Evaporador de Efecto Múltiple en la Elaboración de Pasta de Tomate
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Optimum design and operating conditions of multiple effect evaporators:Tomato paste
R. Simpson *, S. Almonacid, D. Lpez, A. Abakarov
Departamento de Procesos Qumicos, Biotecnolgicos, y Ambientales, Universidad Tcnica Federico Santa Mara, Casilla P.O. Box 110-V, Valparaso, Chile
a r t i c l e i n f o
Article history:
Received 22 January 2008Received in revised form 24 May 2008
Accepted 27 May 2008
Available online 10 June 2008
Keywords:
Multi-effect evaporators
Economic evaluation
Net Present Value
Quality
Lycopene
Process optimization
a b s t r a c t
Agro industry is a very important industrial sector worldwide, especially for countries like New Zealand
and Chile. The main objective of this research was to propose a new economic evaluation procedure to
optimize the design and operation of multiple effect evaporators and compare it with the traditional
chemical engineering approach of total cost minimization. The proposed strategy incorporates a quality
factor expressed as a function of lycopene concentration on the final product to find the optimal number
of effects and operating conditions through the maximization of the net present value.
The mathematical model was implemented using Microsoft Excel and considered mass and energy bal-
ances, specific relations for tomato concentration and a first order degradation kinetic for lycopene. The
results indicate that when augmenting the capacity of the evaporation system of 5 effects from 50 to
75 Ton/h, the lycopene retention increases from 95.25% to 96.27%. When evaluating the system through
the logic of the total cost minimization, an optimum of 4 effects is found, but when evaluating the system
using the maximization of the Net Present Value including lycopene as a quality parameter, the optimum
is 3 effects.
It appears of extreme relevance to consider quality as an intrinsic and integral part of the process
design, as it will then be possible to identify several potential improvements in different food processes.
2008 Published by Elsevier Ltd.
1. Introduction
Process optimization has always been a noble objective of engi-
neers entrusted with the responsibility for process development
and improvement throughout the food industry. Examples of
sophisticated mathematical approaches to process optimization,
in which some objective function is maximized or minimized
subject to chosen constraints, are widely published in literature
(Douglas, 1988). On the other hand, the chemical industry has used
cost analysis in several cases in relation to design and process opti-
mization. A classical example in the chemical industry is the deter-
mination of the optimal number of effects in a evaporation system,
were the optimum is found when there is an economic balance be-
tween energy saving and added investment, this is, a minimization
of the total cost (Kern,1999). In this vision, although correctly, qual-
ityis notconsidered as a parameter in thedetermination of theopti-
mum number of effects, so the process specifications and operating
conditions are assumed independent of both product quality as its
sale price. The purpose of this manuscript is to suggest that the
extrapolation of optimization problems from chemical industry to
the food industry may often be restricted to an unnecessarily nar-
row or local domain, and that a more global perspective may reap
greater rewards. Questions as to just what should be maximized
or minimized, or what are the real constraints, as opposed to only
those that are immediately apparent, are questions often posed
without a broad enough view of the big picture.
China continues to make inroads in the world market. China is
the worlds largest tomato products producer and exporter, fol-
lowed by the EU and the United States. China produces tomato
products mainly for the export market, with exports accounting
for more than 85% of production. Since calendar year (CY) 1999,
Chinas tomato paste exports have had an average annual increase
of 30% (USDA, 2007).
The production of tomato paste is highly seasonal, and then,
maximizing production levels in this industry is of vital impor-
tance. The process is generally done in multiple evaporation sys-
tems, with a different number of effects, through which the
content of water is diminished until a final concentration from
30 to 32Brix is acquired, and where temperatures generally do
not exceed 70 C.
Lycopene is the main carotenoid found in tomatoes and many
studies have showed its inhibiting effect on carcinogenic cell
growth (Shi et al, 2007). It is also the component which generates
the red characteristic color in tomatoes, among other fruits and
vegetables (Goula and Adamopoulos, 2006). A study developed
by the University of Harvard, revealed that the consumption of
lycopene reduced the probabilities of generating prostate cancer
0260-8774/$ - see front matter 2008 Published by Elsevier Ltd.doi:10.1016/j.jfoodeng.2008.05.033
* Corresponding author. Tel.: +56 32 2654302; fax: +56 32 2654478.
E-mail address: [email protected](R. Simpson).
