Khadem i 2009

Chemical Engineering and Processing 48 (2009) 339347

Contents lists available at ScienceDirect

Chemical Engineering and Processing:Process Intensication

journa l homepage: www.e lsev ier .co

Simula poprocess

M.H. KhaChemical and PShiraz 71345, I

a r t i c l

Article history:Received 29 MReceived in reAccepted 21 AAvailable onlin

Keywords:Multi-effect evDesalinationSimulationOptimization

ulatn this-statvapoumede andn dat

1. Introduction

Multi-effect (ME)distillation iswidelyused in chemical industryto concentrtion,MSF isincreasing iments thatFallinglmrate and redsubmerged

Modelinter design, ofrom whichstrategy arelems relatedload transie

Several peling of munon-linearcalculationsolved iteraing point risand compostechniques

CorresponE-mail add

El-Nashar and Qamhiyeh developed a simulation model forpredicting the transient behavior of ME stack-type distillationplants [2]. Transient heat balance equations were written for each

0255-2701/$ doi:10.1016/j.cate solutions and recover solvents. In seawater desalina-considered themostwidely usedprocess; nevertheless,nterest in the ME process has emerged due to improve-have lately been achieved in the evaporator design.evaporators allowtheenhancementof theheat-transferuce the scaling problem as compared to classical MEBtube evaporators.g and simulation of the desalination process allow bet-peration, and insight into the operation of the processan optimal operating condition and advanced controlreached. The dynamic models are used to solve prob-to transient behavior such as start-up, shutdown, and

nts.apers investigated the steady-state and dynamic mod-lti-effect evaporators. Lambert developed a system ofequations governing the MEE system and presented aprocedure for reducing this system to a linear form andtively by the Gaussian elimination technique [1]. Boil-e and nonlinear enthalpy relationships in temperatureitionwere included. The results of linear and nonlinearwere compared.

ding author. Tel.: +98 711 2303071; fax: +98 711 6287294.ress: [email protected] (M.R. Rahimpour).

plant component in terms of the unknown temperatures of eacheffect. The equationswere solved simultaneously to yield the time-dependent effect of temperature as well as performance ratio anddistillate production. The results of the simulations program werecomparedwithactual plant operatingdata takenduringplant start-up, and agreement was found to be reasonable.

Tonelli et al. presented a computed package for the simulationof the open-loop dynamic response of MEE for the concentrationof liquid foods [3]. It is based on a non-linear mathematical model.An illustrative case study for a triple-effect evaporator for applejuice concentratorswas presented. The response of the unit to largedisturbances in steam pressure and feed ow rate based on thesolution of the mathematical model was in excellent agreementwith the experimentally determined response.

Hanbury presented a steady-state solution to the performanceequations of anMEDplant [4]. The simulationwas based on a lineardecrease in boiling heat-transfer coefcient, unequal inter-effecttemperature differences, and equal effect thermal loads from thesecond effect down.

Rosso et al. described a steady-statemathematicalmodel devel-oped to analyze MSF plants [5]. The developed model can analyzethe operating and design variables to identify plant behavior, butthe model was not only developed for design purposes but also tosupport a dynamic model. The model can predict the productionrate, the brine ow rate in all stages and the temperature proles.

see front matter 2008 Elsevier B.V. All rights reserved.ep.2008.04.013tion and optimization of a six-effect eva

demi, M.R. Rahimpour , A. Jahanmirietroleum Engineering Department, School of Engineering, Shiraz University,ran

e i n f o

arch 2007vised form 20 April 2008pril 2008e 2 May 2008

aporators

a b s t r a c t

This study presents the steady-state simsion of its relevant software package. Ibuilding blocks are written in a steadyand process optimization of the entireeffect of different parameters on consfeedmass ow rate, condenser pressurresults are good agreement with desigm/locate /cep

rator in a desalination

ion and optimization of a six-effect evaporator and the provi-investigation, the modeling equations of each of the existinge conditions. These equations have been used for simulationrizing unit while exercising the simplifying assumptions. Thesteam produced distilled water and GOR is presented. Theoperating time are optimized for this system. The simulationa.

2008 Elsevier B.V. All rights reserved.

340 M.H. Khademi et al. / Chemical Engineering and Processing 48 (2009) 339347

The study also presents the effect of top brine temperature (TBT)on the performance of the plant.

