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Energy 75 (2014) 312e326

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Energy

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A high efficient combined multi-effect evaporationeabsorption heatpump and vapor-compression refrigeration part 1: Energy andeconomic modeling and analysis

Iman Janghorban Esfahani a, Yong Tae Kang b, ChangKyoo Yoo a, *

a Dept. of Environmental Science and Engineering, College of Engineering, Center for Environmental Studies, Kyung Hee University, Seocheon-dong 1,Giheung-gu, Yongin-Si, Gyeonggi-Do, 446-701, South Koreab School of Mechanical Engineering, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul, 136-701, South Korea

a r t i c l e i n f o

Article history:Received 17 February 2014Received in revised form16 July 2014Accepted 24 July 2014Available online 21 August 2014

Keywords:Combined systemDesalinationRefrigerationAbsorptionMEE (multi-effect evaporation)VCR (vapor-compression refrigeration)

DOI of original article: http://dx.doi.org/10.1016/j* Corresponding author. Tel.: þ82 31 201 3824; fax

E-mail address: ckyoo@khu.ac.kr (C. Yoo).

http://dx.doi.org/10.1016/j.energy.2014.07.0810360-5442/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

A novel combined system that combines a MEEeABHP (multi-effect evaporationeabsorption heat pump)with a VCR (vapor-compression refrigeration) cycle is proposed to simultaneously generate cooling andfresh water. In the combined system, the condenser of the VCR system is replaced by the MEEeABHPsystem, where a portion of the fresh water produced in the last effect of the MEE (multi-effect evapo-ration) system is used as the refrigerant for the VCR system. In Part 1 of this two-part paper, model-basedenergy and cost analysis is developed to quantify and qualify the performance of the combined system.Parametric analysis is carried out to investigate the effects of absorber pressure (PA), temperature dif-ference between effects of the MEE subsystem (DTMEE), temperature of the strong solution from absorber(T1), and temperature of the weak solution from generator (T4) on the performance of the system. In Part2, thermo-economic and exergy analysis is conducted to evaluate the flexibility of the system for fuelallocation from different available power and heat energy sources. The results of Part 1 showed that thecombined system can save 57.12%, 5.61%, and 25.6% in electric power, heat energy, and total annual costcompared to the stand-alone VCR and MEEeABHP systems, respectively.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

In the Middle East, which is water-deficient region with a warmclimate, fresh water and cooling are often required simultaneouslyand are generated separately by stand-alone desalination andrefrigeration systems [1]. The two most widely used desalinationtechniques are RO (reverse osmosis) membrane separation andthermal desalination. In the thermal desalination salt is separatedfrom water by evaporation and condensations processes, whereasin the RO process semi-permeable and driving forces like pressureare used to separate salts from water. The membrane processeshave rapidly developed and surpassed the thermal process becauseof the lower energy consumption, higher recovery factor and lowerdesalted water costs. Despite of higher energy consumption, ther-mal desalination systems have remained the most frequentlyapplied technology due to lack of the discharge of brine chemical

.energy.2014.07.082.: þ82 31 202 8854.

solution in to the sea, capability in waste heat recovery from thecoast-based power plants, iron and steel plants, and paper and pulpindustries, and the low cost of fossil fuel in many regions such asMiddle East countries [2,3]. Among thermal desalination systems,LT-MEE (low-temperature multi-effect evaporation) desalinationhas received more attention in recent years because it has a lowercorrosion rate, consumes less power, and costs less than MSF(multi-stage flash) desalination systems [4,5]. The LT-MEE desali-nation systems are often combined with heat pumps such as a SJE(steam jet ejector) and ABHP (absorption heat pump), which areknown as MEE-TVC and MEEeABHP (multi-effect evapo-rationeabsorption heat pump) respectively, to increase fresh waterproduction compared to a stand-alone LT-MEE with the samedriving heat source conditions [5].

Recently, several researchers have studied the MEE (multi-effectevaporation) desalination combined with SJE and ABHP systems[4e10]. Janghorban Esfahani et al. [4] analyzed and optimized aMEE-TVC desalination system that combines LT-MEE desalinationsystem with a SJE. They applied MOO (multi-objective optimiza-tion) to minimize the total annual cost, to and maximize the freshwater flow rate, and to gain the output ratio. Wang and Lior [5]

I. Janghorban Esfahani et al. / Energy 75 (2014) 312e326 313

investigated a LT-MEE desalination system combined with a single-effect LiBreH2O ABHP with regard to energy and economics toimprove the understanding of the system. Li et al. [6] studied thefeasibility of using low-grade heat for thermal desalination via ahybrid absorption heat pump system with ammonia-water work-ing fluid. Their results showed that the proposed system wascompetitive with the reverse osmosis technology with regard topower consumption. Gomri [7] compared the influence of absorbertemperature and intermediate heat source temperature on energyefficiency, exergy efficiency, and freshwater production of singleeffect and double effect absorption heat pumps system used forseawater desalination.

As investigated in the literature, the absorption cycles arecombined with the desalination system only to increase the freshwater production not for cooling. Therefore, cooling is often sepa-rately generated by refrigeration cycles. The two most widely usedtechniques to generate cooling are vapor compression and ab-sorption. Recently, several studies have been carried out on appli-cation of refrigeration cycles [11e23]. To continue the refrigerationcycle in both systems, the heat should be absorbed from the coldenvironment by an evaporator and released to the hot environmentby a condenser, which can be recovered as a heat source for manypurposes such as the desalination process [24].

Therefore, refrigeration and desalination systems can be com-bined to simultaneously generate cooling and fresh water moreefficiently and economically than two single-generation systems.Recently, several studies have been conducted on combiningdesalination systems and refrigeration cycles by recovering thewaste heats from the refrigeration cycle as an energy source for thethermal desalination system.

Gude and Nirmalakhandan [25] presented a combined low-grade desalination system with a modified absorption refrigera-tion system. In their study, heat rejected by the condenser of theabsorption refrigeration system was upgraded as an energy sourcefor desalination. Hou et al. [26] presented an open air-vaporcompression refrigeration system for both air-conditioning anddesalination on ships. In their proposed system, fresh water is ob-tained using humid-air dehumidification and a flash desalinationprocess. Wang and Lior [27] proposed a combined absorptionrefrigeration cycle with a LT-MEE desalination system in which thecondenser of the absorption system is replaced by the first effect ofthe LT-MEE system. Janghorban Esfahani et al. [28] proposed a newcombined GT (gas turbine) and RO (reverse osmosis) desalinationsystem that uses a vapor compression refrigeration system to coolthe compressor inlet air and preheat the RO feed water by recov-ering waste heat from the refrigeration system condenser.

As investigated in the literature, recent research efforts havefocused on waste heat recovery from the refrigeration cycle as anenergy source for an LT-MEE desalination system. However,combing highly efficient desalination systems such as MEEeABHPwith refrigeration systems to co-generate freshwater and cooling isscarce.

