Received: 22 October 2016
| Revised: 19 July 2017 | Accepted: 3 August 2017
DOI: 10.1111/jfpe.12616
ORIGINAL ARTICLE
Determination of optimum vapor bleeding arrangements for sugar juice evaporation process S. Chantasiriwan Faculty of Engineering, Thammasat University, Pathum Thani 12121, Mail,
Abstract
Thailand
The sugar juice evaporation process consists of juice heater, evaporator, and crystallizer. The juice heater increases the temperature of diluted sugar juice from the ambient temperature to the boiling
Correspondence
S. Chantasiriwan, Faculty of Engineering,
point. The evaporator removes most water content of diluted sugar juice. The crystallizer removes
Thammasat University, Pathum Thani
the remaining water content, yielding raw sugar as the final product. Since both the juice heater and
12121, Mail, Thailan Thailand. d.
thecrystall thecryst allize izerr req requir uire e vap vapor or ble bled d fro from m theevapo theevaporat rator,thereare or,thereare int intera eracti ctionsbetw onsbetween een thethreecom-
Email:
[email protected]
ponents. A model of interactions between the three components of the sugar juice evaporation proces pro cesss is pre presen sented ted in thi thiss pap paper. er. The mo model del yie yields lds a sys system tem of non nonlin linear ear equ equati ations ons tha that, t, und under er som some e specified speci fied assumpti assumptions ons and cond conditio itions, ns, consists consists of only two free para paramete meters. rs. This implies implies that there there is a uni uniquedistr quedistribu ibutio tion n of a giv given en tot total al jui juice ce hea heater ter sur surfac face e whe when n vap vapor or is ble bled d fro from m the fir first st twoeffec twoeffects ts of th the e ev evap apor orat ator or.. In co cont ntra rast st,, if va vapo porr is bl bled ed fr from om th the e fi firs rstt th thre ree e or fo four ur ef effe fect cts, s, th ther ere e ar are e ma many ny po posssible surface distributions. It is shown that there is an optimum surface distribution when vapor is bled from either the first three or four effects of the evaporator that minimizes the steam economy. The optimum four-effect vapor bleeding arrangement results in the largest steam economy. However, eve r, the tw two-e o-effe ffect ct vap vapor or ble bleedi eding ng arr arrang angeme ement nt pro produc duces es a lar larger ger mas masss flo flow w rat rate e of pro proces cessed sed sug sugar ar juice juic e than eith either er thre three-eff e-effect ect vapo vaporr blee bleeding ding arra arrangem ngement ent or four four-effe -effect ct vapor bleed bleeding ing arran arrangeme gement. nt.
Practical applications Thiss pap Thi paper er pre presen sents ts a mat mathem hemati atical cal mo model del of a sug sugar ar jui juice ce eva evapor porati ation on pro proces cess. s. Alt Altho houghone ughone spe specif cific ic proces pro cesss des design ign is und under er con consid sidera eratio tion, n, the mo model del can eas easily ily be adj adjuste usted d fora dif differ feren entt pro proces cesss des design ign.. Thiss mo Thi model del wi willll be use useful ful foranaly foranalysis sis andoptim andoptimiza izatio tion n of theproce theprocess. ss. Oneopti Oneoptimiz mizati ation on pro proble blem m men men-tioned tio ned in the pap paper er is the opt optimu imum m all alloc ocati ation on of a fix fixed ed to total tal sur surfac face e amo among ng the fou fourr he heat at exc exchan hangers gers of the juice heater, which is used to increase juice temperature to the boiling point before entering the quintuple-effect evaporator. It is found that there are two different optimum surface allocations corresponding to the maximum rate of processed juice and the minimum amount of steam required by the proc process. ess. Resul Results ts of this paper paper shoul should d provide provide a guideline guideline to a process process designer designer in in selecting selecting the the juice juic e heate heaterr that will both satis satisfy fy the requ required ired heati heating ng duty and yield the optim optimum um perfo performan rmance. ce.
1 | INTRODUCTION
Jafarian, Asgari, & Kouhikamali, 2014). An important characteristic of multipl mul tiple-ef e-effec fectt eva evapor porato atorr is the mon monoto otonic nic red reduct uction ion of vap vapor or pre pressu ssure re
Evaporation is an important unit operation in many industrial processes.
from the first effect to the last effect. A supply of low-pressure steam is
These processes processes make use of multip multiple-effec le-effectt evapor evaporators ators to remov remove e
required for the first effect. Vapor produced by an effect is used for
water wat er fro from m dil dilute uted d sol solutio utions ns suc such h as bla black ck liqu liquor or (Jy (Jyoti oti & Kha Khanam, nam,
evapor eva porati ation on in succ succeed eeding ing effe effect ct exc except ept the last effe effect. ct.
