Thermoeconomic optimization of multi effect ...

Applied Energy 87 (2010) 1122–1133

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Thermoeconomic optimization of multi effect distillation desalination systems Hoseyn Sayyaadi *, Arash Saffari Faculty of Mechanical Engineering-Energy Division, K.N. Toosi University of Technology, P.O. Box 19395-1999, No. 15-19, Pardis Str., Mollasadra Ave., Vanak Sq., Tehran 1999 143344, Iran

a r t i c l e

i n f o

Article history: Received 23 September 2008 Received in revised form 9 May 2009 Accepted 16 May 2009 Available online 21 June 2009 Keywords: Multi effect distillation desalination Genetic algorithm Thermal desalination TRR method Thermoeconomic Exergy analysis

a b s t r a c t Thermoeconomic optimization of a multi effect distillation (MED) desalination system with thermovapor compressor (TVC) is performed. A model based on the energy and exergy analysis is presented here. An economic model of the system is developed according to the Total Revenue Requirement (TRR) method. The objective functions based on the thermodynamic and thermoeconomic analysis are developed. The proposed multi effect distillation system including six decision variables is considered for optimization. A stochastic/deterministic optimization approach known as genetic algorithm is utilized as an optimization method. This approach is applied to minimize the cost of the system product (fresh water). Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Energy systems involve a large number and various types of interactions with systems outside their physical boundaries. Engineers must therefore face many issues, which involve with the energetic, economic and so on. Thermodynamic govern energy conversion processes, costs are involved in obtaining the final products (expenses for the purchase of equipment and input energy resources, operation and maintenance costs). The idea of thermoeconomics comes from the basic question about the method to be used for cost balance in large energy systems. Thermoeconomics combines the exergy analysis with the economic principles. It incorporates the associated costs of the thermodynamic inefficiencies in the total product cost of an energy system. These costs can help designers to find out the cost formation process in an energy system. Further, this analysis can be utilized in optimization of thermodynamic systems, in which the task is usually focused on minimizing the unit cost of the system product. Thermoeconomic optimization aims at minimizing the total levelized cost of the system product, which implicitly includes fuel cost and the cost of inefficiencies. A powerful thermoeconomic analysis, evaluation, and optimization techniques have been refined and applied by researchers around the world to solve practical problems in the design and improvement of thermal systems [1–5]. Thermoeconomics aims at minimizing the total levelized cost of the system product, which implicitly includes fuel cost

* Corresponding author. Tel.: +98 21 8867 4212; fax: +98 21 8867 4748. E-mail address: [email protected] (H. Sayyaadi). 0306-2619/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2009.05.023

and the cost of inefficiencies. The principles and methodologies of thermoeconomics are well established by Bejan et al. [6]. On the other side, the need for high-quality water significantly increased during the second half of the last century. The desalination industry is important for several countries and zones around the world, especially the countries around the Persian Gulf. Multi effect distillation (MED) desalination with thermal vapor compression (TVC) system is paid attention more than other thermal systems due to effectiveness, easier operation and maintenance, and good economic characteristics, which is expected to take a considerable portion in the desalination field in the near future [7–9]. A comprehensive review of various desalination systems and application of renewable energy to drive desalination systems is well performed by Kalogirou [10]. Expansion in desalination industry is associated with reduction in the power consumption, increase gain output ratio (GOR) and exergy efficiency, which finally decreases the price of fresh water. Analysis of exergetic flow helps engineers and analysts to identify source, magnitude and importance of thermodynamic inefficiencies. Most of the thermodynamic analysis performed on the MED–TVC system is based on the first law of thermodynamics [11–14]. Uche et al. [15], Kafi et al. [16], Ettouney and El-Dessouky [17], El-Dessouk and Ettouney [18], Jernqvist et al. [19], Alasfour et al. [20] and Ettouney [21] developed thermal analysis simulations for MED system. Raach and Mitrovic [22] performed simulation of heat and mass transfer of a MED. These investigations have been dedicated to energy and exergy analysis or heat and mass transfer simulation of MED system without economic consideration of this type of desalination system. Abdulnasser et al. [1] performed thermoeconomic analysis of some existing desalination process; however, no

H. Sayyaadi, A. Saffari / Applied Energy 87 (2010) 1122–1133

1123

Nomenclature BBY BD Bi BL C CC CP Di Drn Dt E_ E_ D E_ D;tot E_ F E_ L E_ P e F fi fk GOR hf hg ieff j Li Mc Mds MED N n OMC P PEC Pi PPM ROI rele rOM rste S_

balance at the beginning of the year book depreciation brine flow rate outcomes from the effect ith (kg/s) book life constant coefficient carrying charge specific heat capacity (kJ/kg K) distillate from the effect ith entrained vapor from the effect n total product flow rate exergy rate (kW) exergy destruction (kW) total exergy destruction for the entire MED system (kW) exergy of fuel (steam and electricity) (kW) exergy loss (kW) exergy of product (kW) exergy per unit of mass (kI/kg) total feed flow rate (kg/s) feed flow rate for the effect ith (kg/s) thermoeconomic factor for the kth component gain output ratio saturated liquid enthalpy (kJ/kg) saturated vapor enthalpy (kJ/kg) interest rate jth year of operation latent heat at Ti (kJ/kg) total seawater inlet flow rate (kg/s) water consumption in the desuperheater (kg/s) multi effect distillation number of effects vapor return effect operating and maintenance cost pressure (kPa) purchase equipment cost ($) pressure of the effect ith (kPa) parts per million return on investment annual escalation rate for the cost of electricity annual escalation rate for operating and maintenance cost annual escalation rate for the cost of steam rate of entropy (kW/K)

