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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.
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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.
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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
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342 M.H. Khademi et al. / Chemical Engineering and Processing 48
(2009) 339347
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
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M.H. Khademi et al. / Chemical Engineering and Processing 48
(2009) 339347 343
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
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344 M.H. Khademi et al. / Chemical Engineering and Processing 48
(2009) 339347
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.
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M.H. Khademi et al. / Chemical Engineering and Processing 48
(2009) 339347 345
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.
-
346 M.H. Khademi et al. / Chemical Engineering and Processing 48
(2009) 339347
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
-
M.H. Khademi et al. / Chemical Engineering and Processing 48
(2009) 339347 347
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
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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