Journal of Food Engineering 89 (2008) 488497
Contents lists available at ScienceDirect
Journal of Food Engineering
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j f o o d e n g
mailto:[email protected]://www.sciencedirect.com/science/journal/02608774http://www.elsevier.com/locate/jfoodenghttp://www.elsevier.com/locate/jfoodenghttp://www.sciencedirect.com/science/journal/02608774mailto:[email protected] -
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by 45%, in a population of 48,000 subjects who had at least 10 ra-
tions of tomatoes or sub products in their weekly diet. Other re-
search discovered that lycopene also reduces cholesterol levels in
the form of a lipoprotein of low density (LDL), which produces ath-
erosclerosis; this means that the consumption of tomatoes reduces
the effects produced by cardiovascular diseases.
Lycopene as the main organic compound presents a denatural-
ization reaction rate that is time and temperature dependent. Then,
for the mathematical model of the behavior of multi-effect evapo-
rators, it is very important to have a good overview of the general
fluctuation of lycopene retention or loss under different system de-
signs and operating conditions.
As aforementioned, most food processes have been adapted and
extrapolated from the chemical engineering industry without an
adequate consideration of product quality during system designand process optimization. That is certainly a good start, but maybe
somewhat limited and might have inhibited us to take a more glo-
bal view. For example, it appears of extreme relevance to consider
quality more frequently as an intrinsic and integral part of process
design. In the food industry, the main effort is commonly related to
the maximization of the quality of the product, which is not neces-
sarily the case in the chemical industry. Generally the optimization
of food processes have been restricted to determining the optimal
operating conditions of an allegedly, well designed food process.
Nevertheless, if quality is considered as a parameter in the system
design, it is very probable that the new design will differ from the
original one.
For example, in the case of a multiple effect evaporator system
for the processing of tomatoes, the optimization of the design isonly focused on an economic analysis which combines the invest-
ment (number of effects) and the operating costs (steam consump-
tion) (Kern, 1999). This strategy does not include quality as an
integral part of the economic evaluation, even though previous
studies have demonstrated the dependence of the final product
price towards quality of the final product (Schoorl and Holt, 1983).
The main objective of this research work is to propose a new
economic evaluation procedure to optimize the system design
and operation of tomato juice, multiple effect evaporator and com-
pare it to the traditional chemical engineering approach of total
cost minimization. The proposed strategy will incorporate a quality
factor which will be expressed as a function of lycopene concentra-
tion on the final product to find the optimal number of effects and
operating conditions through the maximization of the Net PresentValue (NPV).
2. Methodology
2.1. Problem description
Cost analysis has been extensively and correctly utilized in find-
ing the best process design in several chemical engineering plants.
A classical example is multi-effect distillation. In this case, cost
analysis should aim to determine the optimum number of effects
in multiple-stage equipment. According to the literature in chemi-
cal engineering The optimum number of effects must be found from
an economic balance between the savings in steam obtained by multi-
ple effect operation and added investment. It is important to eluci-
date whether the aforementioned approach is recommendable in
the optimization of food processes? From a microeconomics point
of view, this approach is correct but, it is important to consider thatthe different equipment configurations are producing exactly the
same quality of the end product. Meaning that, independent of
the numberof effects, not onlywill webe able to reach the samede-
gree of concentration, but also the same quality. In addition, by
changing the equipment configuration it is possible to attain the
same degree of concentration but with different product quality.
At least, for multi-effect evaporation in food processing, the re-
ferred approach is not necessarily the right micro-economic tool
to find the optimum number of effects. For this kind of application,
a correct micro-economic analysis should consider not only all
costs but also the expected benefits. According to the relevant tech-
nical literature, an adequate micro-economic procedure is to max-
imize the NPV.
In the case of the evaporation process for tomato paste, the pro-duction is highly seasonal, and, in addition, the product quality
could be highly affected by the operating conditions. Therefore, it
is important to consider the impact of the installed capacity and
the final product quality. In the following, we will compare two dif-
ferent economic approaches: (a) determination of the optimal
number of effects by minimizing the total cost and, (b) maximiza-
tion of the NPV, considering quality as an intrinsic parameter of the
modeled system.