attempt made to optimize desalination systems. In the field of optimization of desalination system, the work conducted by Yahia El-Sayed that optimizes system based on the higher productivity can be pointed out [23]. However, in his optimization, economic factor was not considered. As is clear a few attempts have been performed on thermodynamic and thermoeconomic optimization of desalination systems. The purpose of this work is to present a thermoeconomic optimization of multi effect distillation (MED) desalination systems. A typical MED desalination system is considered for optimization. The thermodynamic modeling is performed based on the energy and exergy analysis, while an economic model is developed according to the Total Revenue Requirement (TRR) method [6,24]. The objective functions based on the thermoeconomic analysis are obtained. Optimization processes is performed with a hybrid stochastic/deterministic approach namely as genetic algorithm (GA). 2. Configuration of MED–TVC The main components of the conventional MED–TVC are the steam ejector, which represents the heart of the system; horizon-

SUC T TCR TDS TRR TVC _ W WC X

start up cost temperature (°C or K) total capital recovery total dissolve solids total revenue requirement thermo-vapor compressor power (kW) working capital salt concentration (%)

Greek symbols q density (kg/m3) s number of operating hours in year (h) etot total MED–TVC exergetic efficiency eejector+desuper exergetic efficiency of ejector and desuper heater DT temperature difference for each effect (°C) DTmin con temperature difference in the condenser (°C) Subscripts b brine boi boiler cond condenser D destruction d distillate ejec ejector eva evaporator F fuel f feed in inlet L loss out outlet P product sw seawater tot total Superscripts CH chemical CI capital investment KN kinetic OM operating and maintenance PH physical PT potential

tal falling film evaporators (effects) and a condenser (Fig. 1). The motive steam with the flow rate equal to S is used to compress a part of the vapor generated in the effect number n with the flow rate of Dr toward the steam ejector. The expanded motive steam and the recompressed vapor for return effect, n, leaves the steam ejector with the flow rate of S plus entrained vapor (Dr) and mixes with the pure water in de-superheater. The amount of consumed water in the de-superheater, denoted by Mds, is mixed with, S+Dr and the entire stream (S+Dr+Mds) is directed to the first effect and condensed there. A part of the condensate equal to S returns to the boiler and the remainder (Dr+Mds) joins the potable water product. The vapor formed in the first effect D1 is directed to the second effect. The vapor generated in each effect is passed through demisters and enters to the next effect to transfer heat to the feed seawater. This vapor heats the feed water with the rate of F2 from temperature equal to Tf1 into boiling temperature T2 and generates vapor at the rate of D2. This process continues up to the vapor return effect (n) where the vapor is bifurcated into Dr and Dn-Dr. The stream Dr is recompressed by the steam ejector and conducted to the first effect, and the remainder stream, Dn-Dr, is directed to the next effect


Fig. 1. Process flow diagram of the base case MED–TVC system.

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H. Sayyaadi, A. Saffari / Applied Energy 87 (2010) 1122–1133 Table 1 Specifications of the base case MED-TVC desalination system. Parameter

Symbol

Value

Capacity of MED (ton/day) Temperature of the sea water inlet (°C) Temperature of ambient (°C) Salt composition of the seawater inlet (%) Salt composition of the brine outlet (%) Number of effects Return effect Temperature of the vapor to the first effect (°C) Temperature of the last effect (°C) Temperature of the boiler (°C) Motive steam/return vapor in TVC (S/Dr) Minimum temperature difference in the condenser (°C) Specific power for the electrical instrument (kWh/m3) Pipe wall thickness in the evaporator (mm) Pipe outside diameter in the evaporator (mm) Pipe length in the evaporator (m) Pipe wall thickness in the condenser (mm) Pipe outside diameter in the condenser (mm) Pipe length in the condenser (m) Average product temperature before the feed-water heater (°C) Return vapor (ton/h) Total Steam consumption (ton/h) Total feed for all effects (ton/h) Total brine outlet (ton/h) Coolant sea water(reject) (ton/h) Total sea water inlet (ton/h) Water consumption in the de-superheater (ton/h) Gain output ratio

Dt Tsw T0 Xsw Xb N n Ts TN Tboi R Tmin cond Pc Wt Deva Leva Wtc Dcon Lcon Tave Drn S F B Rej Mc Mds GOR

2000.00 35 25 0.039 0.065 7 5 71 48 180 1.9 3 1.6 2 38 5 2 38 5 60.050 4.866 9.25 208.33 125.00 276.66 485.00 0.49 9.01

Parameter

Symbol

Effect1

Effect2

Effect3

Effect4

Effect5

Effect6

Effect7

Operating data for each effect Temperatures Streams temp. diff. Gage pressure Vapor production Outlet brine Feed water Feed water temp.