Husain et al. described the modeling and simulation of a multi-stage desalination plantwith 15 recovery stages and three rejectionstages [6]. The study was based on both steady-state and dynamicsimulations; the study was carried out using a FORTRAN programfor the steady-state simulation and also through a SPEEDUP pack-age.

Hamed investigated the thermal performance of a ME desali-nation system [7]. An analytical solution was developed to verifythe impact of different process variables on the performance ofthe MED system as number of effects, TBT, inlet seawater and theamountofproduct. Thedependenceof thewaterproductioncost onthe performance of the plant was also studied. The results showedthat the performance ratio is highly dependent on the number ofeffect, and both the inlet seawater temperature and TBT are slightlyaffected on the plant performance ratio.

Darwish developed thermal analysis of multistage ash desalt-ing systems [8]. In the base of mathematical model, the effect ofnumber of stage on the performance of the system is discussed.

Elkamelcation of artfor simulatoperationaltwo modesANNs basedpropagationrate are devformance obrine tempe

This worfor the mupresents thof operatintion of opertemperaturproduced dis interestin

2. Process

The evapconsistingoash tank asystem. Thethe rst effeent is fed in

Table 1Size of heat exchangers and pre-heaters

Heat exchanger Pre-heater

Tube diameter (mm) 24.2 24.2Tube length (m) 8 9Number of tube pass 3 4Number of tubes 221 17

this tank is kept constant. Efuent is pumped from the balance tankto a ash tank to remove the air from the system, where ashing isconnected to the condenser. Efuent is then pumped from the ashtank through six pre-heaters arranged in series and passes to theash tank of effect I. Steam is supplied to the heat exchanger andpre-heater of effect I. The produced vapor in ash tank I is directedto shell of the next effect heat exchanger as heating medium. Theow of brine at the outlet of ash tank I is divided in two parts. Oneis directed to the ash tank of the next effect and the second oneis recycled to the heat exchanger of effect I by use of a recircula-tion pump (constant ow rate). A similar process takes place in thenext effects. Vapor from effect VI is condensed in a condenser by

oldwgers

cess

steabalaodelof vaed vstedic preamthe mo accth efnclude-heaassuclud

aporntraind hgy lo; thiseen

desalination process.and co-workers described the development and appli-icial neural networks (ANNs) as amodeling techniqueing, analyzing, and optimizing MSF processes [9]. Realdata is obtained from an existing MSF plant duringof operation: a summer mode and a winter mode.on feed-forward architecture and trained by the back-algorithm with momentum and a variable learning

eloped. The networks can predict different plant per-utputs including the distilled water produced and toprature.k focuses on the development of a steady-state modellti-effect evaporator desalination system. The papere model equations, method of solution, optimizationg conditions by sequential simplex method, optimiza-ating time, and the effect of feed mass ow rate, feede and condenser pressure onGOR, consumed steamandistilled water. The paper presents new plant data whichg for industrials.

description

oration plant of Jams Fajr renery is a vacuum stationf six-effect stages. Each stage comprisesheat exchanger,nd pre-heater. Fig. 1 shows a schematic diagram for theefuent has a dry matter content of 2.06% when fed toct stage and 15.0% at discharge from effect VI. The efu-to theplant throughalter to abalance tank. The level in

use of cexchan

3. Pro

TheenergyThe mliquorproducwell-tedynamthe strresult,ing intin the itions iand pr

Thetions in

The vthe eble a

Energiblebetw

Fig. 1. Schematic of multi-effect evaporatorater which is supplied from cooling tower. Size of heatand pre-heaters are shown in Table 1.

modeling

dy-state mathematical model includes material andnce equations as well as heat-transfer rate equations.predicts temperature, vapor, salt concentration andrious streams, consumed steam and GOR (the ratio ofapor to consumed steam). The model includes a set ofempirical correlations for evaluation of the thermo-operties. The correlations are dened as a function ofconditions such as temperature and concentration. As aodel equations are coupled and highly nonlinear. Tak-

ount the heat exchanger, pre-heater and the ash tankfect which have been shown in Fig. 2, the following sec-e the model equations for heat exchanger, ash tankter, specications and solution method.mptions invoked in development of the model equa-e the following:

formed in the evaporator is salt free; this assumes thatnment of brine droplets by the vapor stream is negligi-as no effect on the salinity of the distillate product.sses from the evaporator to the surroundings are negli-is because of operation at relatively low temperatures,

45 and 115 C.