2014; Khanam & Mohanty, 2010), milk (Galvan-Angeles, Diaz-Ovalle,
Multiple-effect evaporator is one of the three components of the
Gonzal Gon zaleses-Alat Alatorr orre, e, Cas Castre trejon jon-Go -Gonza nzales les,, & Vaz Vazque ques-Ro s-Roman man,, 2015 2015;;
juice juic e evapo evaporatio ration n proc process ess in raw sugar manuf manufactur acturing. ing. The othe otherr two
Ribeiro & Andrade, 2003), tomato juice (Simpson, Almonacid, Lopez, &
components are juice heater and crystallizer. The juice heater is used to
Abakar Aba karov, ov, 2008 2008;; Sog Sogut, ut, Ilte Ilten, n, & Okt Oktay, ay, 2010 2010), ), ora orange nge jui juice ce (Bal (Balkan, kan, Colak, & Hepbasli, 2005), sugar juice (Bapat, Majali, & Ravindranath,
raise the temperature of incoming juice to the boiling point before the juice juic e is sent to the evapo evaporato rator. r. The crysta crystallize llizerr is used to evaporate evaporate the
2013), 2013 ), and sea wate waterr (Pia (Piacen centin tino o & Car Cardon dona, a, 2010 2010;; Sagh Saghari arichi chiha, ha,
remaining water content of concentrated juice leaving the evaporator.
J Food Process Eng . 2017;e12616. https://doi.org/10.1111/jfpe.12616
wileyonlinelibrary.com/journal/jfpe
C 2017 Wiley Periodicals, V Periodicals, Inc.
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CHANTASIRIWAN
The output of the crystallizer crystallizer is raw sugar. The evapo evaporatio ration n proc process ess
given give n tota totall juic juice e heat heater er surf surface ace can be dist distribu ributed ted among the heat
requires a supply of low-pressure steam that is either exhausted from a
exchangers so that the process performance is optimized. The following
back-pres back -pressure sure steam turb turbine ine or extracted extracted from an extr extracti action-co on-condens ndensing ing
sections present the detailed description of the evaporation process, the
steam turbine (Chantasiriwan, 2016). The low-pressure steam is used as
math ma thema emati tical cal mo mode dell of th the e pro proce cess, ss, th the e me meth thod od use used d to op opti timi mize ze th the e pr proo-
the heating medium for the evaporator. The heating medium for both
cess perf perform ormanc ance, e, sim simulat ulation ion res results ults,, disc discussi ussion, on, and con conclus clusion ions. s.
the jui juice ce he heate aterr and the cry crysta stalli llize zerr is vap vapor or ble bled d fro from m the eva evapor porato ator. r. The juice evapor evaporation ation process process is a major thermal energy consumer
2 | EVAPORATION PROCESS
in raw sugar manufacturing process. Previous suggestions to improve the process performance have mostly focused on the multiple-effect
The Th e sc sche hema mati ticc of a su sugar gar ju juic ice e ev evapo apora rati tion on pr proc oces esss th that at us uses es
evaporator. They include adding more effects or more heating surface areas (Urbaniec, Zalewski, & Zhu, 2000) and selecting the optimum dis-
quintuple-effect quintuple-effe ct evaporator is shown in Figure 1. The juice heater consists sis ts of five tub tubula ularr hea heatt exch exchang angers ers (HC, H1, H2, H3, and H4). It
tribution of evaporator surface (Chantasiriwan, 2015). In addition, the
receives diluted juice at the flow rate of m f,in from the juice extraction
process performance can be enhanced by optimal operation scheduling
process. After passing successively through H4, H3, H2, and H1, the
of the evapo evaporator rator (Heluane, Colombo, Colombo, Herna Hernandez, ndez, Graells, & Puigja Puigjaner, ner,
juice temperature temperature increases from T h,4 h,4 to T h,0 h,0. The juice pressure at the
2007)) and usi 2007 using ng the opt optimu imum m tub tube e dim dimens ension ionss for the eva evapor porato atorr
exit of the juice heater is slightly above the atmospheric pressure. After
(Thaval, Broadfoot, Kent, & Rackemann, 2016).
passing through FC, dissolved gases in the juice are removed, and its
For many sugar factories, the modification of multiple-effect evapo-
pressure pressu re is equal to the atmospheric atmospheric pressure. Before entering the first
ratorr to opt rato optimiz imize e the juice evap evapora oratio tion n pro proces cesss is not a viab viable le opt option ion
effect of the evaporator, the juice pressure is raised to the pressure in
because of the required investment may be unafford unaffordable. able. Modification Modification of
the first effect (p1), and its temperature is raised to the boiling point in
juice jui ce heat heater, er, whi which ch is ano anothe therr com compon ponent ent of the juice evap evapora oratio tion n pro pro--
HC using low-pressure steam as the heating medium.