Ti (°C) DT (°C) Pi (mbarg) Di (ton/h) Bi (ton/h) fi (ton/h) Tfi (°C)

67.7 3.286 714 13.94 15.82 29.76 56.25

64.4 3.286 752 13.55 32.03 29.76 56.25

61.1 3.286 786 13.44 48.35 29.76 56.25

57.9 3.286 815 12.99 65.11 29.76 45

54.6 3.286 841 12.83 82.05 29.76 45

51.3 3.286 864 8.08 103.7 29.76 45

48 3.286 884 8.49 125 29.76 45

as a heat source, then process continues in a similar way as those effect that are placed before the driving effect. At the end, generated vapor of the last effect, DN, is directed to the condenser where it gives its latent heat to the cooling water with the rate of Mc and raises its temperature from Tsw into Tf. The part of this cooling water is used as feeds for the various effects and the remaining is returned to the sea. Hot brine, Bi, from an effect i at pressure of Pi (starting from i = 1) flows to the next effect i + 1 at the pressure of Pi+1, and this process continues to the last effect N. Since Pi+1 < Pi, flashing occurs in effect i + 1. The brine leaving from the last effect, denoted by BN, is conducted to a feed-water heater and preheats the feed water stream of the effects number 1, 2 and 3. Feed-water heating has two advantages; the first one is preheating of the feed for the effects number 1, 2 and 3, which leads to reduction of the total energy consumption and exergy destruction; the second advantage is reduction of the product water temperature from Tava to TN, which reduces the amount of exergy loss to environment. Specifications of selected MED system as a base case for optimization are indicated in Table 1. The energy and exergy balances for the evaporators (effects), condenser, feed-water heater, thermo-compressor and the entire system can be derived, with the following assumptions: a. All processes are steady state and steady flow with negligible potential and kinetic energy effects. b. Heat transfer and pressure drops in the pipeline are ignored. c. To achieve the optimum operating condition, temperature differences between streams in all effects are assumed equal [14].

d. Equal flow rate is fed to all effects (parallel feed arrangement: f1 = f2 = f3, . . . , = fN = F/N). 3. Mass and energy balance in the MED–TVC process The mass balance for the entire process (black box shown in Fig. 2) can be performed as follows:

F ¼ Dt fi ¼ i¼N X

F N

Xb X b X sw

ð1Þ ð2Þ

Di ¼ Dt

ð3Þ

i¼1

Fig. 2. Entire MED-TVC system as a black box.

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MED system comprises of five sub-systems:

Sub-system 2, 3: Effects 1, . . . , (Figs. 4 and 5)

Sub-system 1: Thermo-vapor compressor and de-superheater (Fig. 3) The energy and mass balance for thermo-vapor compressor and de-superheater can be calculated as follows:

S R¼ Drn Rhg hss ¼

If Di, Bi and fi are assumed to be the flow rates of vapor, brine and feed water in the effect number i, respectively and if the latent heat and heat transfer coefficient of water in the effect i denoted by Cpi and Li, then the energy and mass balance equations for effects 1, . . . , N are as follows:

Ts TN N T 1 ¼ T s DT T iþ1 ¼ T i DT; i ¼ 1; 2; . . . ; N 1 ðS þ Drn þ MdsÞLs ¼ f1 Cpf ðT 1 Tf1 Þ þ D1 L1 ðD1 Dr1 ÞL1 þ B1 CpB DT ¼ f2 Cpf ðT 2 Tf1 Þ þ D2 L2 ðD2 Dr2 ÞL2 þ B2 CpB DT ¼ f3 Cpf ðT 3 Tf1 Þ þ D3 L3 ðDi1 Dri1 ÞLi1 þ Bi1 CpB DT ¼ fi Cpf ðT i Tfi Þ þ Di Li ; i ¼ 4; . . . ; N i – n ) Dri ¼ 0 i i X X Bi ¼ fi Di ; i ¼ 1; . . . ; N

DT ¼

ð4Þ

þ hg n 1þR Mds R1 ¼ S þ Drn hss hgs R1 ¼ hgs hfN boiler

Mds ¼ S R1 1 þ

ð5Þ ð6Þ ð7Þ 1 R

ð8Þ

where S, Mds and Drn are flow rates of motive steam, water consumed in de-superheater and withdrawn vapor from effect n by steam ejector, respectively. hgs is the enthalpy of motive steam and hgn and hfn are saturated vapor and liquid enthalpy at operating pressure of effect number n in which vapor is withdrawn, respectively.

1

ð9Þ ð10Þ ð11Þ ð12Þ ð13Þ ð14Þ ð15Þ ð16Þ ð17Þ

1

Sub-system 4: Feed-water heater (Fig. 6) The energy and mass balance for feed-water heater can be calculated as follows:

Fig. 3. Sub-system 1: thermo-vapor compressor+desuper heater.

Fig. 4. Sub-system 2: effects 1, 2, and 3.


1127

Fig. 5. Sub-system 3: effects 4, . . . , N.

Fig. 6. Sub-system 4: feed-water heater.

N1 X 1

hf 1 þ R1 R1 Di ðhfi hfN Þ þ S hfs R1 þ s hfN R1 þ R R R

¼ ðf1 þ f2 þ f3 ÞCpf ðT f1 T f Þ

ð18Þ

Sub-system 5: Condenser (Fig. 7) A vapor generated in the last effect is passed through the condenser and condensed by seawater. In this process, seawater, which is used as feeding water, is preheated. The remainder part of seawater used as coolant in the condenser is rejected to the sea. The mass and energy balance for the condenser can be written as follows:

T f ¼ T N DT min con

ð19Þ

M c ¼ F þ Re j

ð20Þ

ðDN Dr N ÞLN ¼ ðF þ Re jÞCpsw ðT f T sw Þ

ð21Þ

Where, Mc, F and Re j are mass flow rates of cooling seawater, feed water to MED and rejected water from the desalination system, respectively. DN is the total rate of vapor outflows from the effect number N, and DrN is the flow rate of withdrawn vapor from the last effect (effect N), if it is considered as a withdrawal effect (N = n) (note that in our analysis the withdrawal effect might be altered). Tf and Tsw are feed water and seawater temperatures, respectively. Physical properties utilized in Eqs. (1)–(21) are estimated as a function of temperature and salinity as described in Ref. [20,22].