M.H. Khademi et al. / Chemical Engineering and Processing 48 (2009) 339347 341

No solid m The entir

transmissperaturewith leng

The overais not the

The pre-hany vapor

Steam is ucondition

3.1. Heat ex

Mass balan

mFT(i) = mv

Salt balanc

xFT(i)mFT(i)

Energy bal

mFT(i)H(Tb,

The heatby

qe(i) = Ue(i)mc

where U is tarea; T thecentration;c and i dewater boilively.

3.2. Flash tank

balance:

+ malanc

e(i) +y bal

Hv(T

e-hea

y bal

= mvm

pre-

UPH

=ln[

tion

ardined tat exby pd erin Fi

imiz

blemrobls idetemeFig. 2. A schematic of an effect.

aterial of the liquor is deposited.e of balance equations are lumped together. The heation, from shell to tube is conducted in a constant tem-and the temperature of shell and tube is not changedth.ll heat-transfer coefcient is assumed constant, but itsame for all effects.eaters are worked as total condenser and they have notoutlet.sed in shell side and the liquid leaving is in saturated.

changer

ce:

,e(i) + me(i) (1)

e:

Mass

mv,e(i)

Salt b

xe(i)m

Energ

mv,e(i)

3.3. Pr

Energ

qPH(i)

Theby

qPH(i) =

LMTD

4. Solu

Regrate, feand hesolvedtrial anshown

5. Opt

Proing a prequirebal sta= xe(i)me(i) (2)

ance:

i, xFT(i)) + qe(i) = me(i)H(Tb,e(i), xe(i))

+mv,e(i)Hv(Tb,e(i)) (3)

exchanger thermal load from shell to tube, qe(i), is given

Ae(i)[Tbw,i1 Tb,e(i)] = mv,i1Hv(Tbw,i1)

,e(i)Hc(Tbw,i1) mv,e(i)Hv(Tbw,i1) (4)

he overall heat-transfer coefcient; A the heat-transfertemperature; m the mass ow rate; x the salt con-H the enthalpy; and the subscripts e, FT, bw, b, v,note the exchanger, ash tank, water boiling, saltng, vapor, condensed, and effect number, respecti-

prescribed

The objec The proce

The objein terms ofprocess mothe key varifunction ofof enterprisvariety of co

For optirequired toobjective fudened as b

J = 12(mckIn this eq

of productthe price oe(i) + mi1 = mv,i + mFT(i) (5)e:

xi1mi1 = xFT(i)mFT(i) (6)ance:

b,e(i)) + me(i)H(Tb,e(i), xe(i)) + mi1H(Tb,i1, xi1)= mv,iH(Tb,i) + mFT(i)H(Tb,i, xFT(i)) (7)

ter

ance:

,e(i)(Tbw,i1) = mf,iH(Tf,i, xf,i)

f,i+1H(Tf,i+1, xf,i+1) (8)

heater thermal load from shell to tube, qPH(i), is given

(i)APH(i)LMTD (9)

Tf,i Tf,i+1Tbw,i1 Tf,i+1/Tbw,i1 Tf,i]

(10)

method

g the knowledge of steam temperature, feedmass owemperature, feed concentration, condenser pressurechanger characteristics, prevalent equations have beenrogramming language Matlab.7, using the method ofror. A schematic of programming ow chart has beeng. 3.

ation

formulation is perhaps the most crucial step in resolv-em that involves optimization. Problem formulationntifying the essential elements of a conceptual or ver-nt of a given application, and organizing them into amathematical form, namely

tive function (economic criterion).ss model (constraints).

ctive function represents prot, cost, energy, yield, etc.,the key variables of the process being analyzed. Thedel and constraints describe the interrelationships ofables. In the chemical process industries, the objectiveten is expressed in units of currency because the goale is to minimize costs or maximize prots subject to anstraints [10].

mization of the evaporation unit of Fajr renery, it isdene the objective function and simulate the unit. Thenction in quadratic form related to evaporation unit iselow:

c)2 12(msks)

2 12(mcwkcw)2 (11)

uation, the rst term 1/2(mckc)2 is related to incomecondensed water, where mc is the amount and kc isf one kg of the condensed water. The second term