cess, is an alternative method to improve the process performance. Juice
Low-pressure steam from steam turbine at p 0 is used as the driving
heater consists of heat exchangers, in which sugar juice temperature is
steam for the quintuple-effect evaporator. The thermal energy released
raised from a low temperature to the boiling point before it is fed to the
by the condensation of the driving steam results in the evaporation of
first fir st eff effec ectt of theevap theevapor orat ator or.. Th The e he heat ating ing me medi dium um forjuic forjuice e he heate aterr is vap vapor or
water in sugar juice at a lower pressure ( p1) in the first effect (E1). The
bled from the evaporator. A typical sugar factory uses quintuple-effect
vapor leaving all effects except the last one (E5) is used to evaporate
evaporator, and bled vapor is available from the first four effects, which
water wat er in su sugar gar jui juice ce in the suc succe ceedi eding ng eff effect ect.. Th The e arr arrang angem ement ent in Fi Figur gure e1
can be used for the four heat exchangers of the juice heater. Obviously,
makes use of full condensate flash recovery in order to improve the effi-
the distribution of heat transfer area among the heat exchangers affects
ciency of the evaporator. A flash tank is placed after each effect except
the process performance. Previously, Ensinas, Nebra, Lozano, and Serra
the last one. F1 receives condensate from the first effect at pressure p 0
(2007) (200 7) con conside sidered red a method method of dete determin rmining ing the opt optimu imum m jui juice ce heat heater er and
to pro produc duce e vapo vaporr and con condens densate ate at pressu pressure re p1. Con Conde densa nsate te at p1 is also
evaporator surface distributions that minimize the total cost of a sugar
produced in E1 and H1. F2 uses all condensate to produce vapor and
plant. This method is suitable for the design of a new sugar plant. For an
condensate at pressure p2. Similarly, F3 and F4 receive condensate from
existing exis ting plan plant, t, how however ever,, the surf surface ace dist distrib ributio ution n of the evap evapora orator tor is
three th ree sou sourc rces. es. Th The e con conde densa nsate te lea leavin ving g F4 is col collec lecte ted d in a sto storag rage e ta tank. nk.
known, kno wn, and the opt optimu imum m vapo vaporr blee bleeding ding arr arrange angemen mentt sur surface face dist distrib ributi ution on
Vapor is bled from all effects of the evaporator except the last
is to be determined. In this article, an investigation is made into how a
one. Vapor bled from the first, second, third, and fourth effects are
F I G U R E 1 Schemat Schematic ic representation representation of the system
CHANTASIRIWAN
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used to increa increase se juice tempe temperatur rature e in H1, H2, H3, and H4, respectively. respectively. Additional vapor is bled from the first effect, and used in the crystallizer (C) to evaporate the water content in the concentrated juice leaving the evaporator. The output of the crystallizer is raw sugar.
mf;i x i 5mf;in x in in
(10)
It should be noted that boiling temperature temperature rise due to hydros hydrostatic tatic pressu pre ssure re head is not taken into account account in thi thiss mod model el bec because ause the evaporator is assumed to be of a design in which the effect of hydrostatic pressure head on boiling temperature is negligible.
3 | COMPONENT MODELS
Additional equations are obtained from the requirement that the rate of heat transfer across evaporator evaporator surface ( Ai) in effect i is equal to
The mathematical model of the evaporation process consists of sub-
the rate of thermal energy released by condensing steam in that effect.
models of evaporator, juice heater, and crystallizer. The energy balance equation for each effect i (i 5 1–5) of the multiple-effect evaporator is
"
i21
X
ð12EÞ mv;i21 1mc;i21 hvl;i21 1 mf;0 2ð 1 2di1 Þma 2
ð in Þ
ð out Þ
hf;i 2hf;i
mv; j j 1mb; j j
j51
5 ma di1 1mv;i 1mb;i
ð out Þ
hv;i 2hf;i
#
1
(1)
enthalpy in effect i , and d i1 is the Kronecker delta function ( di1 5 1 if 5
1,
0 if i 6 ¼ 1). It is assumed that a fraction E of heat is lost
in each effect. Rein (2007) suggests that E
5
0.015. Mass balance and
mv; j j 1mb; j j
X j51
f ðT i21 ; T i Þ5
#
f ðT i21 ; T i Þ
(2)
x i–1 1 x i). where x i.ave 5 0.5( x
(3)
mb;i hvl;i 5mf;in cp;i T h;i21 2T h;i
(4)
hv ð T Þ52502:0411:8125T 12:58531024 T 2 29:831026 T 3
(5)
The saturated steam temperature temperature (T ) is related to the saturated pressure p by
(13)
is the average heat capacity of the juice.