This study proposes a new combined MEEeABHP with a VCR(vapor-compression refrigeration) system that simultaneouslygenerates cooling and fresh water with lower energy consumptionand total annual cost compared to the systems proposed in theliterature. In the combined system, the condenser of the VCR sys-tem is replaced by a MEEeABHP system, where a portion of thefresh water produced in the last stage of the MEEeABHP system isused as the refrigerant for the VCR system. Two compressors areused to compress the refrigerant, which increases the flexibility ofthe system by using both electricity and heat as energy sources. Alow pressure compressor is used to compress a portion of therefrigerant, which is condensed in the absorber of the ABHP sub-system. A high pressure compressor is used to provide a portion of

the heat energy required by theMEEeABHP system by compressinganother portion of the refrigerant, which is condensed through thetube side of the first stage of the MEE subsystem.

Part 1 of this two-part paper consists of two major parts. First,simulation models based thermodynamic and economic equationsare developed to simulate and calculate the energy consumptionand TAC (total annual cost) of the proposed system by using EES(Engineering Equation Solver) software [29]. Second, parametricand sensitivity analysis are carried out to investigate the four keyparameters of absorber pressure (PA), temperature difference be-tween effects of MEE subsystem (DTMEE), temperature of the strongsolution from absorber (T1), temperature of the weak solution fromgenerator (T4) and how they influence the performance of thecombined system with one compressor to better understand theprocess. Part 2 as a separate paper consists of the thermo-economicanalysis and optimization of the combined system with two com-pressors to evaluate the flexibility of the system to allocate thedifferent energy sources.

2. Materials and methods

2.1. System configuration

Fig. 1 shows the proposed system, which combines a MEE-eABHP desalination system with six stages in the MEE subsystemby a VCR system. In the proposed system, the condenser of the VCRsystem is replaced with the MEEeABHP desalination system torecover the waste heat of the VCR condenser as a heat energysource for the MEE system. For this purpose, a portion of the freshwater produced in the last stage of the MEEeABHP system (whichhas a lower pressure than the other stages) is used as refrigerant forthe VCR system. The refrigerant is expanded through the expansionvalve (EV2) and passes through the evaporator. The saturated vaporrefrigerant coming from the evaporator (stream 15) is compressedby the compressor and, with the vapor coming from the last stageof the MEEeABHP system (stream 10), is sent to the absorber (A)and absorbed by the strong solution (stream 6). Stream 6 leaves theabsorber with a weak LiBr concentration (stream 1) and is thenpumped to the generator at a higher pressure through the SHX(solution heat exchanger). The weak solution (stream 2) is pre-heated by heat recovered from the strong solution (stream 4)coming from the generator. The strong liquid solution (stream 4)returns to the absorber through the solution heat exchanger andexpansion valve (EV1). The heating steam (stream 0) for the MEEsubsystem is provided by two sources: the first is stream 7, which isgenerated by boiling off the LiBreH2O by heat provided by themotive steam (stream 8) in the generator; the second is stream 12,which is a portion of the condensed vapor in the tube side of thefirst stage of the MEEeABHP system vaporized by recovering thereleased heat of the solution and the compressed vapor in theabsorber [5,24,30,31]. Stream 0 is introduced to the tube side in thefirst stage and condensed by releasing its latent heat into the feedwater for evaporation. Part of the condensate returns to theabsorber (stream 11), and another part passes into the first flashingbox. Demisted vapor formed in the first stage and the flashed vaporfrom the first flashing box are used together as heating sources inthe first pre-heater to preheat the feed water to the first stage. Thecombined vapor from the first pre-heater passes into the secondstage and is used as the heat source to vaporize the feed water inthe second stage. This process is repeated for all stages. At the end,the generated vapor of the last stage passes through the condenser.A portion of the condensed vapor is used as the refrigerant (stream13), and the other portion (stream 18) is introduced into thedistillate tank. The cooling water (stream 17) is divided into twoparts. The first part is used as feed and is distributed among the

Fig. 1. Schematic of the proposed combined MEEeABHP system with VCR system.

I. Janghorban Esfahani et al. / Energy 75 (2014) 312e326314

stages, and the other part is rejected back to the sea (stream 19)[32,33].

The system presented in Fig. 2 is suggested in order to replace aportion of the required energy for the MEE system with electricpower; the system combines the MEEeABHP system and VCRsystem with two compressors. In this system, the refrigerantcoming from the evaporator is divided into two parts: one part iscompressed by the low pressure compressor and sent to theabsorber, and the other part is compressed by a high pressurecompressor and sent to the tube side of the first stage as an energysource. The high pressure compressor operates as a mechanicalheat pump for the MEE subsystem, which can reduce the energyconsumption of the MEE system and consume electric power

Fig. 2. Schematic of the proposed combined MEEeABH

instead of the motive steam flow rate to produce fresh water.Therefore, the combined system with two compressors has theflexibility to allocate heat energy and electric power energy asenergy sources.

2.2. Thermodynamic and economic models of the MEEeABHPeVCRsystem

2.2.1. Thermodynamic modelThe thermodynamic properties of the systemsmust be specified

to conduct energy analyses of the MEEeABHPeVCR system, whichis usually done throughmodeling based thermodynamic equations.This section includes the mass, salinity, and energy balance

P system with VCR system with two compressors.

I. Janghorban Esfahani et al. / Energy 75 (2014) 312e326 315

equations that determine the thermodynamic simulation model ofthe combined system to calculate the energy consumption of thesystem. The models based thermodynamic equations developed byJanghorban Esfahani et al. [33], Huicochea et al. [31], and Hong et al.[34] are used in this study. Several simplifying assumptions madein the development of the thermodynamic model are listed below:

� The systems are operated under steady state conditions.� Heat losses and pressure drops in piping and the componentsare negligible.

� The water/lithium bromide concentration is zero in the steamphase.

� The water/lithium bromide solution in the generator andabsorber outlet is saturated.

� The refrigerant in the evaporator and condenser outlet of thevapor compression refrigeration cycle is saturated.

Each system has been modeled as two subsystems includingMEE-ABHP, and VCR systems, as described below.

2.2.1.1. MEEeABHP subsystem. The MEEeABHP subsystem com-ponents including generator, solution heat exchanger, absorber,expansion value, solution pump, and MEE are simulated throughEqs. (1) to (24) as follows:

2.2.1.1.1. G. (generator). Mass, concentration, and energy bal-ance equations are presented in Eqs. (1)e(3) [31].

_m3 ¼ _m7 þ _m4 (1)

_m3x3 ¼ _m7x7 þ _m4x4 (2)

_QG: ¼ _m4h4 þ _m7h7 � _m3h3 (3)

where _m is the mass flow rate, x is the solution concentration, and_QG: is the heat requirement of the generator.

2.2.1.1.2. SHX. (solution heat exchanger). The energy balance forthe SHX component is given by Eq. (4) [34].

_m2ðh3 � h2Þ ¼ _m4ðh4 � h5Þ (4)

2.2.1.1.3. EV. (solution expansion valve). Mass and energy bal-ance equations for the solution expansion valve are given by Eqs.(5) and (6), respectively [33].

_m5 ¼ _m6 (5)

_m5h5 ¼ _m6h6 (6)

2.2.1.1.4. SP. (solution pump). The power consumption of thesolution pump is given by Eq. (7) [24].

_Wpump ¼ _m1$v$ðPG � PAÞhpump

(7)

where hpump and v are isentropic efficiency of the pump and thespecific volume of the solution.