1/2(msks)and ks is th1/2(mcwkcand kcw is tin order toFig. 3. A schematic of programming ow

2 is related to consumed steam, wherems is the amounte price of one kg of consumed steam. The third termw)2 is related to coolingwater,wheremcw is the amounthe price of each kg of cooling water in the condensercreate vacuum in the effect. Variables of , and

are estimatfrom 0 to 1optimizatioare assumeinvestmentchart.

ing the importance of each variable which could differaccording to the importance of each variable. In thisn the amount of , and are weighting factor andd equal to 1. In the objective function, terms related toand running cost are neglected. In Table 2, the cost of


Table 2Cost of parameters of ks, kcw and kc [11]

Utility

Steam (100psiCooling waterDistilled water

different pa

6. Optimiz

Solid deof themainmation of tand, conseqof evaporatintervaly shFor expectinmized the rtransfer is c

The invebe related t[11]:

1U2

= atb +

where a anoverall heatbeginning o

If Q repoperating ttemperaturtransfer at a

dQdtb

= UA

The rate ofarea and thtially constduring an oof Eq. (13) a Q

0

dQ = A

Q = 2ATa

Eq. (15) canwill permitperiod. EachIf the timethen the tonating the tand rellingE/(tb + tc).

The totato (Q/cycle)

Therefor

QE =2AT

a

Under ordinating time tshows a ma

time can also be obtained by setting the derivative of Eq. (16) withrespect to tb equal to zero and solving for tb. The result is

+ 2a

adtc (17)

tb in Eq. (17) is time per cycle for maximum amount of heatr.optimum operating time given by (17) shows the operat-edule necessary to permit the maximum amount of heatr.to nd the operation time of evaporation system of Fajr

y, the overall heat-transfer coefcient of evaporator I is aunction of operating time tb as below:

.646

uatiatoren cackneg timshowy.

ults a

t is rct I itinga resin efm. Thseqully wthedataof hasseffe

he ms andnow, con4 shoducaterdistil50kgte caf effein refferees trgrow

g con

tsCost

g): ks 0.51.00$/1000 lb(tower): kcw 0.020.08$/1000gal: kc 0.701.20$/1000gal

rameters ks, kcw and kc are given:

ation of operating time

position on heat-transfer area and scale forming is onedifculties in evaporation systems. The continuous for-he scale causes a gradual increase in resistance of heatuently, a reduction in the rate of heat transfer and rateion. Under this condition, the evaporation unit must beut down and cleaned after an optimum operation time.g maximum yield of distilled water, it should be maxi-ate of evaporation and for this propose, the rate of heatonsidered as an objective function and is maximized.rse of the square of overall heat-transfer coefcientmayo operating time by a straight-line equation as follows

d (12)

d d are constants for any given evaporator and U is the-transfer coefcient at any operating time tb since thef the operation.resents the total amount of heat transferred in theime tb, and A and T represent heat-transfer area ande-difference driving force, respectively, the rate of heatny instant is:

T = AT(atb + d)1/2

(13)

heat transfer is time dependent, but the heat-transfere temperature-difference driving force remain essen-ant. Therefore, the total amount of heat transferredperating time of tb can be determined by integratings follows:

T

tb0

(1

atb + d)1/2

dtb (14)

[(atb + d)1/2 d1/2] (15)

be used as a basis for nding the cycling time whichthe maximum amount of heat transfer during a givencycling time consists of an operating time of tb month.

per cycle for emptying, cleaning and recharging is tc,tal in each cycling time is tt = tb + tc. Therefore, desig-otal time used for actual operation, emptying, cleaning,as E, the number of cycles during E month is equal to

l amount of heat transferred during Emonth,QE is equal (cycles/E month)e,

tb = tc

wheretransfe

Theing schtransfe

Nowrenerlinear f

1U2

= 7

This eqevaporhas bethe thicleaninTable 3rener

7. Res

As iin effeas heaery, asvapormediuII. Connot reaposed,designresultsvapor min eachdata.

