Modelling Equations

III. Modelling Equations

( ∆′ ) The modeling of the study state operation of the unit is

∆′

(2) carried out based on the mass and energy conservation

The solar energy is converted into thermal energy and correlations. The latters are used to estimate the heat transferred to heating medium. The energy balance transfer coefficients and the thermodynamics properties, equation for the heating medium is given by the such as thermal capacity, viscosity and density of

equations, heat transfer

and

thermodynamics

following equation:

different streams. The resolution of the obtained model is

done using an iterative algorithm and Matlab

− (3) programming software.

This study takes into account the impact of design

where P loss is the lost thermal power to the ambient by parameters, including the evaporators’ tubes diameter

and length in addition to the operating parameters such as heat transfer through the piping system. the top brine and heating medium temperatures on the

unit performance. The model also considers the

III.1.2. Evaporators following assumptions: Salt concentration equals zero for produced distillated

III.1.2.1.  The First Effect water;

The mass balance equation for the first evaporator is  All the evaporators and the condenser are assumed

given by:

adiabatic

The condenser heat transfer equation is expressed by the following:

The thermal power of the heating medium is used to evaporate a portion of the feed seawater, thus, the energy

( ) (14) balance equation is expressed by the following equation:

III.2. − Heat Transfer Correlations , (5) The global heat transfer coefficient based on the outer where, the mass flow rate of produced distillated water is

surface of the tube is expressed by the following obtained by:

equation:

+ + (15) The required heat transfer area for the evaporator is

related to the power exchanged, the overall heat transfer In the MEE plant, there is a wide range of process coefficient and the log mean temperature difference using streams and operating conditions which make each heat the following relationship: transfer situations a unique one. Indeed, the global heat

( )= transfer coefficient U o − is related to five thermal heat

coefficients:

The convective heat transfer coefficients inside and where, the LMTD is defined as:

o , respectively;  The fouling resistances inside and outside tubes R fi − =(

outside tubes h and h

and R fo − , respectively;

 and the thermal conductivity of tube material k w . In this study, the total heat transfer area is taken as that

III.1.2.2. Effect 2, 3, and 4

in contact with the liquid flowing outside of the tubes. Kern [23] developed the following experimental

The mass balance equations obtained for the other correlations to calculate the convective heat transfer effects are similar to the first one; indeed, they are given

coefficient for liquid flowing inside tubes in the following expressions:

For Reynolds number less than 2000:

For Reynolds number less between 2000 and 10000: The heat balance equation is given by:

µ) The heat transfer equation is given by: (17)

where, . µ ∆T

is the temperature difference between the

condensing vapor and the boiling seawater. ⎝

For Reynolds number greater than 10000:

III.1.3. Last Condenser

An additional mass flow rate of cooling seawater M cw ℎ

µ µ (18) is added to the condenser to ensure the total condensation

= 0.023 µ

of vapor; in this case the last effect vapor’s latent heat of The correlations above are used to calculate the condensation is absorbed by the cooling water and feed convective heat transfer coefficient for hot water seawater. The energy balance equation for the condenser provided by a solar system, used as heating medium in is given by:

the first effect.

Boiling heat transfer coefficient for a thin film of =

seawater flowing over the outside of the vertical tubes seawater flowing over the outside of the vertical tubes

(24) Chung & Seban [26]:

∗ = 0,101

ℎ Fouling resistance can be expressed by the equation = 0,014

(25) vertical tubes falling film evaporators, it is valid when

The above correlation is used for seawater inside

the temperature of evaporated liquid is between 28 and

2 f (m is the asymptotic fouling thermal resistance K/W) and is expressed as: 21000.

where R *

100°C and for Reynolds number between 1600 and

For the horizontal tubes falling film evaporators, Mu and Shen correlation [27] calculate the boiling heat

(26) transfer coefficient for a thin film of seawater flowing

over the outside of horizontal tubes:

and t c is given by the expression below: = 0,0532

(27) with:

ℎ The fouling model above shows that the fouling

=4 and

resistance R

f is time dependent. However, under steady- state conditions and when t becomes greater than 3tc, we

This correlation is valid for Reynolds number between can make the approximation that R f ≈R * f . 163.86 and 826.32, and for Pr number between 2.97 and