2.2. Product quality
To reach the objective of the present research work, a quality
parameter must be considered to the mathematical model of theevaporation system. The chosen parameter is lycopene, because,
Nomenclature
A heat transfer area, m2
Cu cost per unit, US$/kgCp specific heat of concentrate (kJ kg
1C1)
Deb boiling point elevation (BPE) or Boiling point rise (BPR)(C)
E activation energy (kJ/mol)F mass flowrate (kg/h)H enthalpy (kJ/kg)i annual interest rateI total investment (US$)k reaction rate constant (1/h)k0 frequency factor (1/h)K0 constantM mass in the evaporator (kg)m project shelf life, yearsn number of effectsNPV net present value (US$)O evaporation system operation
P pressure (kPa)Pu unit sales price (US$/kg)Q heat flow (kJ)Q*j annual production at periodj (units/year)R ideal gases constant (CkJ/mol)
T temperature (C)t time (h)X concentration of soluble solids, kgss/kgY lycopene concentration kgL/kgss
Subscriptsc condensingd downloade coolingi evaporator effect, i
j evaluation period,jp losses
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as mentioned before, this carotenoid pigment is what gives toma-
toes their characteristic color, and, in addition, it has some medical
benefits.
Usually, degradation rates in sensitive food components are
modeled as a first order kinetic, as follows:
r kY or dY
dt kY 1
The Arrhenius equation relates specific reaction rate constant to
temperature according to:
k k0 exp E
R T
2
The first order kinetic for lycopene degradation has been con-
firmed by Goula and Adamopoulos (2006). In the same research
study an equation was obtained to determine the reaction rate in
the lycopene degradation, as a function of temperature and soluble
solids concentrationXexpressed in Brix.
For X 55; K 0:121238 exp0:0188X
exp 2317
T 273:15 min1
3
ForX 55; k 0:275271exp 0:00241X
exp 2207
T 273:15
min
1 4
In our research study, the system to be modeled should con-
sider tomato concentration in the range of 535 Brix, so only Eq.
(4)will be required.
2.3. Model development
The evaporation process involves mass and heat transfer (Him-
melblau and Bischoff, 1968). The tomato juice was considered as a
binary solution of water and soluble solids, both considered inertin a chemical sense. Under these considerations, one effect of the
industrial evaporator can be shown in the manuscript by Miranda
and Simpson, 2005.
So the macroscopic model is of the knowledge-type based on
conservation laws and also empirical relationships which describe
the equilibrium phases. These relationships have been rearranged
from non-linear algebraic equations from literature, with the expe-
rience taken from the experimental site. Only the juice phase is
considered for modeling.
The modeling assumptions are:
Homogenous composition and temperature inside each
evaporator. Constant juice level in each evaporator. Thermodynamic equilibrium (liquidvapor) for the whole mod-
eled system.
The mathematical model developed in this research study in-
cluded specific relationships for lycopene degradation. The general
system that must be solved (seeFig. 1for a schematic representa-
tion of the system), operates on countercurrent and the total num-
ber of effects varies from 1 to n. The value of n and the
operating conditions will be determined at the end of this work
through the maximization of the NPV.
The total mass balance in evaporator effect i is:
dMi
dt Fi1 Fvi Fi 5
If the mass within the evaporator effect is controlled, then, un-
der steady state, Eq.(5)can be written as:
0 Fi1 Fvi Fi 6
In the same way, a mass balance for soluble solids at effect i, can
be written as:
dMiXi
dt Fi1 Xi1 Fi Xi 7
Under steady state condition:
0 Fi1 Xi1 Fi Xi 8
The corresponding energy balance for the evaporator effect i, is:
dHiMi
dt Fi1 Hi1 Fvi1 Hvi1 Fi Hi Fvi Hvi Fci Hci Qp
9
Under steady state condition:
0 Fi1 Hi1 Fvi1 Hvi1 Fi Hi Fvi Hvi Fci Hci Qp
10
The enthalpy of the tomato paste was estimated through the
specific heat (Cp), utilizing the following expression (Tonelli et
al., 1990):
Hi 4:184 2:9337 Xi Ti 11
The following thermodynamic relationship describes the boil-
ing point rise (BPR) or boiling point elevation (BPE), whose param-eters have been determined experimentally, it is one of the three
important properties (specific heat, viscosity and boiling point
rise), that must be specified in a multiple effects evaporator (Rizvi
and Mittal, 1992). This property (BPR) is significant at high soluble
solids concentration. On a multiple effect equipment, the effective
temperature differences decrease for the combination of boiling
point. The following correlation reported byMiranda and Simpson,
2005, was utilized.
Deb 0:175X1:11e3:86XP0:43 12
Vapor was considered saturated within the evaporator. The fol-
lowing correlations were obtained fromPerry and Chilton (1973),
and allow for the estimation of vapor properties with an error of
less than 1%.For 40 C
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For 70C
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the restriction was equal areas for each evaporator effect. The input
values to the model, shown inTable 1, were the same for all of the
systems and obtained from an actual industrial plant, comple-
mented with available online information from manufacturers.