In txf, Tf, Tare unkon GOR

Fig.and prfeed wducedto 41,8ow ratank oresultsture diincreasshows

Table 3Operatin

Constan[(atb + d)1/2 d1/2]E

tb + tc(16)

ary conditions, the only variable in Eq. (16) is the oper-b. A plot of the total amount of heat transferred vs. tbximum at the optimum value of tb. The optimum cycle

AadEtcT 108tb + 2.75 106 (18)

on is based on Eq. (12) and thickness of scale in thetubes. The diameter of evaporator tubes is 24.2mm andlculated according to the industrial information and

ss of scale in the evaporator tubes during one year. Thee and restarting of the unit is supposed to be oneweek.s the operating constants of evaporator system of Fajr

nd discussion

epresented in the process description, produced vapors directed to shell of the next effect heat exchangermedium. In the evaporation plant of Jams Fajr ren-ult of scale formation and vacuum shortage, producedfect I is not enough for the next effect as heatingerefore, steam is supplied to effect I and also effect

ently, the evaporation unit of Jams Fajr renery doesork and industrial data is not available. For this pro-predicted data (simulation results) is compared with. Table 4 demonstrates the design data and simulationeat exchanger temperature, pre-heater temperature,ow rate, liquor mass ow rate and salt mass fractionct. Model results show good agreement with the design

athematical modeling, since the values of variables mf,condenser pressure are known and the rest of variablesn, it is possible to study the effect of these parameterssumed steam and produced distilled water.ows effect of feed mass ow rate on consumed steamed distilled water. With increasing of mass ow rate offrom 48,000 to 53,500kg/h, consumed steam and pro-led water increase from 8350 to 8470kg/h and 40,900/h, respectively. This means that increasing feed massuses reduction inmass fraction of salt water in the ashct I and therefore in the rst effect evaporator. Thisducing the BPE. Reduction of BPE increases tempera-nce of consumed steam and evaporator of effect I andansferred heat from consumed steam to effect I. Thisth of consumed steam. As it can be seen in this g-

stants of evaporation system of Fajr renery

Values

403.25m2

7.6461082.7510612 months7 days3 C


Table 4Comparison of model predictions and design data for each effect

Heat exchangertemperature (C)

Pre-heater temperature(C)

Vapor mass ow rate (kg/h) Liquor mass ow rate(kg/h)

Salt mass fraction (mol%)

EffectI

Model results 114.9976 106.0733 7187.1341 43646.1079 0.024403Design data 115 105 7552 43,362 0.02462

EffectII

Model results 106.0733 94.6549 7217.6187 36628.4892 0.029226Design data 105 94 7402 35,960 0.03723 (?)

EffectIII

Model results 94.6549 85.951 6723.4521 29905.0371 0.037274Design data 94 84.5 7293 28,667 0.03723

EffectIV

Model results 85.951 74.6878 7055.6473 22849.1898 0.045594Design data 84.5 73.5 7121 21,546 0.04954

EffectV

Model results 74.6878 59.6568 6653.8045 16195.3853 0.064446Design data 73.5 58.5 6763 14,783 0.0722

EffectVI

Model results 59.6568 41.1224 5953.396 10241.9893 0.10054Design data 58.5 40 7667 7116 0.15

Fig. 4. Effect oduced distilledPcond = 7.404kP

ure, increassteam and p

Fig. 5 shincreasingcan increas

Fig. 5. Effectxf = 0.0206 and

it seems that total distilled water increases with a higher rate thanconsumed steam and so increases GOR.

Fig. 6 shows effect of feed temperature on consumed steamand produced distilled water. Increase in feed temperature from51 to 68 C

rease in fntereratnk inand incIncreasature eare genash taf feed water mass ow rate ow rate on consumed steam and pro-water. Operating conditions: Ts = 149 C, Tf = 60 C, xf = 0.0206 and

a.

ing feedmass ow rate by 11.4% can increase consumedroduced distilled water by 1.4% and 2.3%, respectively.ows effect of feed mass ow rate on GOR. At 65 Cthe feed mass ow rate from 48,000 to 53,500kg/he GOR by 2.13%. With increasing feed mass ow rate,

of feed water mass on GOR. Operating conditions: Ts = 149 C,Pcond = 7.404kPa.