2.2.1.1.5. A. (absorber). Mass, concentration, and energy balanceequations are presented in Eqs. (8)e(10), respectively [33].

_mDi$Li þ

h_mF1$Cp

�Ti � Tf i

�i¼ � _mDi�1

$Li�1�þ

24yi�1$

0@ _mDr

þXi�2

j¼1

_mDj

1A

_m1 ¼ _m10 þ _m6 þ _m16 (8)

_m1x1 ¼ _m6x6 (9)

_QA: ¼ _m6h6 þ _m10h10 þ _m16h16 � _m1h1 (10)

where _QA: is the released heat in the absorber.2.2.1.1.6. MEE. (multi-effect evaporation). The MEE subsystem is

modeled in Eqs. (11) to (21).Mass balance equations of the first stage, second to nth stages,

and end condenser are given by Eqs. (11)e(13).

_mB1¼ _mF1 � _mD1

(11)

_mBi¼ _mFi þ _mBi�1

� _mDiþ24yi�1$

0@ _mDr

þXi�2

j¼1

_mDj

1A35

� �ði� 1Þ$ _mFi�1$yi�1

� (12)

_mDCon:¼ _mDn

� _mDrþ"yn$

_mDr

$Xn�1

i¼1

_mDi

!#(13)

where subscripts B, F, and D represent brine, feed, and distillatestreams, respectively. Subscripts i and r represent the number ofstages and entrained steam, respectively, and y represents the flashratio.

The produced fresh water mass flow rate is given by Eq. (14).

_m18¼"ð1�ynÞ$

_mDr

þXn�1

i¼1

_mDi

!#�"yn�1

_mDr

þXn�2

i¼1

_mDi

!#

�"yn�3

_mDr

þXn�4

i¼1

_mDi

!#�"yn�4

_mDr

þXn�5

i¼1

_mDi

!#

��yn�5$ _mDr

�þ _mDCon:� _m13

(14)

where _m18 and _m13 are fresh water and refrigerant mass flow rates,respectively.

The salinity balance equations for the first stage and second tonth stages are given by Eqs (15) and (16).

Xsw$ _mF1 ¼ XB1$ _mB1

(15)

Xsw$ _mF1 þ XBi�1$ _mBi�1

¼ XBi$ _mBi

(16)

where X is salinity, and subscripts i and B represent the number ofstages and the brine stream, respectively.

Energy balance equations of the first stage and second to nthstages are given by Eqs. (17) and (18), respectively.

_mD1$L1 þ

�_mF1$

h�CpðT1Þ$T1

�� �Cp�Tf1�$T�1i�

¼ _m0$L0 (17)

$Li�1

35� �ði� 1Þ$ _mFi�1

$yi�1$Li�1�þ � _mBi�1

$C$�DTi�1;i

��(18)

I. Janghorban Esfahani et al. / Energy 75 (2014) 312e326316

where L is the latent heat of the stream. _m0 is the mass flow rateof stream 0, and DTi�1;i is temperature difference between ith andi-1st effects, respectively which are calculated by Eqs. (19) and(20).

_m0 ¼ _m7 þ _m23 þ _m12 (19)

DTi�1;i ¼ Ti�1 � Ti (20)

In order to achieve the optimum operating conditions thetemperature difference between effects are assumed to be equal asfollow [4]:

DTi�1;i ¼ Ti�1 � Ti ¼ DTMEE (21)

Enthalpy and entropy for pure water, water/LiBr and seawaterhave been calculated by the correlations from previous research[35e37] which are presented in Appendixes A and B.

Table 1Reference costs of components (AR ¼ 100 m2, WR,pump ¼ 10 kW,WR,Motor ¼ 10 kW) [41].

Component (k) Reference cost (ZR) $

Generator 17,500Absorber 16,500

2.2.1.2. VCR subsystem. The VCR subsystem components includingexpansion valve, evaporator, and compressors, are simulated byEqs. (22)e(26) as follows:

2.2.1.2.1. REV. (refrigerant expansion valve). Mass and energybalance for the REV are given by Eqs. (22) and (23), respectively.

_m13 ¼ _m14 (22)

_m13h13 ¼ _m14h14 (23)

2.2.1.2.2. Eva. (evaporator). The energy balance equation of theevaporator is given by Eq. (24).

_QEva: ¼ _m14ðh15 � h14Þ (24)

where _QEva: is the cooling load of the evaporator.2.2.1.2.3. Com. (compressors). The power consumptions of the

low pressure and high pressure compressors are given by Eqs. (25)and (26), respectively.

_Wcom:LP ¼_m21�h16is

� h21�

hcom:LP

(25)

_Wcom:HP ¼_m22�h23is

� h22�

hcom:HP

(26)

where subscripts LP, HP, and is represent low pressure and highpressure, and isentropic, respectively. The specific enthalpy ofsteam is calculated by IPAWS-97 thermodynamic property functionbuilt in EES software [29].

The RR (refrigerant ratio) from the low pressure compressor tothe high pressure compressor is calculated by Eq. (27).

RR ¼ m13 � _m21_m13

(27)

where RR is refrigerant ratio which can be from 0 to 1. The values of0, 1, and the values between 0, and 1 indicate that the systemoperates with a low pressure compressor, high pressurecompressor, and low and high pressure compressors, respectively.

Solution heat exchanger 12,000Evaporator 16,000Condenser 8000Expansion valve 300

2.2.1.3. Performance criteria. The COP (coefficient of performance)of VCR system and GOR (gain output ratio) of MEEeABHP system as

the performance criteria to comprise the performance of combinedsystemwith the stand-alone systems are given by Eqs. (28) and (29)[4,38].

COPVCR ¼_QEva:_Wcom:

(28)

GORMEE�ABHP ¼ _mfresh water_m8

(29)

The exergy efficiency as the robust performance criterion for thesystems with different products is given in Part 2 of this paper forcomparison of the MEEeABHPeVCR system with stand-aloneMEEeABHP and VCR systems in exergy point of view.

2.2.2. Economic modelIn this section we detail the equations that form the economic

model for the VCR, MEEeABHP, and MEEeABHPeVCR systems tocalculate the total annual cost. The models, developed by Jan-ghorban Esfahani and Yoo [39], Alasfour and Bin Amer [40], GarousiFarshi et al. [41], Nafey et al. [42], and Sayyaadi and Nejatolahi [43]are used for our economic model.

The total annual cost of the system is given by Eq. (30).

TAC ¼ ACCþ AOC (30)

where ACC and AOC are the annual capital cost and annual oper-ating cost, respectively. The economic model equations that areused to calculate TAC are presented by Eqs. (31)e(47).

The capital cost of the generator, condenser, evaporator,absorber, and solution heat exchanger are calculated by the powerlaw relation given by Eq. (31) [41].