3.1. Steady state conditions
From the mass and energy balance equations, liquidvaporequilibrium equation and specific relations for the tomato paste,
a steady state model for the evaporator system was developed,
considering one up to seven effects. From this information, it is
possible to verify the decrease in vapor flowrate necessary for
the operational process and an increase in the total system area,
when augmenting the number of effects (Fig. 2).
To have a more precise view of the product behavior in the
evaporation system, residence time and their respective tempera-
tures, are presented inTable 2for each one of the effects in the dif-
ferent systems.
3.2. Lycopene retention
Lycopene retention in the final product was estimated for each
one of the alternative systems from the data obtained under steady
state operation. From the results shown in Fig. 3, it is clear that
lycopene concentration in the final product has a linear decay
when augmenting the number of effects in the evaporation system.
The previous result gives a clue of how the content of lycopene in
the final product is affected as a function of the residence time in
the evaporation system. While the number of effects increases in
the evaporation system, the total residence time increases as well
as the temperature at which the product is exposed, and, therefore,
there is also an increase of the lycopene degradation.
Lycopene retention for the theoretical evaporation system for
tomato paste are shown inFig. 4. Clearly, lycopene retention de-
creases as the number of effects increase, which is justified bythe augmentation of the total residence time of the system and also
because of the temperature rise at which the tomato paste is ex-
posed to. In regards to the supply flowrate, there is an increase
in the lycopene retention when augmenting the flowrate. The in-
crease in lycopene retention is less abrupt when the supply flow-
rate is over 100 ton/h.
3.3. Changes in processing capacity
To have a more precise idea of the effect of temperature and res-
idence time effect on lycopene degradation process capacity was
set to different values in a specific range. This was done by main-
taining the heat exchange area, and consequently, the number of
effects (a 5 effect lineup system was considered, as it is the number
that is regularly used in the tomato paste industry). Increasing the
processing capacity of the system, results in a increment of the
required energy, therefore steam inlet pressure Pv0 will also be
increased. This also implies a rise of temperature in the evapora-
tors effects. As shown in Fig. 5, the required vapor flowrate
increases proportionally to the evaporation system input flowrate,
steam inlet pressure increases in a second order polynomial way.
Fig. 6shows a decrease in the systems total residence time as well
as an increase in each evaporators temperature.
As it was expected, temperature inside each evaporator in-
creases due to the augmentation of the system energy require-
ments. The systems residence time decreases because of the
increase of input flowrate and the conservation of the holdup va-
lue. As it is observed in Fig. 7, there is an increase in lycopene
retention when augmenting the input flowrate associated to theproducts residence time which decreases in the evaporation sys-
tem, with no regard to the increase of the evaporator temperature
increment.
This is of great importance, because it demonstrates that lyco-
pene is not an obstacle to increase the processing capacity of the
evaporation system, therefore the maximum capacity will only
Table 1
Input data for mathematical model implementation
Name Variable Value
Input flowrate FAl, kg/h 50,000
Input temperature TAl, C 98
Initial soluble solids
concentration
XAl, kg ss/kg 0.05
Input concentration
of lycopene
YAl, kg Lic/kg SS 0.01
Final soluble solids
concentration
X1, kg ss/kg 0.3
Steam inlet pressure Pv0, kPa 143.4
Temperature change
in condensator
Tvn Td, C 2
Operation pressure in
evaporator n
Pn, kPa 16.5
Fig. 2. Total transfer area m2 and steam inlet flowrate ton/h vs. number of effects.
492 R. Simpson et al. / Journal of Food Engineering 89 (2008) 488497
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Table 2
Temperature data C and residence time h for systems from 1 to 7 effects with an input flowrate of 50 ton/ha,b
Effect
number
Number of effects in the system
1 2 3 4 5 6 7
Residence
time
Temp. Residence
time
Temp. Residence
time
Temp. Residence
time
Temp. Residence
time
Temp. Residence
time
Temp. Residence
time
Temp.