III.3. Thermodynamic and Physical Proprieties inside vertical tubes is calculated using the laminar

A heat transfer coefficient for vapor condensation

III.3.1. Boiling Point Elevation theory:

The boiling point rises because of the salinity (BPE) = 0,925(

and the hydrostatic head:

Shen and Liu [28], [29] studied the condensation The boiling point rise because of the salinity (BPE) character of a stratified flow inside a horizontal tube and

can be expressed as a function of temperature and developed the following correlation:

concentration of salt [19]. Accordingly:

where A and B are temperature dependent constants, calculated by the following:

Thermal resistance R f is caused by the phenomenon of

material deposition from flowing seawater onto a heat

(31) exchanger, evaporator or condenser surface. The deposit

can reduce the thermal efficiency of the equipment by The values of the constants A i and B i are: imposing a resistance to heat transfer, because the deposit

material has a low thermal conductivity [20]. A fouling

= 0,0257 × 10 model was developed by Kern and Seaton [21], they

= 0,2009 × 10

= 0,0193 × 10 found that fouling is an extremely complex mechanism.

= 0,2867 × 10

Fundamentally, it may be characterized as an unsteady

= 0,0001 × 10 state momentum, mass and heat transfer problem. In desalination process, fouling has always been a

= 0,0020 × 10

where the concentration c is expressed by the chlorinity recognized phenomenon, although poorly understood.

factor and the temperature is expressed in (°C). Watkinson [22] reported the effect of fluid velocity and

the tube diameter on the asymptotic fouling thermal

III.3.2. Latent Heat of Evaporation resistance in the case of calcium carbonate scaling with

constant surface temperature and constant composition: The latent heat of evaporation (or condensation) of water can be expressed as a function of temperature by constant surface temperature and constant composition: The latent heat of evaporation (or condensation) of water can be expressed as a function of temperature by

= 2499,5698 − 2,204864 − 1,596 × 10

iterations methodology which is considered as a reliable convergent iterative procedure for resolving such system.

where T is the saturation temperature in °C and l is the The algorithm is composed of three parts. The first one is latent heat in kJ/kg.

dedicated for the four effects calculations with the assumption that the heat transfer area is equal in all the

III.3.3. Specific Thermal Capacity effects and assuming that low pressure steam is used as heating medium for the first effect. This part of the

The seawater specific heat at constant pressure is algorithm starts by introducing the design of the fixed given by the following correlation: parameters such as the mass flow rate of feed seawater

and the evaporation rate and changing parameters like =(

tubes dimensions and top brine temperature. Then the w

0 , α 1 , α 2 , α 3 constants, calculated by the following:

are salt concentration dependent here α overall heat transfer coefficients (OHTC) for the four

effects are estimated and the first iteration begins, then the heat transfer areas, the number of tubes and the mass

= 4206,8 − 6,6197 + 1,2288 × 10 flow rates of different streams are calculated. New heat transfer coefficients are obtained based on these values,

= − 1,1262 + 5,4178 × 10

− 2,2719 × 10

and then compared with the initial estimated heat transfer coefficients; if the error exceeds 0.1 %, the oldest values

= 1,2026 × 10 − 5,3566 × 10 + of the OHTC are replaced by the newest and the + 1,8906 × 10

calculation procedure is repeated until the error becomes less or equal to 0.1 % for all effects. After that, the

= 6,8777 × 10 + 1,517 × 10 + equality of the heat transfer area is checked; if the error is − 4,4268 × 10

greater than 0.1%, the temperature difference effect will be corrected by the ratio of the calculated heat ∆Ti in each This correlation is valid over salinity between 20000

transfer area and its average value for the four effects. and 160000 ppm and temperature ranges between 20 and Again, the calculation procedure is repeated till the 180°C. achievement of these two convergence conditions.

The second part of the algorithm depends on the

III.3.4. Seawater Dynamic Viscosity results obtained in the first one; it is used for the first effect correction because hot water is used as a heating

The dynamic viscosity of seawater is given by the medium instead of low pressure steam. It takes the mass correlation bellow:

flow rate of feed seawater, brine and distillate as input = 10

data and uses the same procedure in order to calculate the overall heat transfer coefficient and surface area and the

with: characteristics of the first effect. Finally, the third part deals with the condenser’s calculations.