1cpf T h;i21 ; x in in
(14)
juice yields: yields:
T h;i21 5T i 2 T i 2T h;i exp
(6)
2Uh;i Ah;i
mf;in cp;i
(15)
The following equation is proposed by Hugot (1986) for the overall heat transfer coefficient of the juice heater:
3; 816:44
18:30362ln ð7:5pÞ
In addi additio tion, n, the requ require iremen mentt tha thatt the hea heatt tra transfe nsferr acr across oss the
Uh;i 50:007T i
227:03
surfaces of H1, H2, H3, and H4 equals the increase in enthalpy of the
hvl ð T Þ52492:922:0523T 23:075231023 T 2
T
(12)
H2, H3, and H4 yields
enthalpy of saturated steam are obtained from Rein (2007):
densation of the bled vapor equals the juice enthalpy increase in H1,
1 2
hv ð T i21 Þ2hv ð T i Þ2hvl ð T i21 Þ1hvl ð T i Þ hvl ð T i Þ
1
For the juice heater, the requirement that the latent heat of con-
cp;i 5 cpf T h;i ; x in in
Required Requir ed equations for latent heat of evaporation evaporation of water and
52
hvl;i21 (11)
where m f,in is the mass flow rate of juice into the juice heater, and c p,i
i21
where
Ui 56:9796exp 20:038164 x i;ave
vapor mass flow rate from each flash tank (i 5 1–4): mc;i 5 mv;0 ð 12di0 Þ1
5ð 12EÞ mv;i21 1mc;i21
the correlation of heat transfer coefficient is provided by Pacheco and
energy balances of the flash tanks yield the following expression for
"
Frioni (2004).
T i, hv,i is the saturated saturated steam ent enthal halpy py at T i, hf,i is the sugar juice
i
ð out Þ
The evaporator is assumed to be of the falling-film type, for which
where h vl,i is the latent heat of evaporation at saturation temperature
and d i1 5
ð in Þ
Ui Ai T i21 2 2 T f;i 1T f;i
u
0:8
(16)
1:8
The juice vel veloci ocity ty (u) is assumed to be 2.5 m/s, and the above equation becomes
Specific enthalpy of juice at inlet and exit of the ith effect is the Uh;i 50:0091T i
product of specific heat capacity of sugar juice and juice temperature (hf 5 cpfT f). Equation for specific heat capacity is computed from (Bubnik, Kadlec, Urban, & Bruhns, 1995):
(17)
After leaving leaving H1, the juice pressure (pin) is a little above the atmospheric pressure (pout). The juice is allowed to flash in FC, resulting in a
5
cpf ð T f ; x Þ54:186820:0297 x 17:53102 xT f
(7)
Juice Jui ce tem tempera peratur ture e (T f) is ass assum umed ed to be the sat satur urati ation on tem tempe perat rature ure.. It
reduced reduce d mass flow rate (mf,0) that is determ determined ined from mf;0 5mf;in ½ 1 2f ðT in out Þ in ; T out
(18)
is larger than the boiling point of saturated liquid water at the same pres-
where T in respectively, tively, saturated steam temper temperature ature corin and T out out are, respec
sure sur e du due e to the co conce ncentr ntrati ation on of dis disso solve lved d sol solid idss in jui juice ce (H (Hon onig, ig, 196 1963): 3):
responding respo nding to pin and pout. Before entering the first effect, the juice
ð i nÞ T f;i 5T i 1
2 x i21 1002 x i21
2 x i ð outÞ ; i i f 5 1 T T 1002 x i
pressure is increased to p1. Furthermore, its temperature is raised to (8)
medium. The model of HC is represented by the following equations. (9)
Juice concentratio concentrations ns are determ determined ined from mass balanc balances es of dissolved solids:
the boiling boiling point in HC. Low-pres Low-pressur sure e ste steam am is use used d as the heating heating
mv;c hvl;c 5mf;0 cp;c ð T 1 2T out out Þ
1 2
cp;c 5 ½cpf ð T out out ; x 0 Þ1cpf ð T 1 ; x 0 Þ
(19)
(20)
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|
T 1 5T c 2ð T c 2T out out Þexp
2Uh;c Ah;c
mf;0 cp;c
(21)
CHANTASIRIWAN
equal to the ambient temperature. If no heat loss occurs between the outlet of the juice extraction process and the inlet of the juice heater,
Uh,c is approximately 1.0 kW/m K (Peacock & Love, 2003). The
T h,4 h,4 5 30 C. The temperature of sugar juice leaving the juice heater
steam pressure in HC (pc) is assumed to be controlled in such a way
(T h,0 (Rein, n, 2007 2007). ). The sug sugar ar juice is als also o h,0) is assumed to be 103 C (Rei
that the juice temperature is exactly T 1 at the exit of HC. The surface
assumed to be saturated, which means that the juice pressure is above
area of HC ( Ah,c) is 900 m2, which is large enough that pc does not
the atmospheric atmospheric pressure. pressure. The juice is allowed to flash in FC in order to
exceed p 0.
get rid of dissolved gases, and its temperature is raised to T 1 in HC
2
The crystallizer may be modeled as a single-effect evaporator. It
8
8
before entering the first effect of the evaporator.