4. Exergy modeling 4.1. Exergy balances At the steady state, the exergy rate balance for an open system takes the form:

1128


E_ in ¼ E_ steam;boiler E_ condensate ¼ Sbðhgboiler hfs Þ T 0 ðsgboiler sfs Þc

ð29Þ

The output exergy in the system can be expressed by:

E_ out ¼ DE_ distillate þ DE_ brine þ DE_ rej

ð30Þ

The exergy difference between the product water and inlet seawater, DE_ distillate , can be expressed as an outlet exergy of the product water:

TN DE_ distillate ¼ Dt ðedistilate esw Þ ¼ Dt Cpd T N T sw T 0 Ln T sw

ð31Þ

The exergy difference between the brine and inlet seawater, DE_ brine , can be expressed as an outlet exergy of the brine water:

TN DE_ brine ¼ BN ðebrine esw Þ ¼ BN CpB T N T sw T 0 Ln T sw

The exergy difference between the rejected water (coolant) and the inlet seawater, DE_ rej , can be expressed as an outlet exergy of the coolant stream:

Fig. 7. Sub-system 6: condenser.

X X X T0 _ _ cv þ _ i ei _ e ee E_ D m m 0¼ 1 Qj W T j e j i

Tf DE_ rej ¼ Re jðerej esw Þ ¼ RejCpf T f T sw T 0 Ln T sw

Exergy destructions (irreversibilities) of various sub-systems of MED desalination is obtained from the Gouy–Stodola equation as follows:

ð23Þ

The specific exergy transfer terms ei and ee are expressible in terms of four components: Physical exergy ePH, kinetic exergy eKN, potential exergy ePT, and chemical exergy eCH:

e ¼ ePH þ eKN þ ePT þ eCH

Sub-system 1: Thermo-vapor compressor and de-superheater (Fig. 3)

E_ Dðejectorþde sup erheaterÞ ¼ T 0 bSðsgs sgboiler Þ þ Drn ðsgs sgn Þ þ Mdsðsgs sfN Þc ð34Þ

ð24Þ

The first three components are evaluated as follows:

ePH ¼ ðh h0 Þ T 0 ðs s0 Þ 1 eKN ¼ m2 2 ePT ¼ gz

Sub-system 2, 3: Effects 1, . . . , N (Figs. 4 and 5)

ð25Þ ð26Þ

E_ D1 ¼ T 0 bðS þ Drn þ MdsÞðsfs sgs Þ þ B1 sf1 þ D1 sg1 f1 sf1 c E_ D ¼ T 0 bðDi1 Dri1 Þðsf sg Þ þ Bi sf þ Di sg fi sf i

ð27Þ

In Eq. (25) h0 and s0 denote the specific enthalpy and specific entropy at the restricted dead state, respectively. In Eqs. (26) and (27), m and z denote velocity and elevation relative to coordinates in the environment, respectively. In this analysis potential exergy and the kinetic exergy are neglected. 4.2. Developing of the exergy balance for the MED–TVC desalination system The exergy equation for the entire process and its five sub-systems can be derived as below: Entire process as a black box (Fig. 2). Ignoring heat transfer to the surrounding, equation of exergy balance (Eq. (22) is simplified as follows:

_ pump þ ðE_ in E_ out Þ E_ D;tot ¼ W

ð33Þ

ð22Þ

The exergy destruction rate (irreversibility) is related to the entropy generation rate by the Gouy–Stodola equation as follows:

E_ D ¼ T 0 S_ gen

ð32Þ

ð28Þ

The exergy difference between the motive steam (from boiler) and outlet condensate water from the system can be expressed as an entire inlet exergy to the MED system:

i1

Bi1 sfi1 c;

i1

i

i

ð35Þ

fi

i ¼ 2; . . . ; N

ð36Þ

Sub-system 4: Feed-water heater (Fig. 6)

Tf E_ Dfeedwaterheater ¼ T 0 Dt ðsfN sfTav eD Þ þ ðf1 þ f2 þ f3 Þ Cpf Ln 1 Tf

ð37Þ

Sub-system 5: Condenser (Fig. 7)

Tf E_ Dcondenser ¼ T 0 DN ðsfN sgN Þ þ M c Cpsw Ln T sw

ð38Þ

4.3. Definition of exergy parameters and efficiency in the MED–TVC system Definition of product, fuel and losses of the exergy for using in MED system are:

_ pump E_ F ¼ E_ in þ W

ð39Þ

1129


where E_ in is defined by Eq. (29)

E_ P ¼ DE_ distillate E_ L ¼ DE_ brine þ DE_ Re

ð40Þ j

ð41Þ

Hence, exergy efficiency and exergy destruction ratio (efficiency defect) for the entire system is defined as follows:

E_

etot ¼ _ p EF

ð42Þ

5. Economic models The economic model takes into account the cost of components, including amortization and maintenance, and the cost of fuel consumption. In order to define a cost function, which depends on the optimization parameters of interest, component costs have to be expressed as functions of thermodynamic variables [25]. These relationships can be obtained by statistical correlations between costs and the main thermodynamic parameters of the component performed on the real data series. In the evaluation and cost optimization of an energy conversion system, it is required to compare the annual values of capital-related charges (carrying charges), fuel costs, and the operating and maintenance expenditures. These cost components may vary significantly within the system economic life. Therefore, levelized annual values for all cost components should be used in the evaluation and cost optimization [6,25]. The following sections illustrate the Total Revenue Requirement (TRR) method (which is based on procedures adopted by the Electric Power Research Institute (EPRI; 1993) [24]). This method calculates all costs associated with a project, including a minimum required return on investment. Based on the estimated total capital investment and assumptions for economic, financial, operating, and market input parameters, the Total Revenue Requirement is calculated on a year-by-year basis. Finally, the non-uniform annual monetary values associated with the investment, operating (excluding fuel), maintenance, and the fuel costs of the system being analyzed are levelized; that is, they are converted to an equivalent series of constant payments (annuities) [23]. 5.1. Calculation of Revenue Requirements The annual Total Revenue Requirement (TRR, 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 system operation [25]. It consists of two parts: carrying charges and expenses. Carrying charges are a general designation for charges that are related to the capital investment, whereas expenses are used to define costs associated with the operation of a system [25]. Carrying charges (CC) include the total capital recovery and return on investment for preferred stock [25]. Examples for expenses are fuel cost (FC) and the operating and maintenance costs (OMC) [25]. All annual carrying charges and expenses have to be estimated for each year over the entire economic life of a system. 5.2. Levelized costs The series of annual costs associated with the carrying charges CCj and expenses (FCj and OMCj) for the jth year of a system operation are not uniform. In general, carrying charges decrease while

fuel costs increase with increasing years of operation [6]. A Levelized value for the total annual revenue requirement, TRRL, can be computed by applying a discounting factor and the capital-recovery factor CRF:

TRRL ¼ CRF

BL X

TRRj

1

ð1 þ ieff Þj

ð43Þ

where TRRj is the Total Revenue Requirement in the jth year of system operation, ieff is the average annual effective discount rate (cost of money), and BL denotes the system economic life expressed in years. In the case of MED–TVC, the annual Total Revenue Requirement is equal to the sum of the following five annual amounts including the total capital recovery (TCR); minimum return on investment (ROI); electricity cost (FCele); steam costs (FCste); and the operating and maintenance cost (OMC):

TRRj ¼ TCRj þ ROIj þ FC j;ste þ FC j;ele þ OMC j

ð44Þ

Definition and detailed calculation procedure of TCRj and ROIj is given in Ref. [6]. In applying Eq. (43), it is assumed that each monetary transaction occurs at the end of each year. The capital-recovery factor CRF is given by

CRF ¼

ieff ð1 þ ieff ÞBL

ð45Þ

ð1 þ ieff ÞBL 1

In which, ieff is the interest rate. If the series of payments for the annual fuel cost FCj is uniform over the time except for a constant escalation rFC (i.e., FC j ¼ FC 0 ð1 þ r FC Þj ), then the levelized value FCL of the series can be calculated by multiplying the fuel expenditure FC0 at the beginning of the first year by the constant-escalation levelization factor CELF: BL

FC L ¼ FC 0 CELF ¼ FC 0

kFC ð1 kFC Þ CRF ð1 kFC Þ

ð46aÞ

where

kFC ¼

1 þ r FC 1 þ ieff

and r FC ¼ constant

ð46bÞ

The terms rFC and CRF denote the annual escalation rate for the fuel cost and the capital-recovery factor (Eq. (45)), respectively. Accordingly, the levelized annual operating and maintenance costs (OMCL) are given by: BL

OMC L ¼ OMC 0 CELF ¼ OMC 0

kOMC ð1 kOMC Þ ð1 kOMC Þ

ð47aÞ

with

kOMC ¼

1 þ r OMC 1 þ ieff

and r OMC ¼ constant

ð47bÞ

The term rOMC is the nominal escalation rate for the operating and maintenance costs. Finally, the levelized carrying charges CCL are obtained from the following equation:

CC L ¼ TRRL FC L OMC L

ð48Þ

The major difference between a conventional economic analysis and an economic analysis conducted as part of a thermoeconomics analysis is that the latter is done at the system component level. The annual carrying charges or capital investment (superscript CI) and operating and maintenance costs (superscript OM) of the total system can be apportioned among the system components according to the contribution of the kth component to the purP chased-equipment cost PEC total ¼ k PEC k for the overall system:

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6.2. Definition of the thermoeconomic objective in MED–TVC

Table 2 Economic parameters and assumption. Parameters

Symbol

Value

Unit cost of electricity ($/kWh) Unit cost of steam ($/ton) Useful life (year) Profit rate Inflation electricity rate Inflation steam rate Inflation operating and maintenance rate

Cel Cste Y r rfce rfcste rom

0.03 2 30 0.10 0.05 0.05 0.05

CC L

PEC P k Z_ CI k ¼ s k PEC k OMC PEC L P k Z_ OM ¼ k s k PEC k

ð49Þ ð50Þ

Here, PECk and s denote the purchased-equipment cost of the kth system component and the total annual time (in hours) of system operation respectively. Equations for calculating the purchased-equipment costs (PEC) for the components of the thermal distillation system are presented in [17,18].The term Z_ k represents the cost rate associated with the capital investment and operating and maintenance expenses of kth component:

_ OM Z_ k ¼ Z_ CI k þ Zk

ð51Þ

k denotes component of MED system including condenser, feedwater heater, thermo-vapor compressor and effects 1, 2, . . . , N. The annual cost for the first year of operation is given by:

FC 0;steam ¼ C ste :S:s

ð52Þ

_ total FC 0;ele ¼ C ele :s:W

ð53Þ

OMC 0 ¼ DC CRF :02

ð54Þ

In which, Cele and Cste are the unit price of electricity ($/kWh) _ tot are annual operating hours and steam ($/ton), respectively. s, W (8760 h), the total pumping power and the total fed steam to the MED, respectively. The levelized cost rate of the expenditures for electricity and steam C_ F supplied to the overall system is given by:

FC L;steam C_ F;ste ¼

ð55Þ

FC L;ele C_ F;ele ¼

ð56Þ

s

s

_ _ OM _ Levelized costs, such as Z_ CI k ; Z k ; C F;ele and C F;ste are used as input data for the thermoeconomics analysis. Table 2 represents the economical constant, parameters and assumptions that are used in economic analysis of this work. 6. Thermoeconomics analysis and objective

9 82 3 > > n = X X 24 |ffl{zffl} Dt > ; : |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} k¼1

Product

The governing equation of thermoeconomic model for the cost balancing of an energy system is written as follows:

ð58Þ

Fuel of MED—TVC

As is clear, the motive steam and electricity used for pumps are considered as system fuels. It should be noted that in the application of Eq. (57) for the MED–TVC system, the product unit is converted from $/h to $/m3 as indicated on the right hand side of Eq. (58). 6.3. Decision variables In thermal system design and optimization, it is convenient to identify two types of independent variables. These variables are decision variables and parameters. The decision variables may be varied in optimization process. However, the parameters remain fixed in a given application. All other variables are dependent variables. Their values are calculated from independent variables using thermodynamic relations. The selected decision variables in this work are: 1 2 3 4 5 6

Number of effects Return effect Temperature of the inlet vapor to the first effect (°C) Temperature of the last effect (°C) Minimum temperature difference in the condenser Outside diameter of tubes in the evaporator (effects) (mm)

N n Ts TN Tmin Deva

cond

6.4. Physical constraints (feasibility conditions)

36N69 36n6N 60 6 T s 6 71 42 6 T N 6 48 2 6 T min cond 6 4 Dev a ¼ 24; 28; 32; 38 mm Re j 6 0 Dn 6 Dr n 6 0 T av e 6 T f 1

ð59Þ ð60Þ ð61Þ ð62Þ ð63Þ ð64Þ ð65Þ ð66Þ ð67Þ

Total maximum product flow rate for this kind of MED systems is 24,000 ton/day, therefore,

Dt 6 24; 000 ton=day

ð68Þ

Salt concentration in the outlet brine is maximum 69,000 ppm (environmentally limited), therefore,

X b 6 69; 000 ppm

6.1. Cost-balance equation

_ _ OM C_ F;tot þ Z_ CI tot þ Z tot ¼ C P;tot

Application of Eq. (57) to the MED–TVC system for minimizing the unit cost of product ($/m3), leads to the following expression for the thermoeconomic objective:

ð69Þ

It is required to say that seawater temperature and salt concentration in Persian Gulf is between 15–35 °C and 35,000– 45,000 ppm, respectively.

ð57Þ

where C_ F;tot and C_ P;tot are cost rate of system fuel and product ($/h), _ OM respectively. Z_ CI tot and Z tot are the total capital investment and operating and maintenance costs obtained using the economic model ($/h).

7. Description of the optimization algorithm Genetic algorithms were developed by John Holland in the 1960s as a means of importing the mechanisms of natural adaptation into

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Parents’ selection

Initial random population No Max. No of Generation

Evaluation (Pareto ranking)

Reproduction (cross-over + mutation) Survival of the fittest

Yes

Table 3 Tuning parameters for optimization program. Tuning parameters

Value

Population size Maximum no. of generations Pc (Probability of crossover) Pm (Probability of mutation) No. of cross over point Selection process Tournament size

500 300 70% 1% 2 Tournament 2

STOP Fig. 8. Scheme for the multi-objective evolutionary algorithm used in the present work.

starting population for the next generation. Table 3 shows tuning parameters for genetic algorithm. 8. Results and discussion

computer algorithms and numerical optimization [24]. Those are implemented as a computer simulation in which a population of abstract representations (called chromosomes or the genotype of the genome) of candidate solutions (called individuals, creatures, or phenotypes) to an optimization problem evolves toward better solutions. The evolution usually starts from a population of randomly generated individuals. In each generation, the fitness of every individual in the population is evaluated, multiple individuals are stochastically selected from the current population (based on their fitness), and modified (recombined and possibly randomly mutated) to form a new population. The new population is then used in the next iteration of the algorithm. Commonly, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory fitness level has been reached for the population. If the algorithm has terminated due to a maximum number of generations, a satisfactory solution may or may not have been reached. In genetic algorithms, a candidate solution to a problem is typically called a chromosome, and the evolutionary viability of each chromosome is given by a fitness function. This method is a powerful optimization tool for nonlinear problems [26]. The structure of the algorithm used in the present work is illustrated in Fig. 8. As a first step, parent selection is performed with each individual having the same probability of being chosen. Suppose n is the size of generated population. Then n numbers of parents enter the reproduction step, generating n offspring through a crossover strategy in which the decision variable values of the offspring fall in a range defined by the decision variable values of the parents. Some decision variable values of the offspring are also randomly mutated with a probability Pm. The objective function values of the n offspring are then evaluated. Finally, the number of generations elapsed is compared to the established maximum number of generations. If the termination condition is met, the process stops, otherwise the surviving solutions become the