V. Results of Evaporators and Condenser

Optimization and Sizing

= 1,474 × 10 + 1,5 × 10 + V.1. (37) Horizontal Tubes Falling Film Evaporators − (HTFFE) 3,927 × 10

V.1.1. First Effect = 1,073 × 10 − 8,5 × 10

+ 2,23 × 10 Figure 4 shows that the OHTC for the first effect decreases from 1.35 to 0.7kW/m 2 /°C when the diameter

where μ is in kg/(m s), T is in °C, and c is in gm/kg. of tubes increases from 20 to 40 mm. However, its value The above correlation is valid over salinity range

remains approximately constant towards the tubes’ length between 0 and 130 gm/kg and temperature range between

variation.

10 and 180 °C. This is so, because in the case of the first effect, the limiting factor for the heat transfer rate is the convective heat transfer coefficient in the side of the heating

IV. Computational Algorithm

medium flowing inside tubes. Thus, when the tubes’ diameter increases; the cross section area for heating

The developed model describing the system is medium increases, too as shown in Fig. 6 and then the composed of highly nonlinear equations. For this reason, specific mass flow rate decreases as presented in Fig. 5. there is need to use a powerful, but simple and

This his mean means mean s that that th t the R he Rey eynol olds s numb number umber fo r for or heatin heating eating leads lead eads to to red reduci ducing ing the the requir requir uired h d heat eat tran transfe nsfer area r area area by rea by abo about about mediu edium ium d um decreas ecreas reases, es, as as a fi a final nal res result, ult, the the co conve nvecti ctive tive heat eat

9 9 %. %. Th . The d diminis e dimi inishing hing of g of U1 f U1 wh when when T T s increased increas creased eased could ed could ld be be transfer transfe sfer in fer inside side tu de tubes bes falls falls dow falls do wn. expl ex plained ined b by the decr ed by t decrease he decr ease of e of th f the re e requ quired ired m d mass ass flow flow rate w rate rate Figure Figure re 7 shows that shows 7 sho ows that that when when en th the he heat eating ting m g medium edium edium

of h o f heat eating ing m medium edium dium w which ich red reduces reduces tur reduces turbulenc urbulenc ulence inside e insi de temper tem emperatu ature T re Ts i s incre ncreases ases b ses by about y abou about 1 ut 10°C, °C, th C, the o he over verall all heat heat

tubes tu bes. Al . Also Also, o, Fig ig. 8 show 8 show ows that hat the that the red redu eductio uction of n of he f the transfe transfer sfer co fer coeffi efficien ficient nt dec declines by ecline s by ab y abou about 2 20% 0%. H . Howev wever, as wever, er, as

req required requ red h heat eat transf transf transfer er area area area cou could ld als also be be done be done by e by shown show wn in in Fig Fig. 9 t the log 9 the log mean means eans tem temperat emperatu perature re LMTD LMTD TD has an TD has has an

reducing red redu cing th the to he top brin op brin brine tem e tempera emperat erature ature T T 1 and increa an nd increa increasing creasing g the he oppo opposit osite b e beh ehavio vior t or towards owards ards T T s chan chan ange; e; ind indeed eed w d with ith the the

h heati eating ng med mediu dium tem temperature emperature tak tem peratur aking i e taking ng into nto accoun accoun ccount foul t foulin uling ng sam same chan ame chan change of T ge of s , LM ,L LMTD TD increas increase creases es by by abo about 36 about 36 %. 6 %. A . As a sa

ri risks sks.

conseq consequence, sequen equence, the pro ce, th e product roduct oduct U U1.LM 1.LMT MTD increas ncreases D increas es whi which hich

Fig. ig. 3. C . Comp mputat utationa onal Alg l Algorith orithm m

Fig. ig. 4. H . HTFF FFE- U U 1 vs T vs Tub ubes d s diame meter a er and le d length ngth Fig. 5 Fig . 5. HT TFFE FE- Gv Gvvs T s Tube bes dia s diamet eter an r and le length gth Fig. ig. 4. H . HTFF FFE- U U 1 vs T vs Tub ubes d s diame meter a er and le d length ngth Fig. 5 Fig . 5. HT TFFE FE- Gv Gvvs T s Tube bes dia s diamet eter an r and le length gth