fraction offraction ofdifferencesand also heain rst effecfeed tempeand increas

Fig. 7 shpressure 7.results in revapor and t

Fig. 8 shand produc6.6 to 8.2 kPwater fromtively. Thistemperatur

Fig. 6. Effect oOperating condecreases consumed steam from 8477 to 8412kg/hes produced distilled water from 41,100 to 42,200kg/h.eed temperature causes an increase in theuid temper-ing the ash tank of rst effect. Therefore, more vaporsed. As a result themass fraction of salt water exiting therst effectwill increase. Growth in amount of saltmass

ash tank in effect I results in increasing of salt massevaporator. This increases BPE, decreases temperaturebetween consumed steam and evaporator in rst effectt transferred between consumed steamand evaporatort. This shows reduction in consumed steam. Increasingrature by 33.3% can decrease consumed steam by 0.7%e produced distilled water by 2.6%.ows effect of feed temperature on GOR. At condenser4kPa, increasing feed temperature from 51 to 68 Cduction of consumed steam and increase of producedherefore it will increase GOR by 3.6%.ows effect of condenser pressure on consumed steamed distilled water. Increasing condenser pressure fromawill decrease consumed steam and produced distilled8620 to 8250kg/h and 42,500 to 41,070kg/h, respec-show with increasing condenser pressure, condensere will increase too. As a result boiling temperaturef feed temperature on consumed steam and produced distilledwater.ditions: Ts = 149 C, mf = 51,816kg/h, xf = 0.0206 and Pcond = 7.404kPa.


Fig. 7. Effect of feed temperature on GOR. Operating conditions: Ts = 149 C,mf = 51,816kg/h and xf = 0.0206.

of evaporatdistilled wadecreases devaporatorsumed steaAs it can be24.2% can dby 4.3% and

Fig. 9 show rate 58.2 kPa willsure, it seemthan consum

In the oow rate 5ture 149 C,consumed srelative errosumed steagiven simulated by usisix effects cpredicted d

Fig. 8. Effectwater. Operati

Fig. 9. Effect of condenser pressure on GOR. Operating conditions: Ts = 149 C,xf = 0.0206 and Tf = 60 C.

systemcanbeoptimizedbyusingdenedobjective function)) and simulation of the system as a constraint. The Sequen-plex

ndenbjecterticom ttroid

e betthroon. Tnewtil ththe eectivC, sultsserty ofkg/hsideroratchaor in rst effect will increase and therefore producedter will decrease too. Increase in boiling temperatureifference of temperature between consumed steam andof rst effect and also heat transferred between con-m and evaporator. This will decrease consumed steam.seen in this gure, increasing condenser pressure by

ecrease consumed steam and produced distilled water3.2%, respectively.

ows effect of condenser pressure on GOR. At feed mass1,816kg/h, increasing condenser pressure from 6.6 toincrease GOR by 1.2%. With increasing condenser pres-s that total distilled water decreases with a lower rateed steam and so increases GOR.

perating conditions of feed temperature 60 C, mass1,816kg/h, salt mass fraction 0.0206, steam tempera-and condenser pressure 7.4044kPa, the design data ofteam and GOR are 8429kg/h and 5.3, respectively. Ther (RE) between design data and predicted data for con-m and GOR are respectively 0.1% and 6.7%. Since in thelation, produced vapor in each effect has been calcu-ng trial and error method, then accumulated error forauses on considerable error between design data andata of GOR but it is good agreement with design data.

The(Eq. (11tial Simand comize othree vaway frthe centhe linwill godirectiand aued unshowsthe objture 60the rescondenquanti42,360

Conof evapstudiedof condenser pressure on consumed steam and produced distilledng conditions: Ts = 149 C, mf = 51,816kg/h, xf = 0.0206 and Tf = 60 C.

Fig. 10. Effecttion. Operating[12] method is used to optimize feed mass ow rateser pressure. In this method at each iteration, to maxi-ive function, objective function is evaluated at each ofes of the triangle. The direction of search is orientedhe point with the lowest value for the function throughof the simplex. By making the search direction bisect

ween the other two points of the triangle, the directionugh the centroid. Anewpoint is selected in this reectedhe objective function is then evaluated at the newpoint,search direction is calculated. This method is contin-e objective function is directed to the optimum. Fig. 10ffect of feed mass ow rate and condenser pressure one function. In the operating conditions of feed tempera-altmass fraction 0.0206, and steam temperature 149 C,are shown optimum values of feed mass ow rate andpressure are 51,408kg/h and 7.6 kPa, respectively. Theproduced distilled water at these optimized values is.ing thecontentsof thispaper, optimizedoperating timeion system of Fajr renery can be calculated. It can benges in transferred heat of evaporator surface (effect I)of feed mass ow rate and condenser pressure on the objective func-conditions: Ts = 149 C, xf = 0.0206 and Tf = 60 C.