The proposed base case MED plant with specifications mentioned in Table 1 and Fig. 1 including six decision variables (N, n, TS, TN, DTmin con and Deva) and thermoeconomic objective described by Eq. (58) and constraints expressed by Eqs. (59)–(69) is optimized using the genetic algorithm described in Section 7. Table 4 indicates the magnitude of decision variables for the base case design and corresponding magnitudes obtained in the thermoeconomic optimization. It indicates that in the optimized system, the number of effects is reduced from seven to six. The return effect from fifth effect of the base case is replaced to the effect number 6 in the optimized system. The tube outside diameter of the evaporators (effects) from 38 mm is reduced to 24 mm. Table 5 compares important exergoeconomic elements of the base case and optimized systems. This table indicates that there is improvement on all important exergetic factors of the entire MED system. Moreover, this table indicates that a 20.7% improvement on the unit cost of the treated water (product). The fuel (Steam and electricity) cost and capital investment are reduced by 14.3% and 27.8% from their corresponding values for the base case system, respectively. The cost of thermodynamic inefficiencies (exergy destructions) in the optimized system is decreased by 9.6%. This cost is defined as the total exergy destruction product in the fuel cost (C_ D ¼ cF E_ D;tot ). Total capital investment plus the cost of Table 4 The values of decision variables for various cases. Decision variables

Base case

Thermoeconomic optimized system

N n Ts TN Tmin Deva

7 5 71 48 3 38

6 6 71 43.5 2.5 24

cond

Table 5 Comparison of important exergoeconomic elements between the base case and optimized MED-TVC systems. Costing element

Base case

Thermoeconomic optimized system

Improvement (%)

Exergy of fuel (kW) Exergy of product (kW) Exergy destruction (kW) Exergy loss (kW) Ratio of exergy destruction to the fuel exergy (%) Exergetic efficiency (%) Product cost ($/m3) Fuel cost ($/m3) P Capital investment ( Z_ k ) ($/m3) Cost of exergy destruction (C_ D;tot ¼ cF E_ D;tot ) ($/m3) P ðC_ D;tot þ Z_ k Þ ($/m3)

2189.10 2.35 1872.60 315.05 87.5 0.107 1.309 0.490 0.681 0.520

1876.40 4.58 1641.80 230.02 85.5 0.244 1.037 0.420 0.492 0.470

14.3 38.5 12.3 27.0 2.3 128.0 20.7 14.3 27.8 9.6

1.201

0.962

19.9

Return on investment (year)

6.04

5.71

5.5

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Table 6 Comparison of important thermoeconomic parameters between the base case and optimized MED–TVC systems. E_ D;k (kW)

E_ L;k (kW)

C_ D;k ($/m3)

Z_ k ($/m3)

Z_ k

C_ D;k þ Z_ k ($/m3)

Component

ek (%) B.Ca

Opt.b

B.C

Opt.

B.C

Opt.

B.C

Opt.

B.C

Opt.

B.C

Opt.

B.C

Opt.

Evaporators Condenser TVC+desuper heater Pumps Feed-water heater

74.5 – 11.8 90.0 88.7

57.6 – 35.1 90.0 85.3

524.5 133.2 1069.3 133.3 11.2

741.0 79.0 673.0 133.3 15.0

98.7 215.3 – – –

98.7 131.3 – – –

0.550 0.048 0.026 0.031 0.026

0.340 0.054 0.036 0.039 0.023

0.126 0.032 0.257 0.032 0.003

0.208 0.019 0.161 0.032 0.004

81.36 60.25 9.00 49.36 90.70

62.10 75.00 18.20 55.00 86.30

0.676 0.080 0.282 0.063 0.029

0.548 0.072 0.197 0.070 0.027

a b

fk ¼ C_

_

D;k þZ k

(%)

B.C: base case system. Opt.: optimized system.

P exergetic inefficiencies ðC_ D;tot þ Z_ k Þ is reduced by 19.9% as indicated in Table 5. Further, Table 5 indicates that the return on investment for the optimized system is by 5.5% lower than the corresponding return on investment for the base case MED system. Table 6 compares some important thermoeconomic parameters of the MED–TVC system for the base case and optimized designs at the component level. The table reveals that the exergetic efficiency, exergy destructions and losses are increased for the evaporator and feed-water heater of optimized system. These exergetic efficiencies are reduced in order to have a lower investment cost for these components. It implies that optimization caused reduction on the investment cost of these component at the cost of reduction on the exergetic efficiency of them. This fact can be observed as indicated by thermoeconomic factor, f k, which is the ratio of the owning and operating costs, Z_ k , to the sum of owning and operating and of exergetic inefficiency costs, C_ D;k þ Z_ k . In other words, for these components, the capital investment is dominant cost in comparison to the cost of exergetic inefficiency. For components such as TVC+de-superheater and the condenser, the exergetic performance is improved since in these components, the cost of inefficiencies are dominant. However, since the major part of exergy destructions of MED system occurs in the TVC+de-superheater, therefore, the overall effect of the optimization is reduction in the total cost of exergy destruction, as already observed in Table 5. Moreover, Table 6 indicates that the highest exergetic efficiencies (lowest exergy destructions and losses) belonged to pumps and the feed-water heater. TVC+de-superheater has the lowest thermodynamic performance, however the cost of their thermodynamic inefficiency is improved in the optimized system. More expensive component is evaporators (due to very large heat transfer surface) and the cheapest equipment is TVC+de-superheater. The last column of Table 6 indicates that for all components, the inefficiency cost plus the capital investment and operating & maintenance costs (C_ D;k þ Z_ k ) are decreased in the optimized system. One important conclusion which can be seen from the results presented in Table 6 is that thermoeconomic optimization aims at reduction of sub-components total costs by reducing either the cost of inefficiencies or the cost of owning and operating of components, whichever is dominant. Therefore, for some components such as evaporators, this improvement is obtained by reducing the owning and operating cost of the sub-system under consideration at a cost of reduction in the thermodynamic efficiencies. For components like TVC+de-superheater improvement is achieved by increasing the thermodynamic efficiency and hence reducing the inefficiency cost because in such components inefficacy is the dominant cost.