The Th erform e perfo rformance ance rati ance ratio P PR d does oes no not ch t chan hange according e accordi rding ng to th to the co e cons nsider dered parameter ed para meters meters an and i d its v s value alue is is nearl nearly abo nearly about out

3 3.89 .89. Th . This i is is b is because ecause ause PR PR depen depen ends s ds stro trongl ngly o y on the n the num the num mber er of effect o effects wh effect which which is ich is ke is kept constant pt cons constan tant in t in thi this st s study. dy.

V.2. V.2. V.2 Ver Vert ertica rtical Falling l Fallin alling F ng Film Eva ng Film m Evapo vaporat orators tors (VT s (VTFFE) FFE) E) The Th case e cas ase of of using using ver using g vert ertical ical t tubes bes es fallin falling alling film film lm

evap ev aporat orators tors is al s is also also studie lso studied udied i ed in th the sa e same ma me ma mann nner. ner.

Fig ig. 6. H HTFFE- 6. HTF - First irst effe effect C ct Cross Cross sec section tion area rea vs T s Tube bes dia s diamet meter an r and le d length gth

Fig. 9 F . 9. HT HTFFE FE- Fi First e irst effect fect LMTD LMTD TD vs T sT S and T an 1 1

Fig. ig. 7. HT . HTFF FFE- U U 1 vs T vs T S and T a dT 1

Fig. 10 Fig HTFFE 10. HT FE- U U 3 vs T s Tube ubes dia s diamet eter a r and le d length gth

Acco Acco According Accordin ing to to Fig. ig. 11, , the 11, the first ef he firs t effect fect ha ct has has the the sam same ame reaction react react ion to on to tub tubes tubes dim dimensio ensions ions v s vari ariatio ation c n com ompared pared ared to to the he cas case case o of u of using using ng horizon horizont rizontal tal fal falli falling ng fil film evaporators. evaporato evapora rators. rs. Whereas Whereas Whereas, t W , the the obta obtained ined results results ed resu ults for for the the re e remainin mainin aining effe effects g effec ts show s ow th ow that hat for or tube tubes’ s’ diam diamet ameter g er growt rowth wth from from 20 m 20 t 20 to 40 o 40 m mm, 0 mm, Fig. ig. 8. HT . HTFF FFE- A A 1 vs T vs T S and T a dT 1 th the ov overall e ove rall hea heat tra t transf transfer nsfer coef coeffi efficient cient in nt increas ncreases eases w es with ith abou about ut

6 6%, %, also also, wh , whe when tu en tubes bes leng length gth decre decreases h decrea eases from s from m 4 to to 3m, 4 to 3m m, the he

V.1 V.1.2. .2. Effect N Effect Ef ect Num umber ber i=2 i=2, 3 , 3, an , and 4 d4 OHTC OHTC i OHTC increas O ncreas reases w es with with about ith about ut 4.5 4.5%. %. Th Thes ese res results e resul ults also also prov prove rove th e that at the the us the use of se of hor of hori horizonta zontal l

The secon he seco econd, the th d, the third third and and the the fourth e fou rth effect effect effects s ts show how fallin fal falling fi film ev g film evaporato aporato porators rs allo allows ows heat heat trans heat t transfer coef transfer er coefficie coefficien cients ents similar sim milar beh behav behavior ior toward towards ards th rds the tube e tubes ubes d es dimen imensi ensions variati ensions ons va ariation iation.