Zk ¼ ZR:k$�AkAR

0:6(31)

where Zk is capital cost of the component k, and ZR,k is the referencecost of the component k at the reference year. Ak and AR are the heattransfer area of component k, and reference heat transfer area,respectively. The reference costs of the heat exchangers for thereference year 2000 are listed in Table 1 [41]. The component costscalculated by Eq. (31) using the reference costs presented in Table 1are not reliable because the costs are valid around the year 2000.Therefore all the component costs obtained from Eq. (31) areupdated to the year 2009, which is more reliable for economicanalysis of this study using Eq. (32).

Zk;2009 ¼ Zk

�CI2009CI2000

(32)

where Zk,2009 is the component cost at year 2009, Zk is thecomponent cost at year 2000 which is calculated by Eq. (31) and

Table 3Initial operating parameters and thermodynamic parameters for VCR, MEEeABHP,and MEEeABHPeVCR systems.

Parameter Value Units

VCR systemDTmin,Eva. 10 �CDTmin,con. 10 �Chcom 91 %Refrigerant type Steam e

Tamb. 40 �CT14 6 �CQcooling 30,000 kWElectric power price 0.07 $/kWhMEEeABHP systemPA 7.5 kPaEffect number 6 e

DTMEE 3 �CPmotive steam 500 kPa

I. Janghorban Esfahani et al. / Energy 75 (2014) 312e326 317

Table 1. CI2009, and CI2000 are theMarshall and Swift equipment costindex at year 2009, and 2000, respectively, which can be found inRef. [41].

The heat transfer area of each component in Eq. (31) is given byEq. (33).

Ak ¼ QkUk$LMTDk

(33)

where A is heat transfer area, Q is heat transfer flow rate throughthe component, U is heat transfer coefficient which considered as1.5, 1.5, 0.7, 1 kW/m2K for generator, evaporator, absorber, andsolution heat exchanger respectively [44], and LMTD is loga-rithmic mean temperature difference which is calculated byEq. (34).

LMTDk ¼�Th;i � Tc;i

�� �Th;e � Tc;e�

ln Th;i�Tc;iTh;e�Tc;e

(34)

where, h and c represent hot and cold streams, i and e representinlet and outlet streams.

The heat transfer area, overall heat transfer coefficients, and thelogarithmic mean temperature differences for each effect, the pre-heaters, the condenser, and the total heat transfer area can be ob-tained by using Eqs. (C.1)e(C.14) as presented in Appendix C.

The capital cost of the pump is calculated by Eq. (35) [43].

Zpump ¼ 308:9$ _WCpump

pump (35)

where _Wpump is the power consumption of pump, Cpump is 0.25 forpump power consumption in the range of 0.02e0.3 kW, 0.45 forpump power consumption in the range of 0.3e20 kW, and 0.84 forpump power consumption in the range of 20e200 kW [43].

The capital cost of the compressor is given by Eq. (36) [42].

Zcom: ¼ 7364$ _mrefrigerant$

�PoPi

$

�hcom:

1� hcom:

(36)

where Po and Pi are outlet and inlet pressures of the compressor,respectively.

The capital cost of the MEE subsystem is calculated by Eqs.(37)e(43) listed in Table 2 [40]. Zeffects,MEE, and Zcon.,MEE in Table 2

Table 2Economic model equations for MEE subsystem for the calculations of the capital andoperating costs [40].

Equations Descriptions

Capital costs

CA ¼ Zeffects;MEE þ Zcon;MEE (38)Area cost ($)

Ceq ¼ 4$CA (39) Equipment cost(evaporator, condenser…)

Csite ¼ 0.2$Ceq (40) Site cost ($)Ctr ¼ 0.05$(CA þ Ceq þ Cs) (41) Transportation costs ($)Cb ¼ 0.15$Ceq (42) Building costs ($)Cen ¼ 0.1$Ceq (43) Engineers and salary costs ($)Cc ¼ 0.1$(CA þ Ceq þ Cs) (44) Contingency costs ($)Operating costCl ¼ 0.1 pf$Q$365 (45) Labor cost ($/yr)Cch ¼ 0.04 pf$Q$365 (46) Chemical material costs ($/yr)Cin ¼ 0.005$CA (47) Insurance costs ($/yr)

are calculated through Eqs. (31)e(34) for evaporators andcondenser of MEE subsystem. As the plant is assumed to operate330 days, the pf (plant load factor) is considered to be 0.9.

The ACC (annual capital cost) is obtained by multiplying capitalcost by the amortization factor. The amortization factor is given byEq. (47).

CRF ¼ i$ð1þ iÞLCð1þ iÞLC � 1

(37)

where CRF is amortization factor. i and LC are interest rate and plantlife cycle which are assumed to be equal to 15% and 20 years,respectively.

The AOC (annual operating cost) mainly includes the cost ofenergy (heat and power), labor cost, chemical cost, and insurancecost. The equations for calculation of last three terms of the annualoperating cost are presented in Table 2. The costs of the power andheat are assigned based on the price of electricity and saturatedsteam at pressure 0.25 MPa being 0.07 $/kWh and 11 $/ton [5].

2.3. Model validation

The simulated models were validated by comparing the simu-lation results of the MEEeABHP and VCR systems with those foundin the relevant literature [1,4,24] under the same conditions (forexample, the relative errors of the net power generation of the SIGTand the gain output ratio of the METVC desalination system areboth within 2.75%).

hpump 91 %Xsw 30,000 ppmXB6 70,000 ppmT1 79.2 �CT4 117.4 �CQfresh water 15,000 m3/dPrice of steam 11 $/tonMEEeABHPeVCR systemPA 7.5 kPaEffect number 6 e

DTMEE 3 �CPmotive steam 500 kPahcom 91 %hpump 91 %Xsw 30,000 ppmXB6 70,000 ppmT1 79.2 �CT4 117.4 �CT14 6 �CQfresh water 15,000 m3/dQcooling 30,000 kWElectric power price 0.07 $/kWhPrice of steam 11 $/ton

I. Janghorban Esfahani et al. / Energy 75 (2014) 312e326318

3. Energy and cost analyses

The energy and cost analyses were conducted to determine theenergy consumption and TAC (total annual cost) of the MEE-eABHPeVCR system with one compressor under the specifiedconditions presented in Table 3. As presented in Table 3, the sys-tems operate to generate 15,000 m3/d of fresh water and cooling of30,000 kW, which are generated separately by the MEEeABHPdesalination system and VCR system, respectively, and simulta-neously by theMEEeABHPeVCR system. Parametric and sensitivityanalyses were performed to evaluate the effects of four keyparametersdabsorber pressure (PA), temperature difference be-tween effects of the MEE subsystem (DTMEE), temperature of thestrong solution from absorber (T1), and temperature of the weaksolution from generator (T4)don the energy consumption and totalannual cost of the combined systemwith one compressor (Fig.1). Inthe parametric analysis, one parameter was varied while otherswere kept constant.

3.1. Parametric analysis

In theMEEeABHPeVCR systemwith one compressor, the effectsof PA, DTMEE, T1, and T4 on the net power consumption, heat energyconsumption, and TAC of the combined systemwere analyzed. Thevariation range of PA, DTMEE, T1, and T4 are considered from 5 to12 kpa, 2e4 �C, 74e84 �C, and 112.5e122.5 �C, respectively.