9. Conclusions Thermoeconomic optimization of the multi effects distillation (MED) desalination system with thermo-vapor compressor is

presented. The proposed method covers both thermodynamical and economical aspects of the system design and the component selection. Irreversibilities (exergy destructions) for the MED–TVC component are determined based on derived equations. In this research, a definition and complete expression of the product and fuel in the exergy analysis of the MED–TVC system was expressed. This definition can show true realization of the exergetic efficiency. The economics model of the system was developed based on the Total Revenue Requirement method (TRR method). Further, the thermoeconomic model was developed based on the exergy analysis. The thermoeconomic objectives were formed according to the thermodynamic and thermoeconomic models. The configuration of optimization problem was built with the six decision variables and the appropriate feasibility and engineering constraints. The optimization process was carried out using genetic algorithm due to its robustness against the conventional mathematical approach. Improvements in all costing elements of optimized system were obtained. It is found that thermoeconomic optimization aims at reduction of sub-components costs by reducing either the cost of inefficiencies or the cost of owning and operating of components, whichever is dominant. References [1] Abdulnasser A, Mabrouk AS, Nafey HE, Fath S. Thermoeconomic analysis of some existing desalination processes. Desalination 2007;205: 354–73. [2] Kotas TJ. The exergy method of thermal plant analysis. Tiptree, Essex: Anchor Brendon Ltd; 1985. [3] Valero A, Lozano MA, Munoz M. A general theory of exergy savings. Part I: On the exergetic cost. Part II: On the thermoeconomics cost. Part III: Energy savings and thermoeconomics. New York: ASME; 1986. p. 22. [4] Frangopoulos CA. Thermoeconomics functional analysis and optimization. Energy 1987;12:7563–71. [5] Valero A. CGAM problem: definition and conventional solution. Energy 1994;19:268–79. [6] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. J. Wiley; 1996. [7] Choi HS, Kim YG, Song SL. Performance improvement of multiple-effect distiller with thermal vapor compression system by exergy analysis. Desalination 2005;182:239–49. [8] Hamed OA, Zamamiri AM, Aly S, Lior N. Thermal performance and exergy analysis of a thermal vapor compression desalination system. Energy Convers Manage 1996;37:379–87. [9] Al-Najem NM, Darwish MA, Youssef FA. Thermovapor compression desalters: energy and availability — analysis of single- and multi-effect systems. Desalination 1997;110:223–8. [10] Kalogirou SA. Seawater desalination using renewable energy sources. Prog Energy Combust Sci 2005;31(3):242–81. [11] Aly SE. Energy savings in distillation plants by using vapor thermocompression. Desalination 1984;49:37–56. [12] Darwish MA, Al-Najem NM. Energy consumptions and costs of different desalting systems. Desalination 1987;64:83–96. [13] Hamed OA, Ahmed KA. An assessment of an ejector compression desalination process. Desalination 1994;96:103–11. [14] Kamali R.K, Abbassi A, Sadough SA. A simulation model and parametric study of MED–TVC process. In: EDS international conference, EuroMed; 2006. p. 203. [15] Uche J, Artal J, Serra L. Comparison of heat transfer co-efficient correlations for thermal desalination units. Desalination 2002;152:195–200.

H. Sayyaadi, A. Saffari / Applied Energy 87 (2010) 1122–1133 [16] Kafi F, Renaudin V, Alonso D, Hornut JM. New MED plate desalination process: thermal performances. Desalination 2004;166:53–62. [17] Ettouney HM, El-Dessouky H. A simulator for thermal desalination process. Desalination 1999;125:277–91. [18] El-Dessouky HT, Ettouney HM. Multiple effect evaporation desalination systems: thermal analysis. Desalination 1999;125:259–76. [19] Jernqvist A, Jernqvist M, Aly G. Simulation of thermal desalination process. Desalination 2001;134:187–93. [20] Alasfour FN, Darwish MA, Bin Amer AO. Thermal analysis of METVC+MEE desalination systems. Desalination 2005;174:39–61. [21] Ettouney H. Visual basic computer package for thermal and membrane desalination processes. Desalination 2004;165:393–408.

1133

[22] Raach H, Mitrovic J. Simulation of heat and mass transfer in a multi effect distillation plant for seawater desalination. In: EDS international conference, EuroMed; 2006. p. 22. [23] El-Sayed YM. Designing desalination systems for higher productivity. Desalination 2001;134:129–58. [24] Technical Assessment Guide (TAGTM). Electric Power Research Institute, TR100281, vol. 3, Revision 6; 1991. [25] Tsatsaronis G, Cziesla F. Thermoeconomics. In: Meyers R, editor. Encyclopedia of physical science and technology, 3rd ed., vol. 16. Academic Press; 2002. [26] Holland JH. Adaptation in natural and artificial systems. Ann Arbor: University of Michigan Press; 1975.