valu v alues, es, wh which ich are are h re higher gher t er than han thos hose of those of vertica vertica vertical fall l fallin falling ng Fig. ig. 10 10 0 demo emon monstra strates tes that that the that the o overal erall rall heat heat t at transf transfer ansfer

film fi lm ev evapo aporat orators. ors. T They hey ar are between e bet ween en 3.18 3.18 18 and nd 3. 3.32 .32 coeffici coeffi cien cient (OHTC) (OHTC (OHT HTC) depe depends depe nds s sligh lightly tly o y on the tubes he tub es’

k kW/ W/m 2 / /K K for for horiz horizonta horizontal ontal f al falli alling film ev g film evaporat evaporators aporators orators an rs and and diamet diam ameter; er; it i it is decreas decreas creases eases by ses by abou about out on only ly 1 % 1 % wh when tube when n tubes tubes’

ran rang range bet e betw etween 2.15 etween n 2.15 a 15 and nd 2.4 kW/m 2.4 kW/ 2.4 kW/m 2 /K for vertical /K /K for vertica vertical rtical falling falling ng diam diamet ameter ri er rises rises fro from om 20 to 40 20 to 4 mm mm. O m. On th the o other han e other r hand, hand, the the

film evapo fi lm evap evaporat aporato rators ( rs (Fig. ig. 12). 12).

OHT HTC TC ex expand pands nds wi with abou with about bout 4% 4% when 4% w en tu ubes le tubes s length length is gth is

highe

Typ Feed Prod Reje Tem Press Ui ( Hea Exte Len Numb Mat Diame Len Mat

ype eed sea roduce

ejected empera

ressure Ui (kW/ Heat tra

xternal ength o

Number aterial Diamete ength o aterial

Mass Flow

(kg/s) 1.371

V.3.

he res est p

Desi seawat

ced fre ted brin erature

ure insid W/m2/

t transfe nal dia th of tu ber of t rial (se

eter of sh th of sh rial (se

V.3. result

possi

esign c ater Fi

fresh w brine Bi ure insid

inside e 2/°C) sfer are diamete

f tubes L f tubes (see ap of shell

f shell (see ap

Cold stre In Temp (°

11. V

12. V

Reco ults sh

ssible

n chara r Fi (kg

sh water e Bi ( inside e e effec

area Ai eter (in es L (m bes Nt

append shell (m ll (m) append

stream (Mf Inlet mperat (°C)

Recommen show

ble he

aracteristic (kg/s)

ater Di i (kg/s e effec ffect Pi

Ai (m2 (inche

L (m)

endix) (m)

ommended ow th

heati

teristic

r Di (kg g/s) ffect Ti (° Pi (kP

(m2) hes)

U1vs T

U 3 vs T

ended how that

ating

stics

(kg/s) Ti (°C

(kPa)

+ Mcw) Ou Temp

(°C

U1vs Tub

vs Tub

commended D that it is

ng mediu

(°C)

w) Outlet mperatu

s Tubes d

ubes d

ded Design

it is recom

edium

R ECOMME

let rature

M. Gh

es diam

s diam

esign fo

recommen ium t

M. Ghazi

iameter

iameter

n for Eva recommen

um temp

Ho Mass Flow

(kg/s) 0.0534

azi, E.

ter and

ter and

r Evap mmend

emperat

DED D

1 st effe FF evap

R E Hot stre

nd leng

nd leng

D ESIG effect vapora

on stee

orator ded to

ature an

SIGN A

OMMEN m (V4

erature (°C)

iqi, M.

M. Mada,

Mada, M

at effi

u co

TABLE I

TABLE III

lowes the re benefi instea valu

Bas fallin desal and select

In energ system

Feed

be h order t

Co need to at for each using redu is nece use h shoul

Mo at th

In effici used cons

BLE II

IMENS

2 d effe FF evap

west p

e requ enefici stead alues o

Based falling

esalinat

d sizi elected

In th ergy stem

VI

Feed

e heated rder to Conv eeds to attain r each sing mo reduce

neces se hot

ould u

Moreo the lo In thi

efficient sed t

nsump

NSION

effect vaporat

inium .518 4.2 on stee

T HE C Tube

Outsi diam

(inch 1”1

. Faqir,

est poss required

eneficial t

ead of

es of h Based on

g film ination

izing ected an

the n y integ em and

VI. Feed seawat

eated t rder to beg

nvers s to be tain thi

each st

more

ce both necessary

ot streams ould use mu

Moreover,

e lowes

this cient m

to umptio

IONS F O

C OND Tubes ch

utside iameter (inches)

1”1/4

a, M. Faqir, A.