Fig. 11. Transf

of Fajr rento operatinTransferredating time 6Fajr reneryit can expec

8. Conclus

This stution of a sifeed temperduced distiplays mostoptimizatiodenser pressystem; alsunit in this

The unstWith unsteoptimized t

Appendix A

A heBPE boE to

reH enk prm mP prq heQ hetb optc tim

(mT teU ov

orU5U1

x sa

Greek symbol latent heat (kJ/kg)

ptsbrwcococoevfeaefprstvaw

dix B

folloprop

orre

42.6

e P isa ranalculatur

10.17

1.7e P ie ca175tab

apor

2500

a raniquid

0.580erred heat of evaporator surface of rst effect vs. operating time.

ery (QE) according to Table 3 and Eq. (14), with respectg time tb. These changes have been shown in Fig. 11.heat from surfaces of evaporator is maximum in oper-.247 months. This means optimized operating time ofis 6.247 months or 187 days. By use of this condition,t maximum yield of distilled water.

ion

dy presents the steady-state simulation and optimiza-x-effect evaporator. The effect of feed mass ow rate,ature andcondenserpressureonconsumedsteam,pro-lled water and GOR was discussed. Feed temperatureimportant role in the evaporation plant. The results ofn show that feed mass ow rate 51,408kg/h and con-sure 7.6 kPa are optimized operating conditions for thiso optimized operating time for operation of vaporizingrenery is the period of 187 days.eady-state simulation is recommended for futurework.ady-state simulation, the economic inuence of theime of operation can be analyzed.

. Nomenclature

at-transfer area (m2)

SubscribbwccondcwefFTiPHsvw

Appen

Thenamic

The cby

T =(

wheroverthe c

The sP =

wherfor thof 10steam

The vH =with

The lH =iling point elevation (C)tal time for actual operation, emptying, cleaning andlling (month)thalpy of liquid and vapor phases (kJ/kg)ice of each kgass ow rate (kg/s)essure (kPa)at-transfer rate (W)at-transfer rate (J)erating time (month)e per cycle for emptying, cleaning and rechargingonth)mperature (C)erall heat-transfer coefcient (W/m2 C). (For evap-ators are U1 =3100, U2 =2900, U3 =2600, U4 =2400,= 1900 and U6 =1600W/m2 C and for pre-heater I is= 1500W/m2 C)lt mass fraction (%)

with a ran The laten

= 2589where T iover a temfor the ca

The enthaH = A + BA = (0.00B = 4.145C = 0.00D = (0.0E = (0.02

where T iover a temineater boiling temperaturendensatendenseroling wateraporatoredsh tankfect numbere-heatereamporater

. Model correlation

wing correlations are used to calculate the thermody-erties of saturated water and seawater.

lation for the water vapor saturation pressure is given

776 3892.7[ln(P/1000) 9.48654]

) 273.15 (19)

in kPa and T is in C. The above correlation is developedge of 10110 C with percentage errors less than 2% forated and the steam table values [13].ation temperature correlation is given by

246 0.6167302(T) + 1.832249 102(T)2

7376 104(T)3 + 1.47068 106(T)4 (20)s in kPa and T is in C. The above correlation is validlculated saturation temperature over a pressure range0kPa. The percentage errors for the calculated vs. thele values are less than 0.1% [13].enthalpy of pure water is given by

.152 + 1.947036(T) 1.945387 103(T)2 (21)ge of 0.01145 C and R2 =0.9999 [13].enthalpy of pure water is given by

2129 + 4.151904(T) + 3.536659 104(T)2 (22)ge of 0.01145 C and R2 =0.9999 [13].t heat correlation for the water vapor is

.583 + 0.9156T 4.8343 102T2 (23)s in C and is in kJ/kg. The above correlation is validperature range of 10140 C with errors less than 0.4%

lculated and the steam table values [13].lpy correlation for the aqueous sodium chloride is

T + CT2 + DT3 + ET405 + 0.0378X 0.3682X2 0.6529X3 + 2.89X4) 103 4.973X + 4.482X2 + 18.31X3 46.41X4

07 0.0059X + 0.0854X2 0.4951X3 + 0.8255X4048 + 0.0639X 0.714X2 + 3.273X3 4.85X4) 10302 0.2432X + 2.054X2 8.211X3 + 11.43X4) 106

(24)

s in C and H is in kJ/kg. The above correlation is validperature range of 0300 C and over a sodium chloride


mass fraction (X) range of 0.0060.26 with errors less than 0.08%[14].