3.1.1. Effect of the absorber pressure (PA)Fig. 3aec shows the effect of absorber pressure on energy con-

sumption, TAC, ACC (annual capital cost), and AOC (annual oper-ating cost), respectively, for the MEEeABHPeVCR system with onecompressor at a fixed DTMEE (3 �C), T1 (79.2 �C), and T4 (117.4 �C). Asshown in Fig. 3a, the net power consumption and the heat energyconsumption increases and decreases as PA increases.

According to Fig. 3b, increase of the absorber pressure results indecrease of TAC until a given absorber pressure is reached, and thenfurther increase in absorber pressure results in increasing TAC.Fig. 3c shows the effect of the absorber pressure on ACC (annualcapital cost) and AOC (annual operating cost) of the system. Sincethe annual capital cost and annual operating cost of the systemincreases and decreases, respectively, with the increase of absorberpressure, total annual cost which is the sum of the annual capitaland annual operating costs decreases and increases with the in-crease of the absorber pressure.

Fig. 3. Effect of absorber pressure on (a) net power and heat energy consumptions (b)total annual cost (c) annual capital and operating costs for an MEEeABHPeVCR systemwith one compressor.

3.1.2. Effect of the temperature difference between effects of theMEE subsystem (DTMEE)

Fig. 4a-4c show the effect of the temperature difference be-tween effects of the MEE subsystem (DTMEE) on the energy con-sumption, TAC, and annual capital and operating costs, respectively,for the MEEeABHPeVCR system with one compressor at a fixed PA(7.5 kPa), T1 (79.2 �C), and T4 (117.4 �C).

As shown in Fig. 4a, the power consumption slightly increasesand heat energy consumption highly increases with the increase ofthe DTMEE. Fig. 4b shows that the total annual cost decreases withthe increase of the DTMEE. The reason can be explained throughFig. 4c which shows the effect of DTMEE on annual capital andoperating costs. As shown in Fig. 4c the annual capital cost de-creases while the annual operating cost increases with the increaseof the DTMEE. Since the variation of the annual capital cost withrespect to the increase of theDTMEE is higher than that of the annualoperating cost, the TAC, which is the sum of the annual capital andannual operating costs, decreases with the increase of the DTMEE.

3.1.3. Effect of the temperature of the strong solution from absorber(T1)

Fig. 5a-5c show the effect of temperature of the strong solutionfrom absorber (T1) on net power consumption and heat energyconsumption, TAC, and annual capital and operating costs,respectively, for the MEEeABHPeVCR systemwith one compressorat a fixed PA (7.5 kPa), DTMEE (3 �C), and T4 (117.4 �C).

As shown in Fig. 5a the heat energy consumption increases withthe increase of the T1 because the heat energy recovery through thesolution heat exchanger decreases with the increase of the T1. Thepower consumption is constant with the increase of the T1. Sincethe outlet pressure of the compressor is constant with the increaseof the T1.

Fig. 4. Effect of DTMEE on (a) net power and heat energy consumptions (b) total annualcost (c) annual capital and operating costs for an MEEeABHPeVCR system with onecompressor.

Fig. 5. Effect of T1 on (a) net power and heat energy consumptions (b) total annual cost(c) capital cost and operating cost for an MEEeABHPeVCR system with onecompressor.

I. Janghorban Esfahani et al. / Energy 75 (2014) 312e326 319

According to Fig. 5b the total annual cost increases with theincrease of the T1 which is summation of annual operating andcapital costs. As shown in Fig. 5c the annual capital cost and annualoperating cost increase with the increase of the T1.

3.1.4. Effect of the temperature of the weak solution from generator(T4)

Fig. 6aec shows the effect of temperature of the weak solutionfrom generator (T4) on net power consumption and heat energyconsumption, TAC, and annual capital and operating costs,

respectively, for the MEEeABHPeVCR systemwith one compressorat a fixed PA (7.5 kPa), DTMEE (3 �C), and T1 (79.2 �C).

As shown in Fig. 6a, the heat energy consumption decreaseswith the increase of the T4. The power consumption which issummation of compressor power consumption and pump powerconsumption slightly decreases with the increase of the T4. Thepump power consumption decreases due to the decrease of themass flow rate through the pump with the increase of the T4, whilethe compressor power consumption is kept constant with the in-crease of the T4 since the variation of the T4 has no effect on pres-sure ratio of the compressor.

Fig. 6b shows the effect of the T4 on the total annual cost. TheTAC decreases with the increase of the T4. As shown in Fig. 6c theannual operating cost decreases with the increase of the T4 whilethe annual capital cost is kept constant. Since the TAC is sum of the

Fig. 6. Effect of T4 on (a) net power and heat energy consumptions (b) total annual cost(c) capital cost and operating cost for an MEEeABHPeVCR system with onecompressor.

I. Janghorban Esfahani et al. / Energy 75 (2014) 312e326320

annual capital and operating costs, the TAC decreases with the in-crease of the T4.

3.2. Sensitivity analysis

The sensitivity analysis was conducted to compare the sensi-tivity of the system responses including net power and heat energyconsumptions, TAC, and annual capital and operating costs forMEEeABHPeVCR system with one compressor with respect tovarious conditions of 4 parameters including PA, DTMEE, T1 and T4.

In order to define the significance of the parameter’ effects onthe system responses, the polynomial regressionwas used tomodelthe relationship between each response and each parameter byfitting a polynomial equation. The polynomial equations for fiveresponses with respect to four parameters are presented inTable D.1 in Appendix D. The goodness of fit of the models waschecked by the multiple correlation coefficients (R2). The values ofR2 for each polynomial equation are presented in Table D.1 inAppendix D. For all the models the values of R2 are very high,which indicates the goodness of fit of the models. Since the slope ofthe polynomial equation corresponding to parameter value showsthe sensitivity of the response to change in the parameter, thepolynomial equation's derivative which is a function to calculatethe slope of the polynomial equation was defined for eachresponse. Since the values of the slope of the polynomial equationsvaries with the variation of the parameter values, the maximumslope of the polynomial equation was defined as the sensitivityvalue of each response with respect to each parameter by maxi-mizing the polynomial equation's derivative function in the rangeof the each parameter. The polynomial equation's derivative func-tions with the sensitivity values are presented in Table D.2 inAppendix D.

The sensitivity values for each response were normalized tobetter comparison of significance of the each parameter effect.

Fig. 7a to 7e show the normalized sensitivity values for heatenergy consumption, power consumption, annual capital cost,annual operating cost, and total annual cost, respectively. Asshown in Fig. 7a the parameters of DTMEE, PA, T4, and T1 have thehighest to lowest influence on the value of heat energy con-sumption, respectively. Since the sensitivity values of the DTMEE,PA, and T1 are positive and the sensitivity values of the T4 isnegative, it can be concluded that the effects of the DTMEE, PA, andT1 are additive while the effects of the T4 is ablative on the heatenergy consumption.

It can be seen in Fig. 7b that, the parameter of PA has the highestsensitivity value with an ablative influence on power energy con-sumption among the parameters. Also the effect of the DTMEE ispositive, and T1 and T4 have no any influence on power consump-tion of the system.