ossible t quired heat

al to us

of the of heat t

on thi film ation u

ng of

d and pres

next ntegra and heat

He

seawa

ed to th o begin ev

ersely,

be co this res strea

ore heat

oth en

ry to tream se much

eover, owest po

is part

metho

comb tion a

OR T

NDENS

charac de

ter es)

A. Ben

ible top

heat o use

the verti eat transfer n this, it

evaporat unit. of the

d presente ext part, egration

heat exch

Heat Exc

awater to the satu

gin evapor onversely, a rejec

cooled is result, tream in

e heat

h energy y to des eams to

much less er, the st poss part, P

ethod for

combine on and

T HE E

NSER racterist

e top br heat tran

use the

he vertical transfer this, it has

evaporator nit. Th the fou

resente

part, thes ion usi

at exch

eat Exch

eawater is su

he satu evapor

a rejecte oled do result,

in the heat ene

nergy cons to design

s to he uch less

the heat possible rt, Pinch

hod for

bine and the

E VAPO

HF

eristics Nt

abdella

top brine

transfer

the horizontal vertical ansfer coeff

it has been aporator

The opt four effec sented in

rt, thes on using

exchangers

t Exch

Usin

is supplied saturation vaporation.

rejected led down

sult, heaters

in the

energy rgy consu design a

to heat cold

less energy

heat exch ible cost.

nch analy for heat bine betw

the cost

ine tem sfer are

horizo cal config

coeffic has been orator type

e opti r effect

d in Table these resu using pinc

angers

Exchan

Using P

supplie

ration ation.

ejected brin

wn to heaters the pro

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n a hea

at cold

energy heat exchanger

e cost. nch analys

heat in

betw cost of

RATOR

3 d effe HFF evap

e temperat fer area o

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config efficien

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type ptimal effects

ables

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lied to on temp

n.

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ld stream ergy to

chang

alysis eat integ

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t of the h

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sugges pe wi mal charac and ables II an results wi

ch ana netwo

nger N Pinch A

d to th temperat

rine and

a lower and c

process. Ho and more mption t recovery streams

to preheat anger

sis wh ntegrati ween mi of the heat

perature i

f the fi al fallin uration ent of th gested will charact and the

II and ts will analys work o

r Netw nch An

the effect mperatu

and pr wer temp

d cool . Howev more h n and recovery reams, an

preheat er netwo

which ration mini

he heat ex

Leng (m

re in o

e first lling f ion, du

f the fo gested th ill be haracteri the la

I and III. will be lysis f work opti

etwor Analys

e effect rature o

produ er temper oolers Howev heat and inv recovery sys s, and eheat feed etwork

ich c on and minimizi

e heat exchan

Shell Length

(m) 4.2

in order irst effect.

g film , due

he form that th

be use cteristics

e last conde

d III. l be com is for heat ptimizatio

ork alysis

ffects re of each

oduced mperature.

lers shou owever, eat exchangers. investm system nd the t feed

ork m

h cons and optim imizing xchanger

HF

hell ch D

order to effect. ilm evapor ue to

former. t the hor used

ristics t conden

combined or heat izatio

rk Design lysis

cts and of each

uced fresh perature. should er, this exchang investme stem in then the

eed seaw rk must

considered

d optim zing anger

charac D (m)

er to decrea fect. It

evaporato to the er.

e horiz used for acteristics of design condenser

bined heat recove ization.

Design

and ne each effect

fresh ature. In hould be

this leads exchangers. stment cost in order then the proce seawater. ust be

idered optimization ng the

nger netw

th effec evapo

40 7.23 3.208 5.5 1”1/4 3.5 16

Aluminiu 0.518 4.2 rbon st

racterist m)

to decrease It is a evaporator the hig

horizontal for this of desi ndenser

bined w eat recover

esign

nd needs

ch effect fresh water

ure. In orde ld be us leads hangers. nt cost, in order the process ater. ust be done

dered as ization

he he etwork.

ffect porato 36

ristics Mate Carb

ste

ecrease s also rators

e high zontal

r this esign er are

ed with covery

ign

eds to effect in

water order

e used eads to angers. To cost, it rder to

rocess

be done as an

ion is heat work.