The boiling point elevation correlation for the seawater isBPE = [565.757/T 9.81559 + 1.54739 ln T (337.178/T

6.41981 + 0.922743 ln T) A + (32.681/T 0.55368+0.079022 ln T) A2] [A/(266919.6/T2379.669/T + 0.334169)]

A = (19.819X)/(1 X)

(25)

where T is in degree K, X is the salt concentration, mass fraction,and BPE is the boiling point elevation in C [15].

In steadyoperationpractically all of theheat thatwasexpended increating vapor in the rst effectmust be given upwhen this samevapor condenses in the second effect. In ordinary practice theheating areas in all the effects of a multiple-effect evaporator areequal. Therefore, if boiling points elevation is neglected, the tem-perature drops in amultiple-effect evaporator are approximatelyinversely proportional to the heat-transfer coefcient. Thus,

Ti = (Ts Tcond)1/Ui6i=11/Ui

(26)

It is considerable that ash tank of each effect and heatexchanger of next effect have the same temperature.

References

[1] R.N. Lambert, D. Joyo, F.W. Koko, Design calculations for multiple-effect evap-orators 1. Linear method, Ind. Eng. Chem. Res. 26 (1987) 100104.

[2] A.M. El-Nashar, A. Qamhiyeh, Simulation of the performance of MES evap-orators under unsteady state operating conditions, Desalination 79 (1990)6583.

[3] S.M. Tonelli, J. Romangoli, A. Porras, Computer package for transientanalysis of industrial multiple-effect evaporators, J. Food Eng. 12 (1990)267281.

[4] W.T. Hanbury, Proc., IDA World Congress on Desalination and Water Sciences,vol. 4, Abu Dhabi, UAE, 1995, p. 375.

[5] M. Rosso, A. Beltramini, M. Mazzotti, A. Morbidelli, Modeling multistage ashdesalination plants, Desalination 108 (1996) 365.

[6] A.Husain,A.Woldai, A. Al-Radif, A. Kesou, R. Borsani,H. Sultan, P.B.Deshpandey,Modeling and simulation of a multistage ash desalination plant, Desalination97 (1994) 555.

[7] O.A. Hamed, Thermal assessment of a multiple effect boiling MEB desalinationsystem, Desalination 86 (1992) 325339.

[8] M.A. Darwish, Thermal analysis of multistage ash desalting systems, Desali-nation 85 (1991) 5979.

[9] K.A. Al-Shayji, S. Al-Wadyei, A. Elkamel, Modeling and optimizationof a multistage ash desalination process, Eng. Optim. 37 (6) (2005)591607.

[10] T.F. Edgar, D.M.Himmelblau, Optimization of Chemical Processes,McGraw-Hill,Inc., Singapore, 1989.

[11] Max S. Peters, Klaus D. Timmerhaus, Plant Design and Economicsfor Chemical Engineers, 2th edition, McGraw-Hill, Inc., Tokyo, Japan,1968.

[12] W. Spendley, G.R. Hext, F.R. Himsworth, Sequential application of simplexdesigns in optimization and evolutionary operation, Technometrics 4 (1962)441461.

[13] F. Mandani, H. Ettouney, H. El-Dessouky, LiBr-H2O absorption heat pumpfor single-effect evaporation desalination process, Desalination 128 (2000)161176.

[14] Benjamin S. Sparrow, Empirical equations for the thermodynamicproperties of aqueous sodium chloride, Desalination 159 (2003)161170.

[15] Narmine H. Aly, K. El-Fiqi, Thermal performance of seawater desalination sys-tems, Desalination 158 (2003) 127142.

Simulation and optimization of a six-effect evaporator in a desalination processIntroductionProcess descriptionProcess modelingHeat exchangerFlash tankPre-heater

Solution methodOptimizationOptimization of operating timeResults and discussionConclusionNomenclatureModel correlationReferences

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Khadem i 2009