating steam temperature and TBT on PR. Fig. 9. Effect of motive steam on cost of water.

performing optimization. As mentioned in Table 6, the first approach is a global optimization, which optimizes the entire combined system and minimizes the cost of water (Cw). The second one, as an innovative method, is the local optimizations approach, which at the first stage, minimizes the cost of produced steam in HRSG. Then, by applying optimum parameters that obtained from the first stage, the second stage of optimization is run and the cost of water is minimized. In other words, this novel approach, at the first stage optimizes HRSG and at the second stage optimizes ME-TVC from the economic point of view. As it was mentioned in the previous sections of the paper, in order to perform the optimization study, GA and PSO algorithms are chosen. However, in addition to these heuristic algorithms, two hybrid algorithms, namely, GA-SQP and PSO-SQP were also performed. Since SQP (successive quadratic programming) method is a nonlinear programming method that needs an initial point to start the optimization process and finds a solution, an initial point was created by applying GA or PSO and then SQP was run. The results obtained from these two hybrid methods did not show any improvement over the results of single PSO and GA although Modares and NaghibiSistani [31] achieved a better solution. Table 7 shows the optimal design of fresh water production system obtained by the optimization study. Comparison of the results of the first and second approaches show that the minimum amount of objective function that achieved by PSO is slightly better than GA while PSO spends less time than GA. On the other hand, the results obtained by PSO and second approach present a HRSG not only with lower product

cost but also with lower capital cost investment. Although the objective of authors of developing the second approach was to achieve lower cost of water, the results show that the difference between various results is about 2%. Whereas, steam is identified as the fuel for ME-TVC, it was expected that by minimizing the cost of steam in the first stage of the second approach, the system could reach lower cost of water. Since, steam pressure is a key parameter that affects the performance of both HRSG and ME-TVC, when the second approach is applied, at the first stage, the optimum amount of steam pressure is obtained. The obtained results show that the optimum amount is almost close to the upper bound. However, according to the ME-TVC simulation presented in the previous section, it is clear that the minimum cost of water is achieved at intermediate pressure of lower and upper bound of optimization study. Consequently, application of the second approach rather than first approach demonstrates slight improvement. One of the most important thermodynamic parameters of distillation desalination is GOR. The amount of GOR is fairly low for all cases. It seems that for higher GOR, the cost of water must probably increase. Therefore, in order to study the effect of increasing GOR on the cost of water, a multi objective optimization was conducted as the third approach. As Fig. 13 and Table 7 describe, the result of the third approach with the objective of minimizing the cost of water and optimizing GOR leads to a system with higher GOR and higher cost of water. The cost of water increases by 7% with respect to the lowest value that obtained by first and second approaches while water production rate and capital investment cost of the plant increases by 8% and 22%, respectively. 64000

Tpp=45 Tpp=40

63000

Tpp=30

mass of water (m3\day)

2.3

Cost of water ($/m3)

2.25 2.2 2.15 2.1 2.05 2

Tpp=30

62000

Tpp=25

61000 60000 59000

1.95 1.9 78

58000 77

65 76

66 75

Ts(oC)

74

67 73

68 72

TBT (oC)

69

Fig. 8. Effect of heating steam temperature and TBT on cost of water.

57000 5

10

15

20

25

30

35

Pm(bar) Fig. 10. Effect of motive steam on productivity.

40

45

50

374

S.E. Shakib et al. / Desalination 285 (2012) 366–376 METVC

HRSG

Table 5 Decision variables and constrains of the optimization problem.

Capital investment ($/s)

0.5

0.4

0.3

0.2

0.1

10

15

20

25

30

35

40

45

Pm(bar) Fig. 11. Dependence of capital investment of HRSG and METVC on motive steam pressure.

According to Table 7, it could be concluded that, pressure drop of flow gas for two single objective approaches is the same value and thus the amount of power loss due to HRSG is equal to 0.95 Mw. It should be noted that, the power loss that achieved by the third approach does not show a significant decrease in comparison with other approaches. Eventually, it could be concluded that, application of local and global optimization for this problem leads to the similar results from thermodynamic and economic points of view although the multi objective approach presents an optimal design with higher productivity as well as higher product and capital cost.

Parameters

Lower band

Upper band

Ts (°C) [2] TBT(°C) [2] Pm (bar) [2] Cr [2] N [16] ΔTcond (°C) [24] Leff (m) [8] deff (mm) Tpp (°C) Tapp(°C) Lhrsg (m) dhrsg (mm) [22] nf (fin/m) [23] tf (mm) [23] hf (mm) [23] pt (mm) [23]

60 60 5 2 3 5 4 15 5 5 10 25 50 0.9 13 35

80 80 45 5 10 10 5 40 50 30 20 150 285 3 25 600

was done using the multi objective genetic algorithm (MOGA) as the third approach. The results of this approach had the advantages of higher GOR and lower power loss. However, the amount of water cost and capital investment increased by 7% and 22%, respectively. It could be concluded that, the application of local and global optimization for this problem led to the similar results from thermodynamic and economic point of view although the multi objective approach presented an optimal design with higher productivity as well as higher product and capital cost.