uses the vapor bled from the first effect to evaporate the remaining
Saturated steam at a specified pressure p 0 must be available as an
water content in the syrup leaving the evaporator. Ideally, the amount of water to be evaporated is the water content of the syrup. In prac-
input to the multiple-effect multiple-effect evaporator. evaporator. Superh Superheated eated steam is either exha ex haus uste ted d fro from m a ba back ck-pr -pres essu sure re tu turb rbin ine e or ex extr trac acte ted d fr from om a
tice, however, crystallization is usually carried out in three stages. In
condensing-extraction turbine. It is then mixed with water in a desu-
each eac h sta stage, ge, water may be add added, ed, and hea heatt los losss occ occurs urs.. The ratio
perheater to produce the saturated steam required for the evaporation
between the two quantities is in the range of 2.0 –2.2 (Reid & Rein,
proces pro cess. s. Vap Vapor or pressure pressure at the exit of the fifth effect effect (p5) is also also
1983; Rein, 2007). In this article, the ratio of 2.0 is assumed, yielding
assumed to be fixed because the temperature of sugar juice in the fifth
the relation
effect eff ect is con contro trolled lled at a low value to min minimi imize ze col color or form formatio ation n and ma 5
2mf;5 ð 12 x 5 =100Þhvl;5 hvl;1
sucrose degradation losses. In this study, the values of p0 and p5 are, (22)
respectively, 200 and 16 kPa. With x in in, x 5, T h,0 h,0, T h,4 h,4, p 0, and p 5 specified, there are eight remaining free parameters. It is additionally assumed that the surface areas of the
4 | VAPOR BLEEDING ARRANGEMENTS
A1– A5) are specified parameters. It is assumed multiple-effect evaporator ( A
thatt the evaporat tha evaporator or sur surfac face e are areas as are 5,600 m2 for the firs firstt effe effect, ct, Because the juice temperature at the exit of HC is assumed to be T 1, HC is uncoupled from the rest of the system as far as the solution to the system is concerned. Inspection of the above mathematical model
4,000 m2 for the second effect, and 1,900 m2 for the third, fourth, and Ah,tot 5 Ah,1 1 Ah,2 1 fifth effects. If the total juice heating surface area ( A Ah,3 1 Ah,4) is also specified, the number of free parameters is reduced to
reveals that there are 44 variables ( mf,in, m f,0–mf,5, m a, m v,0–mv,5, m b,1–
two.. Thi two Thiss means means that that the syst system em of equ equati ations ons can be sol solved ved pro provid vided ed tha thatt
mb,4, x in in, x 0– x 5, p 0–p5, T h,0 h,0–T h,4 h,4, A 1– A5, and A h,1– Ah,4) and 30 equations
two tw o of th the e ju juic ice e he heat ater er sur surfa face ce ar area eass ar are e giv given en..
(Equations 1, 2, 10, 11, 13, 15, 18, and 22). Therefore, the number of
Three vapor bleeding arrangements are considered. In two-effect
free parameters is 14. Their values must be specified in order for the
vapor bleeding arrangement, vapor is bled from the first and second
solution of the system of nonlinear equations to be found. Six of these
effects,, which means that Ah,3 5 Ah,4 5 0. There is a unique diseffects
parameters are design variables, consisting of the juice concentration
tribution of a given total surface between H1 and H2 in this arrange-
at the inlet of the process ( x in in), the juice concentration at the outlet of
ment. men t. Thr Three-e ee-effe ffect ct vapo vaporr ble bleedin eding g arr arrang angeme ement nt requ require iress vapo vaporr
x 5), the juice temperature at the inlet of the juice heater the process ( x
bleeding from the first, second, and third effects, which means that
(T h,4 h,4), the juice temperature at the outlet of the juice heater ( T h,0 h,0), the steam pressure at the inlet of the evaporator (p0), and the vapor pressure at the outlet of the evaporator evaporator ( p5), Sugar juice that enters the evaporation process comes from a juice extraction process using sugar milling machinery. The juice extraction process requires water addition, which results in low concentration of outgoing juice. Chantasiriwan (2016) showed that there is the optimum amount of water addition under certain conditions. It is assumed that this optimum amount of water addition results in the juice concentration at the outlet of the juice extraction process equal to 15%. The juice leavin leaving g the extrac extraction tion proce process ss goes direct directly ly to the juice heater without water addition, Therefore, x in in
5
15%. The second design vari-
x 5), able abl e is the juice concentr concentratio ation n at the outlet of the evaporat evaporator or ( x
which is controlled to be at a high value to improve energy efficiency
Ah,4 5 0. Bec Becaus ause e the there re is one free para paramet meter er in thi thiss arr arrang angeme ement, nt,
there are several distributions of total surface among H1, H2, and H3 that satisfy a specif specified ied juice heati heating ng requir requirement. ement. Four-effect Four-effect vapor bleeding arrangement requires vapor bleeding from the first, second, third, and fourth effects. Because there are two free parameters in this arrangement, there are several distributions of total surface among H1, H2, H3, and H4 that satisfy a specified juice heating requirement. Since there are many surface distributions in the three-effect and four-effect vapor bleeding arrangements, it is likely that there is an optimum juice heater surface area distribution that maximizes steam economy, which is defined as SE5
ð 120:01 x in in Þmf;in mv;0 1mv;c
(23)
of the system. However, x 5 should not be too high because it will cause
In addition to SE, another important performance parameter is the
difficulty in the crystallization process. It is assumed in this study that
mass flow rate of processes sugar juice ( mf,in). The former is related to cost of manufacturing raw sugar. The latter is related to the revenue
If water added to the milling unit is at ambient temperature, the
earned by the sugar factory. It is, therefore, desirable for the sugar fac-
x 5 5 70%.
temperature of juice leaving the milling unit may be assumed to be
tory to maximize both parameters.