According to Fig. 7c the sensitivity value of the DTMEE is higherthan the sensitivity value of the PA, which means the influence ofDTMEE is higher than influence of the PA on the value of annualcapital cost. Since the sensitivity values of DTMEE and PA arenegative, it can be concluded that the capital cost of the systemdecreases with the increase of DTMEE and PA. Also it is found thatthe effect of T1, and T4 appear to be negligible on annual capitalcost.

Fig. 7d illustrates that the parameters of DTMEE, PA, T4, and T1,have the highest to lowest influences on value of annual operatingcost, respectively. The influences of DTMEE, and T1 on annual oper-ating cost is additive while the influence of PA, and T4 on operatingcost is ablative, which means that the annual operating cost of thesystem increases with the increase of the DTMEE, A, and T1 while theannual operating cost of the system deceases with the increase ofthe PA, T4. The effect of DTMEE is found to be larger than the effect ofPA, and highly larger than the effects of T1 and T4. Also due to the bigdifference between sensitivity values of DTMEE, and PA with T4 andT1, it can be concluded that the effects of T4 and T1 on the operatingcost are negligible.

As shown in Fig. 7e among the parameters, PA, and DTMEE havethe highest and lowest sensitivity values, respectively, with thenegative sign, which means the effects of DTMEE and PA are ablativeon the total annual cost. It is also found that the effects of the T1 andT4 on total annual cost appear almost negligible.

Fig. 7. Sensitivity analysis results for the MEEeABHPeVCR system parameters: (a) heat energy consumption (b) power energy consumption (c) annual capital cost (d) annualoperating cost (e) total annual cost.

I. Janghorban Esfahani et al. / Energy 75 (2014) 312e326 321

3.3. Comparisons of the systems

Table 4 compares the power consumption, heat energy con-sumption, total annual cost, and performances of the VCR, MEE-eABHP, and MEEeABHPeVCR systems under the operationconditions presented in Table 3 with RR values of 0, 0.5, and 1.

The results show that, to generate 30,000 kW of cooling and toproduce 15,000 m3/d of fresh water, 11,486 kWh of electric power

Table 4Comparison of energy consumption, total annual cost, and performance of the VCR, MEE

System Heat energyconsumption (kW)

Electric powerconsumption (kW)

VCR e 11,486MEEeAHP 41,208 e

MEEeABHPeVCR (low pressure com.) 38,896 4925Comparison 5.61% 57.12%MEEeABHPeVCR (RR ¼ 0.5) 29,677 6462Comparison 27.98% 43.74%MEEeABHPeVCR (high pressure com.) 20,459 7999Comparison 50.35% 30.36%

and 41,208 kW of heat energy are consumed by the stand-aloneVCR and MEEeABHP systems, respectively.

As presented in Table 4, the MEEeABHPeVCR system with RRvalues of 0, 0.5, and 1 can simultaneously generate 30,000 kW ofcooling and produce 15,000 m3/d of fresh water by consuming4925, 6462, and 7999 kWof electric power and 38,896, 29,677, and20,459 kW of heat energy. We conclude that the MEEeABHPeVCRsystem decreases the heat energy consumption by 5.61, 27.98, and

eABHP, and MEEeABHPeVCR systems.

Fresh waterproduction (m3/d)

Coolinggeneration (kW)

TAC ($/yr) GOR COP

e 30,000 10,690,000 e 2.6115,000 e 16,860,000 9.19 e

15,000 30,000 20,500,000 9.736 6.093e e 25.6% 5.61% 57.13%15,000 30,000 20,340,000 12.76 4.64e e 26.17% 27.97% 43.7%15,000 30,000 20,180,000 18.51 3.751e e 26.75% 50.35% 30.36%

I. Janghorban Esfahani et al. / Energy 75 (2014) 312e326322

50.35% and decreases electric power consumption by 57.12, 43.74,and 30.36% compared to the stand-alone MEEeABHP and VCRsystems, respectively. Therefore, it can be concluded that with in-crease in the share of high pressure compressor to compress therefrigerant, the heat energy consumption of the MEEeABHPeVCRsystem more decreases while the power consumption of theMEEeABHPeVCR system less decreases than the stand alonesystems.

As presented in Table 4 the total annual cost of the VCR systemto generate 30,000 kW of cooling and total annual cost of theMEEeABHP system to produce 15,000 m3/d of fresh water are10,690,000 $/yr and 16,860,000 $/yr, respectively, while the totalannual cost of the MEEeABHPeVCR system to cogenerate30,000 kW of cooling and 15,000 m3/d of fresh water are20,500,000 $/yr, 20,340,000 $/yr, and 20,180,000 $/yr, respectively,for MEEeABHPeVCR systems with RR values of 0, 0.5, and 1.Therefore, it can be concluded that the MEEeABHPeVCR systemcan save 25.6, 26.17, and 26.75% in total annual cost compared tothe stand-alone VCR and MEEeABHP systems.

According to Table 4 the COP and GOR of the stand-alone VCRand MEEeABHP systems to generate 30,000 kW of cooling and15,000 m3/d of fresh water are 2.61, and 9.19, respectively, whilethe COP values of MEEeABHPeVCR systems are 6.093, 4.64, and3.751 and the GOR values are 9.736, 12.76, and 18.51, respectively,for MEEeABHPeVCR systems with RR values of 0, 0.5, and 1.Therefore, MEEeABHPeVCR systems with RR values of 0, 0.5, and 1can increase the COP of the cooling process by 57.13, 43.7, and30.36%, and increase the GOP of the fresh water production processby 5.61, 27.97, and 50.35% compared to the stand-alone MEEeABHPand VCR systems, respectively.

4. Conclusions

In this study as Part 1 of two parts paper, new cooling and freshwater combined system, which combines the MEEeABHP desali-nation system and VCR system, is suggested and investigated basedon energy and cost measurements. The energy and cost perfor-mance of the combined system are greater than those of theMEEeABHP and VCR systems (which separately generate freshwater and cooling) for three reasons. First, the condenser of the VCRsystem is replaced by an MEEeABHP system as the waste heat ofthe VCR system is recovered as an energy source for theMEEeABHPsystem. Second, the pressure ratio of the compressor in the MEE-eABHPeVCR system is less than that of the stand-alone VCR sys-tem. Third, the temperature of the compressor outlet stream isincreased by the ABHP subsystem and is used as an energy sourcefor theMEE system. The energy and economic analysis results showthat the electric power and heat energy can be decreased by 57.12%and 5.6% and COP and GOR can be increased by 57.12% and 5.6% bythe MEEeABHPeVCR system with low pressure compressorcompared to the stand-alone systems for fixed fresh water andcooling production, respectively. Also, the total annual cost of theMEEeABHPeVCR system is 25.6% less than that of the stand-aloneVCR and MEEeABHP systems.

Acknowledgments

This work was supported by the National Research Foundationof Korea (NRF) grant funded by the Korea government (NRF-2012R1A1B3001400).

Appendix A. Correlations for enthalpy calculation

Correlations for calculating the enthalpy of pure water, lithiumbromideewater, and seawater are as follow:

A.1. Pure water

The enthalpy of pure water states including saturated water,saturated vapor, and superheated vapor can be calculated throughEqs. (A.1)e(A.6).