7. Conclusion Appendix A. (heat transfer and pressure drop calculation of HRSG) In this paper, a fresh water production system consisting of HRSG and ME-TVC units was coupled to an available gas turbine power plant located in the south of Iran, near the seashore. First, HRSG and ME-TVC system were modeled and simulated and energy and exergy equations were developed for all parts of system. After the simulation, in order to evaluate economy of the system, a detailed thermoeconomic analysis was performed and afterwards in order to achieve an optimal design, three approaches were considered. It seems that the minimum amount of objective function achieved by PSO was slightly better than that of GA. Although the objective of developing the second approach was to achieve lower product cost, the results showed that the difference among various results was about 2%. In addition to the product cost, one of the other most important thermodynamic parameter of distillation desalination is GOR. In order to study the effect of increasing GOR on the cost of water, a multi objective optimization

In this section, the heat transfer and pressure drop calculation of considered HRSG is briefly explained. A.1. Heat transfer area calculation The energy transferred in heat transfer equipment, Q, is given by the basic equation: A¼

Q UΔT LM

ðA:1Þ

In the above equation, A, U and ΔTLM represent heat transfer area, overall heat transfer coefficient and corrected log-mean temperature difference, respectively. The log-mean temperature difference can be calculated as [23]:

0.6 Capital investment of METVC ($/s)

METVC HRSG

ΔT LM ¼ F T 

P=30 bar

0.5

ðA:2Þ

min

Where, FT is the correction factor for flow arrangement. For counter flow cases, FT is equal to 1.0. For other types of flow, it varies from 0.6 to 0.95. ΔTmax and ΔTmin are the maximum and minimum terminal differences.

0.4

0.3

Table 6 Different objective function of optimization study.

0.2

0.1

ΔT max −ΔT min
 max ln ΔT ΔT

25

30

35

Tpp(oC)

40

45

50

Fig. 12. Dependence of capital investment of HRSG and METVC on pinch point temperature.

Approach

Optimization type

Objective function

1 2

Global, single objective Local, single objective

3

Global, multi objective

min. Cw firstly: min. Cs secondly: min. Cw min. Cw max. PR

S.E. Shakib et al. / Desalination 285 (2012) 366–376

A.2. Pressure drop

Table 7 Optimal results given by optimization study for the objective function. Parameters

Base case

Optimal design app. 1

mms (kg/s) ΔPg (kPa) Wloss (Mw) Tg2 (°C) Md (m3/day) GOR ηex (%) Cs ($/ton) Cw ($/m3) ZHRSG($/s) ZMETVC ($/s)

68.9 1.2 0.38 133 48380 8.1 3.5 11.13 2.08 0.25 0.43

app. 2

app. 3

GA

PSO

GA

PSO

MOGA

66.5 3 0.95 143 68590 11.9 2.7 10.81 1.77 0.17 0.70

68.6 3 0.95 131 69980 11.8 2.4 10.14 1.73 0.14 0.73

68.0 3 0.95 135 69450 11.8 3.5 10.24 1.74 0.14 0.72

68.7 3 0.95 130 70450 11.8 3.4 9.82 1.69 0.10 0.72

65.3 2.9 0.93 151 76300 13.5 4.0 10.92 1.82 0.15 0.92

In order to calculate the gas side pressure drop, below equation can be applied [23]. ΔPg ¼ Z 

T g;ave ¼

do 1 1 A A 1 At do ln di ¼ þ fo þ t fi þ t þ U ηo ho Awi Awi hi Aw 2K m

ðA:3Þ

At, Ai and Aw are surface area of finned tube, tube inner surface area and average wall surface area, respectively. Km is thermal conductivity of the tube wall and do and di is also tube outer and inner diameter. In addition, fi and fo represent fouling factors inside and outside the tubes while hi and ho are tube-side and gas-side heat transfer coefficients. Surface area of finned tube can be written as follows: At ¼ Af þπdo ð1  nf tf Þ

ðA:4Þ

2

Af ¼πnð2do hf þ 2hf þ tf do þ 2tf hf Þ

ðA:5Þ

Af is the surface area of a fin. nf, hf and tf are the density, height and thickness of fins, respectively. Tube inner surface area and average wall surface area can be calculated as: Awi ¼ πdi

ðA:6Þ

  di þ do 2

ðA:7Þ

ðA:8Þ

T g;i þ T g;o 2

ðA:9Þ

ðA:10Þ

In above equations, Nr is number of rows deep. The gas mass velocity G is given by: Gg ¼




Gg Nr 500  ρg

640:8  ρg ¼
1:8T g;ave þ 32 þ 460

For extended surfaces, U can be obtained from [23]:

Aw ¼ π

375

_ M g Nw ðST −Ao ÞL

ðA:11Þ

Ao ¼ do þ 2nf t f hf

ðA:12Þ

where, Ao is obstruction area and ST is the transverse pitch. The pressure drop in economizer tubes is calculated by DarciVisbakh relation [23]: ΔP eco ¼ f

le V 2 ρN di 2 f w

ðA:13Þ

where, Nw and le is number of rows wide and equivalent length, respectively. The pressure loss of evaporator due to have two-phase flow includes three terms, namely, friction loss, gravity loss and acceleration loss. ΔP eva ¼ ΔP f þ ΔP g þ ΔP a ΔP g ¼ 0:82  10

−15



vf f m le G2 r 3 14:5di

ðA:15Þ

−10



N w le r 4 14:5vf

ðA:16Þ

−16



vf G2 r2 14:7

ðA:17Þ

ΔP g ¼ 142:359  10

ΔP a ¼ 0:34074  10

ðA:14Þ

Coefficients r2 to r4 and fm are given by ref. [23]. 14.2

References

14 13.8 13.6

GOR

13.4 13.2

Optimal solution

13 12.8 12.6 12.4 12.2 12 1.76

1.78

1.8

1.82

1.84

1.86

1.88

Cost of water ($/m3) Fig. 13. Pareto-optimal solution for objective function of third approach.

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