CHANTASIRIWAN
5 | RESULTS AND DISCUSSION
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H2,, an H2 and d H3 be beca caus use e th ther ere e is a fr free ee pa para rame mete ter, r, wh whic ich h is th the e su surf rfac ace e ar area ea of H3 ( Ah,3). Figure 3a shows how the distribution of the total juice heater
If vapor is bled from the first and second effects, there is a unique dis-
surfa su rface ce of 1, 1,500 500 m2 am amon ong g H1 H1,, H2 H2,, an and d H3 va vari ries es wi with th Ah,3. Itca Itcan n besee beseen n
tribution of the total surface between H1 and H2. It can be seen from
that th at th the e ma maxi ximu mum m va valu lue e of Ah,3 is 807 m2. At th this is va valu lue, e, va vapo porr is bl bled ed fr from om
Figure 2a that A h,tot must be at least 1,160 m 2. At this value, vapor is
the th e fi firs rstt an and d thi third rd ef effec fects ts be beca caus use e Ah,2 5 0, an and d Ah,1 1 Ah,3 5 Ah,tot. Fig Figure ure
bled from onl only y the fir first st effe effect ct bec becaus ause e Ah,2 5 0 and Ah,1 5 Ah,tot.
3b shows that, with a fixed value of A h,tot, there is the optimum value of
Increasing Ah,tot results in decreasing A h,1 and increasing A h,2. The maxi-
Ah,3 that maximizes SE. However, mf,in is a monotonically decreasing func-
mum mu m val value ue of Ah,tot for two two-ef -effect fect vapo vaporr ble bleedi eding ng arra arrangem ngement ent is
tion of Ah,3. Therefore, mf,in of the three-effect vapor bleeding arrange-
2
2,005 m . At this value, vapor vapor is bled from only the sec second ond effect effect
mentt is les men lesss tha than n tha thatt of the two two-eff -effect ect vap vapor or ble bleedi eding ng arr arrange angemen ment. t.
because A h,1 5 0, and A h,2 5 Ah,tot. Figure 2b shows that steam economy (SE) increases monotonically with Ah,tot. A plot of mf,in in Figure 2b
Simila Sim ilarr res result ultss are obt obtain ained ed whe when n Ah,tot is di diffe ffere rent nt fro from m 1,5 1,500 00 m . For a given value of Ah,tot, the optimum value Ah,3 can be found
shows that it also increases monotonically with Ah,tot.
and the result is the optimum three-effect vapor bleeding arrangement.
2
If vapor is bled from the first, second, and third effects, there are
The total juice heater surface distribution among H1, H2, and H3 in
many possible distributions of the total juice heater surface among H1,
the optimum three-effect vapor bleeding arrangement as a function of
F I G U R E 2 (a) Distribution Distribution of the total juice heater heater surface
F I G U R E 3 (a) Distribution Distribution of the total juice heater heater surface of
between H1 and H2 and (b) variations of the steam economy (SE) and the mass flow rate of processed sugar juice ( mf,in) with the total juice heater surface in the two-effect vapor bleeding arrangement
1,500 m2 among H1, H2, and H3 as a function of Ah,3 and (b) corresponding variations of the steam economy (SE) and the mass flow rate of processed sugar juice ( mf,in) in three-effect vapor bleeding arrangement
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Ah,tot is shown in Figure 4a. The total juice heater surface can be opti-
and m f,in with A h,3 and A h,4 are shown in Figure 5. It can be seen from
mally ma lly di distr strib ibut uted ed am amon ong g H1 H1,, H2 H2,, an and d H3 wh when en Ah,tot is at le leas astt
Figure 5a that SE is convex function of Ah,3 and Ah,4. Therefore, the
2
1,181 m . As Ah,tot increases, Ah,1 decreases decreases,, where whereas as Ah,2 and Ah,3
optimum surface distribution that maximizes SE can be found. By con-
increase. increa se. Increa Increasing sing Ah,tot results results in a mon monoto otonic nic increase increase in SE, as
trast, Figure 5b shows that The maximum value of m f,in occurs when
shown in Figure 4b.
Ah,3 5 Ah,4 5 0. This means that m f,in of the four-effect vapor bleeding
In the fou four-e r-effec ffectt vap vapor or blee bleeding ding arrangeme arrangement, nt, the there re are man many y possible distributions of the total juice heater surface among H1, H2,
arrangement is always less than that of the two-effect vapor bleeding arrangement.