The enthalpy of saturated water can be calculated by Eq. (A.1)which is valid for 5 � T � 200 �C [35].

hf ¼�0:141355þ 4:20207$T � 0:000535$T2

þ 0:000004$T3�.

1000(A.1)

The enthalpy of saturated vapor is calculated by Eq. (A.2) [45].

hv ¼ hf þ hfg (A.2)

where hv is saturated vapor enthalpy, and hf is saturated waterenthalpy calculated by Eq. (A.1). hfg is latent heat of evaporationcalculated by (A.3) which is valid for 0 � T � 200 �C [35].

hfg ¼�2:501$106 � 2:369$103$T þ 2:678$10�1$T2

� 8:103$10�3$T3 � 2:079$10�5$T4�.

1000 (A.3)

The enthalpy of superheated vapor is calculated by (A.4) [37].

hðp; tÞRT

¼ t�g0t þ grt

�(A.4)

where p ¼ p/p* and t ¼ T*/T with p* ¼ 1 MPa and T* is 540 K g0tand gr

t are the ideal-gas and residual parts of dimensionless Gibbsfree energy respectively, which are given by Eqs. (A.5) and (A.6)[37].

g0t ¼X9i¼1

n0i J0i t

J0i �1 (A.5)

grt ¼X43i¼1

nipIi Jiðt� 0:5ÞJi�1 (A.6)

where the numerical values of the coefficients and exponents canbe found in Ref. [37].

A.2. Seawater

The enthalpy of seawater is calculated by Eq. (A.7) [35] which isvalid for 10 � T � 120 �C and. 0 � X � 0.12 kg/kg,

hsw ¼ hf ��X�a1 þ a2X þ a3X

2 þ a4X3 þ a5T þ a6T

2 þ a7T3 þ a8XT þ a9X

2T þ a10XT2��.

1000

a1 ¼ �2:348� 104; a2 ¼ 3:152� 105; a3 ¼ 2:803� 106; a4 ¼ �1:446� 107; a5 ¼ 7:826� 103;a6 ¼ �4:417� 101; a7 ¼ 2:139� 10�1; a8 ¼ �1:991� 104; a9 ¼ 2:778� 104; a10 ¼ 9:728� 101

(A.7)

I. Janghorban Esfahani et al. / Energy 75 (2014) 312e326 323

where X and T are salinity and temperature of seawater,respectively.

A.3. Lithium bromideewater

The enthalpy of lithium bromideewater is calculated by Eq.(A.8) [36] which is valid for 0 � T � 190 �C and. 40 � x � 75 wt.%,

hLiBr�water ¼X4n¼0

anxn þ TX3n¼0

bnxn þ T3d0

a0 ¼ �954:8; a1 ¼ 47:7739; a2 ¼ �1:59235; a3 ¼ 2:09422� 10�2; a4 ¼ �7:689� 10�5

b0 ¼ �3:293� 10�1; b1 ¼ 4:076� 10�2; b2 ¼ �1:36� 10�5; b3 ¼ �7:1366� 10�6

c0 ¼ 7:4285� 10�3; b1 ¼ �1:5144� 10�4; b2 ¼ 1:3555� 10�6

d0 ¼ �2:269� 10�6

(A.8)

where x and T are solution concentration and temperature oflithium bromideewater, respectively.

In all cases of entropy calculation the reference temperature isconsidered as 25 �C [35e37].

ssw ¼ sf ��X�a1 þ a2X þ a3X

2 þ a4X3 þ a5T þ a6T

2 þ a7T3 þ a8XT þ a9X

2T þ a10XT2��.

1000

a1 ¼ �4:231� 102; a2 ¼ 1:463� 104; a3 ¼ �9:880� 104; a4 ¼ 3:095� 105; a5 ¼ 2:562� 101;a6 ¼ �1:443� 101; a7 ¼ 5:879� 10�4; a8 ¼ �6:111� 101; a9 ¼ 8:041� 101; a10 ¼ 3:035� 10�1

(B.2)

Appendix B. Correlations for entropy calculation

Correlations for calculating the entropy of pure water, lithiumbromideewater, and seawater are as follow:

sLiBr�water ¼ a1 þ a2 þ a3T2 þ A4xþ a5xT þ a6xT

2 þ a7x2 þ a8

a1 ¼ �1:01961E3; a2 ¼ 1:101529E � 1; a3 ¼ �1:042150E � 2a4 ¼ 1:036935E2; a5 ¼ �5:87032E � 2; a6 ¼ 8:63107E � 5;a7 ¼ �3:266802; a8 ¼ �3:16683E � 4; a9 ¼ 4:100993E � 2;a10 ¼ �1:790548E � 4

x2T þ a9x3 þ a10x

4

;(B.3)

B.1. Pure water

The entropy of saturated water can be calculated by Eq. (B.1)which is valid for 5 � T � 200 �C [35].

sf ¼�0:1543þ 15:383$T � 0:02996$T2 þ 0:00008193$T3

� 0:000000137$T4�.

1000

(B.1)

B.2. Seawater

The entropy of seawater is calculated by Eq. (B.2) [35] which isvalid for 10 � T � 120 �C and 0 � X � 0.12 kg/kg,

where X and T are salinity and temperature of seawater,respectively.

B.3. Lithium bromideewater

The entropy of lithium bromideewater is calculated by Eq. (B.3)[36] which is valid for 0 � T � 190 �C and. 40 � x � 75 wt.%,

where x and T are solution concentration and temperature oflithium bromideewater, respectively.

I. Janghorban Esfahani et al. / Energy 75 (2014) 312e326324

Appendix C

Table C.1Heat transfer area, heat transfer coefficient and logarithmic mean temperature difference equations [4].

Equations Descriptions

Ae1 ¼ m0$L0Ue1$ðT0C � T1Þ

(C.1)

Area of effect 1

Aej ¼

��Di�1 þ

��Dr þ

Pi�2j¼1 Dj

�$yi�1

����

i� 1�$yi�1$Fi

��$Li�1

�Uei$ðTvi�1 � TiÞ

(C.2)

Area of effect 2 to n

Atot ¼Xni¼1

Ai (C.3)

Total area of effects

AHi¼�i$Fi$C$

�Tf i � Tf iþ1

��UHi

$LMTDHi

(C.4)

Pre-heaters area in effects 1 to n�1

AHn¼�n$Fn$

�Tfn � Tf

��UHn

$LMTDHn

(C.5)

Pre-heater area in effect n

Acon: ¼

�Dcon: þ

��Dr þ

Pn�1j¼1 Dj

�$yn��

$Ln

Ucon:$LMTDcon:(C.6)

Condenser area

Ue1 ¼ 1:9394þ�1:40562� 10�3

�$T0c �

�2:07525� 10�5

�$T20c þ

�2:3186� 10�6

�$T3

0c (C.7)

For effect 1

Uei ¼ 1:9394þ�1:40562� 10�3

�$Tvi�1 �

�2:07525� 10�5

�$T2vi�1

þ�2:3186� 10�6

�$T3vi�1

(C.8)

For effects 2 to n

UHi¼ 14:18251642þ 0:011383865$Tvi þ 0:013381501$Tf iþ1

(C.9)For pre-heaters of effects 1 to n�2

UHn�1¼ 14:18251642þ 0:011383865$Tvn�1 þ 0:013381501$Tf (C.10)

For pre-heaters of effects n�1

Ucon: ¼ 1:6175þ�1:537� 10�4

�$Tvn �

�1:825� 10�4

�$T2

vn þ�8:026� 10�8

�$T3vn (C.11)

For end condenser

LMTDHi¼�Tf i � Tf iþ1

� ln

Tvi � Tf iþ1

Tvi � Tf i

!(C.12)

For effects 1 to n�1

LMTDHn�1¼�Tfn�1

� Tf�

lnTvn�1 � Tf

Tvn�1 � Tfn�1

!(C.13)

For effects n�1

LMTDcon: ¼�Tf � Tsw

� ln

Tvn � TswTvn � Tf

!(C.14)

For end condenser

I. Janghorban Esfahani et al. / Energy 75 (2014) 312e326 325

Appendix D

Table D.1Polynomial equations for responses with respects to parameters.