rator

Material Carbon

steel

rease so rs

gh tal

is gn are

with ery

to in

water er

ed to To it er to cess

ne an

is at rk.

rial n

In other words, the objective is to minimize the total in heat exchangers, giving increased capital cost. Indeed, cost. In this section, pinch analysis and its methodology

the partial flows of reject brine, produced distilled water, is used to identify the optimal heat exchanger network

and feed seawater could be mixed in a different manner for the present seawater desalination unit, the

which gives three possible configurations of streams as methodology is in four steps.

shown in Figs. 13 and Tables IV, V and VI. First step is extracting stream data from process flow- sheet. Second step is selecting the minimum temperature difference values

VI.2. ∆T The Minimum Temperature Difference min . Third step is sizing and ∆T min

designing the heat exchangers and finally the fourth step Lower values of ∆T min give lower hot and cold utilities is the selection of the optimal design which allows the

but larger and more costly heat exchangers; this is so minimum total cost.

because the heat transfer area needed is inversely proportional to the temperature difference. So, small

VI.1. Stream Data Extraction for three Possible values of ∆T min can lead to very large heat exchangers.

The cost of thermal heat required for feed sweater Configurations heating is proportional to energy usage which decreases

Mixing can cause problems in stream data extraction. when ∆T min becomes smaller. If we sum the operating Process streams of the same composition leaving each

and capital cost, the total cost (annualized heat cost and effect at different temperatures could be mixed and

capital costs) passes through a minimum value which considered as one stream, and then, the heating could be

corresponds to the optimal ∆T min [30]. In this study we performed by single heat exchanger. However, mixing

have considered five values of which are: 2, 4, 6, 8, and will degrade temperatures and reduce the driving forces

10°C.

Figs. 13. Three possible configurations for streams mixing (configurations 1, 2 and 3)

TABLE IV

TABLE VII

P LATE H EAT E XCHANGER C HARACTERISTICS Stream

S TREAMS D ATA F OR C ONFIGURATION (1)

Nature of

b(m) Area per plate (m 2 ) stream

0,004 0,88 F1 Cold Stream

(kg/s)

(kW/K)

F2 Cold Stream 0.2181

35 50 13.53 For the plate heat exchangers, heat transfer rate can be F4 Cold Stream

F3 Cold Stream 0.2158

35 40 4.46 evaluated based on the correlations of the most widely B1 Hot stream

70 30 23.21 used plates for the turbulent flow [34]: B2 Hot stream

(µ/µ) , (39) B4 Hot stream

B3 Hot stream 0.1554

60 30 6.38 where the Reynolds number Re is based on equivalent D3 Hot stream

D1 Hot stream 0.0617

D2 Hot stream 0.0611

50 30 3.78 diameter, D e , defined by:

D4 Hot stream 0.0598

TABLE V

S TREAMS D ATA F OR C ONFIGURATION (3)

Stream Nature of M

CP

Tf

stream (kg/s)

(kW/K)

Ti (°C)

(°C)

Q (kW)

For laminar flow:

Mf1 Cold Stream 0.4384

Mf2 Cold Stream 0.4294

Md1 , Hot stream 0.1228 0,5133 65 35 15.39 = ( ) (µ/µ) (41) Md2

Hot stream 0.1202

Mb1 Hot stream 0.3157

Mb2 Hot stream 0.3092

45 35 12.92 where c 1 = 1.86-4.50 depending on geometry, and L is the effective plate length. TABLE VI

S TREAMS D ATA F OR C ONFIGURATION (2)

Stream Nature of M

VI.4. Case study: Configuration C & ∆T min =2°C stream

(kg/s)

(kW/K)

It is recalled that the pinch analysis is applied for three Md

Mf Cold stream 0.868

55 35 20.3 different configurations (1, 2, and 3) with five different Mb

Hot stream 0.243

Hot stream 0.625

55 35 52.2 values of ∆T

min (2, 4, 6, 8 and 10°C), which means fifteen cases. Configuration 2 and a minimum temperature

VI.3. Heat Exchangers Selection and Sizing difference of 2°C are selected in this case study. It is of great importance to make appropriate choices

when it comes to heat exchanger types and material to

VI.4.1. Shifted Temperatures ensure proper operation to avoid, as much as possible,