H3, and H4 because there are two free parameters, which are the sur-
Figure 6a shows the distribution of A h,tot among H1, H2, H3, and
face area of H3 and H4 ( A Ah,3 and A h,4). Surface plots of variations of SE
H4 in the optimum four-effect vapor bleeding arrangement. It can be seen that the total juice heater surface can be optim optimally ally distributed distributed among H1, H2, H3, and H4 when A h,tot is at least 1,250 m2. As A h,tot increases, Ah,1 decreases, whereas Ah,2, Ah,3, and Ah,4 increase. Figure 6b shows that SE increases monotonically with Ah,tot. Simulation results corresponding to three different vapor bleeding arrangements are compared in Table 1. The total juice heater surface for all arr arrang angeme ements nts is 1,50 1,500 0 m2. It can be seen that that the opt optimu imum m three-effect vapor bleeding arrangement increases SE by 3.16% compared with the two-effect vapor bleeding arrangement, and the optimum four-effect vapor bleeding arrangement increases SE by 0.80% compared with the optimum three-effect vapor bleeding arrangement.
F I G U R E 4 (a) Distribution Distribution of the total juice heater heater surface among among
F I G U R E 5 Variati Variations ons of (a) the steam economy economy (SE) and (b) (b) the
H1, H2, and H3 and (b) variation of the steam economy (SE) with the total juice heater surface in the optimum three-effect vapor bleeding arrangement
mass flow rate of processed sugar juice (mf,in) with A h,3 and A h,4 in four-effect vapor bleeding arrangement that has the total juice heater surface of 1,500 m2
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TAB L E 1 Comparison of of simulation results of sugar juice juice evapora-
tion processes having two-effect, optimum three-effect, and optimum four-effect vapor bleeding arrangements Vapor bleeding arrangement Para Pa rame mete terr
2-Ef 2Effe fect ct
Opti Op timu mum m 33-ef effe fect ct
Opti Op timu mum m 44-ef effe fect ct
Ah,1 (m 2)
323.1
464.6
533.5
Ah,2 (m 2)
1176.9
425.8 42
346.7
Ah,3 (m 2)
0
609.6
344.2
Ah,4 (m )
0
0
285.6
SE
2.312
2.385 2.
2.404
mf,in (kg/s)
154.4
150.2
149.1
2
F I G U R E 7 Compar Comparison ison of the steam economy economy (SE) of sugar juice
evaporation processes that use the 2-effect, optimum 3-effect, and optimum optimu m 4-effect vapor bleedin bleeding g arrang arrangements ements
F I G U R E 6 (a) Distribution Distribution of the total juice heater heater surface among among
6 | CONCLUSIONS
H1, H2, H3, and H4 and (b) variation of the steam economy (SE) with the total juice heater surface in the optimum four-effect vapor bleeding arrangement
Three components of the sugar juice evaporation process are multiple-
It is interesting to note that m f,in decreases by 2.72 and 3.43% as the
this paper takes into account interactions between the three compo-
two-effect vapor bleeding arrangement is changed, respectively, to the
nents nen ts thr throug ough h mas masss and ene energy rgy bal balanc ances. es. The syst system em of non nonlin linear ear equ equaa-
optimum optim um threethree-effect effect vapor bleedi bleeding ng arrang arrangement ement and the optim optimum um
tions in this model has 44 variab variables les and 30 equati equations. ons. By specifying the
four-effect vapor bleeding arrangement.
total juice heater surface area and imposing certain assumptions and
effect evaporator, juice heater, and crystallizer. The model presented in
Figure 7 shows further comparison of SE in the two-effect, opti-
conditions, the number of free parameters decreases from 14 to 2,
mum three-effect, three-effect, and optim optimum um four-e four-effect ffect vapor bleed bleeding ing arrang arrangee-
which whi ch are the surf surface ace area areass of two exc exchang hangers ers of the the juic juice e hea heater ter.. In the the
ments. men ts. It can be see seen n tha thatt the optimum optimum four four-eff -effect ect vapor ble bleedi eding ng
two-eff two -effect ect vapo vaporr blee bleedin ding g arr arrang angeme ement, nt, the there re is a uniq unique ue solu solutio tion n to the
arrangement arrang ement gives the best perfor performance mance in maximizing maximizing SE. It is also
system of the equations. Simulation results show that both the steam
interesti intere sting ng to not note e tha thatt all cur curves ves exhi exhibit bit the tren trend d of dimi diminis nishin hing g returns. This means that, although SE can be increased by installing
economy and the rate of processed sugar juice increase with the total juice heater heater surface. In either three-effect three-effect or four-effect four-effect vapor bleeding bleeding
more juice heater surface, the return for the cost of installing additional
arrangement, there is the optimum surface distribution that maximizes
surface decreases monotonically as the total surface increases.