Polynomial equations R2 (%)

For heat energy consumptionQðPAÞ ¼ 45353:7� 809:574$PA þ 19:888$P2A 99.99QðDTMEEÞ ¼ 37166� 83:7122$DTMEE þ 219:77$DT2

MEE 99.96QðT1Þ ¼ 5:049673E4� 3:741358E2$T1 þ 2:874453$T21 99.97QðT4Þ ¼ 288458� 6089:14$T4 þ 49:6028$T24 � 0:134949$T34 99.99For power consumptionPowerðPAÞ ¼ 730:923þ 685:767$PA � 16:9873$P2A 99.99PowerðDTMEEÞ ¼ 4921:65þ 2:55595$DTMEE � 0:975026$DT2

MEE þ 0:149924$DT3MEE 99.99PowerðT1Þ ¼ 4:94312E3� 0:5272619$T1 þ 3:70358E � 3$T21 99.96PowerðT4Þ ¼ 4966:85� 0:673947$T4 þ 0:00267495$T24 99.98For capital costCCðPAÞ ¼ 2:52712E7� 5:49809E6$PA þ 835247$P2A � 58241:7$P3A þ 1530:69$P4A 99.95CCðDTMEEÞ ¼ 5:58619E7� 3:15783E7$DTMEE þ 7:51610E6$DT2MEE � 6:47956E5$DT3MEE 99.99CCðT1Þ ¼ 1:156886E7� 8:134481E3$T1 þ 59:79869T2

1 99.97CCðT4Þ ¼ 1:220102E7� 1:520654E4$T4 þ 64:13320$T24 99.96For operating costOCðPAÞ ¼ 7:27305E6þ 319198$PA � 8275:65$P2A 99.99OCðDTMEEÞ ¼ 8:93068E6� 1:417006E4$DTMEE þ 3:517890E4$DT2MEE 99.96OCðT1Þ ¼ 1:106149E7� 5:982119E4$T1 þ 4:593880E2$T21 99.97OCðT4Þ ¼ 4:906959E7� 9:726187E5$T4 þ 7922:78$T24 � 21:5542$T3

4 99.99For total annual costTACðPAÞ ¼ 7:64892E7� 3:741E7$PA � 1:04432E7$P2A 99.96TACðDTMEEÞ ¼ 6:44208E7� 3:12021E7$DTMEE þ 7:41811E6$DT2

MEE � 633158$DT3MEE 99.99

TACðT1Þ ¼ 2:26304E7� 67955:7$T1 þ 519:187$T21 99.97TACðT4Þ ¼ 6:17212E7� 9:99347E5$T4 þ 8:085095E3$T24 � 21:83293$T34 99.99

Table D.2Polynomial equations' derivative functions with sensitivity values

Polynomial equations' derivative functions Sensitivity value

For heat energy consumptiondQdPA

¼ �809:574þ 39:776$PA þ39.776

dQdDTMEE

¼ �83:7122þ 439:54$DTMEEþ439.54

dQdT1

¼ �3:741358E2þ 5:748906$T1 þ5.75

dQdT4

¼ �6089:14þ 99:2056$T4 � 0:404847$T24�11.69

For power consumptiondPowerdPA

¼ 685:767� 33:9746$PA �33.9746

dPowerdDTMEE

¼ 2:55595� 1:950052$DTMEE þ 0:449772$DT2MEEþ1.952

dPowerdT1

¼ �0:52726191 þ 7:40716E � 3$T1 þ0.0074dPowerdT4

¼ �0:673947þ 0:0053499$T4 þ0.0053For capital costdACCdPA

¼ �5:49809E6þ 1670494$PA � 174725:1$P2A þ 4592:07$P3A �759,876

dACCdDTMEE

¼ �3:15783E7þ 15:0322E6$DTMEE � 19:43868E5$DT2MEE�2,517,000

dACCdT1

¼ �8:134481E3þ 119:59738$T1 þ119.597dACCdT4

¼ �1:520654E4þ 128:2664$T4 128.266For operating costdAOCdPA

¼ 319198� 16551:3$PA �16551.3

dAOCdDTMEE

¼ �1:417006E4þ 7:03578E4$DTMEE þ70357.8

dAOCdT1

¼ �5:982119E4þ 9:18776E2$T1 918.776dAOCdT4

¼ �9:726187E5þ 15845:56$T4 � 64:6626$T24 �1881For total annual costdTACdPA

¼ �3:741E7� 2:08864E7$PA 20,886,400

dTACdDTMEE

¼ �3:12021E7þ 14:83622E6$DTMEE � 1899474$DT2MEE�2,232,000

dTACdT1

¼ �67955:7þ 1038:374$T1 1038.37dTACdT4

¼ �9:99347E5þ 16:17019E3$T4 � 63:49879$T24 28,623

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Nomenclature

A: absorberABHP: absorption heat pumpACC: annual capital cost, $/yrAOC: annual operating cost, $/yrBPE: boiling point evaluation, �CCon.: condenserCom.: compressorCp: specific heat capacity, kJ/kg �CCRF: amortization factorex: specific exergy, kJ/kgEx: exergy, kJG: generatorh: specific enthalpy, kJ/kgHP: high pressureL: latent heatLC: life cycleLP: low pressureMEE: multi effect evaporationMSF: multi stage flashingm: mass flow rate, kg/sNEA: non-equilibrium allowancen: number of effects in the MED-TVC systemP: pressure, barpf: plant load factorQ: heat flow rateQfresh water: fresh water flow rateRR: refrigerant flow-rate ratios: specific entropy, kJ/kg KSJE: steam jet ejectorSHX: solution heat exchangerT: temperature, �CTAC: total annual cost, $/yrT0: temperature of brine in each effect

T: temperature of brine after coolingU: heat transfer coefficient, kW/m2kv: specific volume, m3/kgW: power, MWX: salinity, ppmx: solution concentration based on mass fraction of LiBry: flashing fraction

Subscripts

amb: ambientA: absorberB: brineD: distillatef: feed waterF: seawater streamsw: seawatern: saturated vapor

Greek

DT: temperature difference, �Ch: efficiency