The shifted temperatures are set at 1 ⁄2×∆T min above problems that may limit the heat exchanger and heat

cold stream temperatures and 1 ⁄2×∆T min below hot stream recovery efficiency.

temperatures. They are used to ensure that the The choice of the suitable type of heat exchanger

temperature differences between hot streams and cold depends on several parameters, essentially, cost, heat

streams are equal to or greater than ΔT min . Data for transfer coefficient, and maintenance. It was found out

shifted temperatures for this case study are shown in that the most suitable type of heat exchanger for our plant

Table VIII.

is the plate type heat exchanger; its characteristics are TABLE VIII shown in Fig. 14 and Table VII.

T ARGET A ND S HIFTED T EMPERATURES

Stream data

Target temperatures Shifted

temperatures

Stream

Nature of

Ti (°C)

(°C) (°C) T*f (°C)

Cold stream

Md

Hot stream

Mb

Hot stream

VI.4.2. Temperature Intervals Figure 15 shows that streams’ data are divided into

three temperature intervals (I, II, and III), each interval represents a sub-network. And each interval is defined by

a process stream supply and target temperature. For each sub-network, there is either a net heat deficit or surplus, Fig. 14. Plate dimensions–Plate heat exchanger

but never both. As a sign convention, a heat deficit is

considered negative and a heat surplus is considered positive.

depending on the minimum temperature difference ∆T min for the three configurations 1, 2 and 3, it is known that the optimal value of ∆T min is approximately equal to 6°C as shown in Figs.18, 19 and 20.

VI.5.2. Optimal Design of the Heat Exchanger Network Fig. 15. Temperatures intervals - configuration c, ∆T min =2°C

It is obvious from Fig. 21 that the configuration 2 is the most advantageous compared to configuration 1 and

VI.4.3. Problem Table Cascade 3; consequently, the configuration 2 was selected to be used for the final design of heat exchanger network. In

In the problem table cascade the heat input from this case the total cost passes through a minimum value external utility is assumed equal to zero and the heat

of 14000 US Dollar which corresponds to ∆T min =6°C. surplus from higher temperature interval can be used to

make up for heat deficit of lower temperature intervals. For each sub-network the output is calculated by adding the surplus to the input, the calculation of heat in this manner is shown in Fig. 16.

In order to have a feasible configuration, the transmission of heat from high temperature interval to low temperature interval must be positive. Therefore, if negative values are obtained, the external hot utility must

be increased from zero to a minimum positive value in order to make all heat flows positive or equal to zero. In addition to this, the minimum cold utility is equal to the

heat flow out of the coldest sub-network.

Fig. 17. Grid diagram - configuration c, ∆T min =2°C

Fig. 16. Problem table cascade - configuration c, ∆T min =2°C

VI.4.4. Grid Diagram

Fig. 18. Variation of different costs vs ∆T min for configuration (1) In the grid diagram representation, as shown in Fig.

17, hot streams (rejected brine and distillate) are represented at the top of their supply temperatures on the left side to target temperatures on the right side.

Cold stream (feed seawater)is represented below hot streams and it runs in countercurrent direction. Also, in the grid diagram, the heat exchanger network is constructed according to [30].

VI.5. Results and Discussion for Heat Exchanger Network Design Using Pinch Analysis

VI.5.1. Determination of the Optimal ∆T min From the graphical representation of the annualized

hot utility cost, the investment cost and the total cost

Fig. 19. Variation of different costs vs ∆T min for configuration (2) Fig. 19. Variation of different costs vs ∆T min for configuration (2)

The total heat consumption of this pilot unit is about 158 kW, the last condenser is used to condense the steam of the last effect (effect 4), and also it’s used to preheat feed seawater from 20°C to 35°C. The heat recovered using the condenser is about 54.42 kW. The feed seawater is heated from 35°C to 49°C using the heat recovery heat exchangers (1) and (2).

TABLE IX N UMERICAL R ESULTS O F H EAT E XCHANGERS S IZING

Heat exchanger

Thermal power

Required total Number of

(kW)

area (m2) plates

0,741 9 Fig. 20. Variation of different costs vs ∆T min for the configuration (3)