the steam economy. Simulation results for a hypothetical process with
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the total juice heater surface area of 1,500 m 2 indicate that the steam economy increases by 3.16 and 3.98% as the two-effect vapor bleeding arrang arr angeme ement nt is cha change nged, d, res respec pectiv tively, ely, to the opt optimu imum m thr threeee-effe effect ct vapo vaporr bleeding bleedi ng arrang arrangement ement and the optimum four-effect four-effect vapor bleeding arrangement. arrang ement. However, the two-ef two-effect fect vapor bleeding arran arrangement gement yields a larger value of the rate of processed sugar juice than either a three-effect threeeffect vapor bleedi bleeding ng arrang arrangement ement or a four-effe four-effect ct vapor bleedi bleeding ng arrangement. arrang ement. Therefore, Therefore, the two-e two-effect ffect vapor bleedi bleeding ng arrang arrangement ement is the mor more e sui suitab table le arr arrang angemen ementt if max maximi imizin zing g the rat rate e of pro proces cessed sed sug sugar ar
CHANTASIRIWAN
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Hugot, E. (1986 Hugot, (1986). ). Handbook Handbook of cane sugar engineering engineering (3rd ed.). Amsterdam: Elsevier.
A heat transfer surface of evaporator (m2) Ah heat transfer surface of juice heater (m2)
Jyoti, G., & Khanam, S. (2014). Simulation of heat integrated multiple effect evaporator evapo rator system system.. Inter Internation national al Journ Journal al of Therm Thermal al Scie Sciences nces, 76, 11 110 0–117.
cp specific heat capacity (kJ/kg C) 8
h
enthalpy (kJ/kg)
Khanam, S., & Mohanty, B. (2010). Placement of condensate flash tanks in multiple effect evaporator system. Desalination, 262 , 64–71.
m mass flow rate (kg/s) p
pressure (kPa)
SE
steam ste am ec econ onom omy y
T
saturated steam temperature in evaporator ( C)
Pacheco, C. R. F., & Frioni, L. S. M. (2004). Experimental results for evaporation oratio n of sucro sucrose se soluti solution on usin using g a clim climbing/ bing/fallin falling g film evaporator. evaporator. Journal of Food Engineering , 64 , 471–480.
8
T h juice temperature in evaporator ( C) 8
2
U heat transfer coefficient of evaporator (kW/m
2
Uh heat transfer coefficient of juice heater (kW/m x
Heluane, H., Colombo, M., Hernandez, M. R., Graells, M., & Puigjaner, L. (2007). Enhancing Enhancing sugar cane process performance through optimal proEngineering ring and Process Processing ing , 46, 19 duction schedul scheduling. ing. Chemical Enginee 198 8–209.
C)
8
C)
8
concentration of sugar juice (%)
Subscripts
Peacock, Peacoc k, S. D., & Lov Love, e, D. J. (20 (2003) 03).. Cle Clear ar jui juice ce heaters heaters—Do we need them? Proceedings of the South African Sugar Technologists Association, – 77, 452 462. Piacentino, A., & Cardona, E. (2010). Advanced energetics of a MultipleEffects-Evaporation (MEE) desalination plant. Part II: Potential of the cost formation process and prospects for energy saving by process integration. Desalination, 259 , 44–52.
0
inle in lett to ev evap apor orat ator or
b
bled bl ed vap vapor or to ju juic ice e he heat ater er
Reid, Rei d, M. J., & Rei Rein, n, P. (19 (1983) 83).. Steam Steam bal balanc ance e for the newFelix newFelixton ton II mil mill. l. Proceedings of the South African Sugar Technologists Technologists Association, 57, 85–91.
c
vapor vap or ou outl tlet et fr from om fla flash sh ta tank nk
Rein, P. W. (2007). Cane sugar engineering . Berli Berlin: n: Verlag Verlag..
f
suga su garr juice
i
effe ef fecct nu numb mber er
in
into in to ju juic ice e he heat ater er
Ribeiro, C. P., JR., & Andrade, M. H. C. (2003). Performance analysis of the milk conce concentrati ntrating ng system from a Brazi Brazilian lian milk powd powder er plant plant.. Journal of Food Process Engineering , 26 , 181–205.
v
vapor
vl
vapor vap or to li liqu quid id
Superscripts
(in) (i n)
inle in lett to an ef effe fect ct
(out) (ou t)
outlet out let fro from m an effe effect ct
OR CI D
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S. Chantasi Chantasiriwan riwan http://orcid.org/0000-0003-1274-8326
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How to cite this article: article: Chantasiriwan Chantasiriwan S. Deter Determinati mination on of
Bubnik, Z., Kadle Bubnik, Kadlec, c, P., Urban Urban,, D., & Bruhn Bruhns, s, M. (1995). Sugar technologists manual (8th ed.). Berlin: Verlag.
optimum vapor bleeding arrangements for sugar juice evaporation process. J Food Process Eng . 2017;e12616. https://doi.org/ 2017;e12616. https://doi.org/
Chantasiriwan, S. (2015). Optimum surface area distribution in co-current multiple-effect evaporator. Journal of Food Engineering , 161, 48–54.
10.1111/jfpe.12616