1 1.10 55.9 0.23 55.6 0.17 55.6 0.15 55.6 0.14 55.6 0.13 55.6 0.13 55.6
2 0.84 76.8 0.28 67.5 0.20 63.8 0.17 61.8 0.15 60.5 0.14 59.63 0.78 84.7 0.31 74.3 0.22 69.3 0.19 66.3 0.17 64.3
4 0.75 89.3 0.34 78.9 0.24 73.3 0.20 69.8
5 0.73 92.3 0.36 82.3 0.26 76.4
6 0.71 94.4 0.38 84.8
7 0.70 96.1
1 effect 2 effects 3 effects 4 effects 5 effects 6 effects 7 effects
Output pressure at each effect
P1, kPa 16.5 40.18 56.4 67.7 76.05 82.41 87.5
P2, kPa 16.5 27.7 36.5 44.76 51.6 57.31
P3, kPa 16.5 23.8 29.75 34.91 40.15
P4, kPa 16.5 21.82 26.38 30.32
P5, kPa 16.5 20.65 24.28
P6, kPa 16.5 19.86
P7, kPa 16.5
a Feed enters effect 1.b Fresh vapor pressure: 143.4 kPa.
Fig. 3. Lycopene retention% vs. number of effects for an input of 50 ton/h.
Fig. 4. Lycopene retention% for a system from 1 to 7 effects.
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Fig. 5. Changes in energy consumption represented by the vapor flowrate kg/h and steam inlet pressure kPa as a function of the input flowrate ton/h.
Fig. 6. Residence time (min) and temperature C as a function of the input flowrate ton/h.
Fig. 7. Lycopene retention% as a function of the input flowrate ton/h.
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be restricted by available vapor pressure, minimum specific hold-up, pumps power among others.
3.4. Economic evaluation
The economic evaluation consists of determining the optimum
number of effects and operating conditions of the system. The eco-
nomic evaluation of the system was done in two different ways.
Firstly, an economic evaluation with the concept of minimizing
the total costs, and secondly, an economic evaluation to maximize
the NPV taking into account the impact of the process design and
operating conditions on product quality.
3.5. Optimum number of effects
The economic evaluation was carried out by simple inspection.
This is where the steady state conditions for systems with 17 ef-
fects were found, and then total cost minimization and NPV max-
imization methodologies were used. The search was focused to
find the number of effects that minimize the total cost and, in addi-
tion, to find the number of effects that maximize the NPV.
The results for each evaluation systems are shown in Figs. 8
and 9. The total cost minimization (Fig. 8) shows an optimum of
4 effects. Nevertheless, when doing NPV maximization (Fig. 9),the number of optimum effects was 3 due to the inclusion of the
quality parameter on the evaluation procedure. Naturally, for dif-
ferent processing capacities, the optimum number of effects varies
for both evaluation procedures. This is why differences are encoun-
tered in the optimum number of effects in some operation ranges.
InFig. 10, the optimum number of effects is presented for different
operation ranges. As it is observed inFig. 10, when evaluating the
evaporation system, including the quality parameter, in the range
of 25 ton/h through 50 ton/h, the optimum number of effects de-
creases, in comparison to the evaluation done based on total costs
only. This is explained with previous results where a decrease of
lycopene retention was a result of the increase of the number of ef-
fects. It is for this reason that the NPV maximization, in this partic-
ular case tends to be a lower number of effects.
3.6. Optimum operating conditions
In the search for the optimum operating conditions of evapora-
tion system, the system was economically evaluated under a vari-
able steam inlet pressure (Pv0) where the inclusion of lycopene as a
quality parameter was considered. As a constraint to the problem,
it was estimated that the output temperature of the tomato paste
Fig. 8. Cost evaluation for an evaporator system with an input flowrate of 50 ton/h.
Fig. 9. Net Present Value evaluation for evaporator systems with input flow of 50 ton/h.
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(highest temperature), with the optimum number of effects for adefined vapor pressure, could not be higher than 95 C. Results ob-
tained shown an increase in the project profitability when steam
inlet pressure is augmented. Optimum operating conditions, with
the previous stated constraints, is found to be a 3 effects system
with a steam inlet pressure of 260 kPa (seeTable 3). This result dif-
fers from that obtained from the evaluation based on the total cost
minimization (5 effects system).
Table 4depicts the results obtained by both economics ways;
total cost minimization and NPV maximization.
4. Conclusions
The steady state values of the evaporator system were able to
be linked to the reaction kinetics of the target attribute, lycopene.A mathematical model was successfully developed, and then an
economic evaluation of the optimum design and operating condi-
tions of the evaporation system (17 effects operated under coun-
tercurrent) was carried out.
It was possible to determine that the lycopene retention has a
linear decay respect to the number of effects used in the evapora-
tion system.
When analyzing the behavior of a 5 effect evaporator system, an
increase in the processing capacity from 50 ton/h to 75 ton/h aug-
ments the lycopene retention in the final product from 95.25% to
96.27%.
The previous result is due to the decrease in residence time, and
independent of an increase in the evaporators temperature. This
result is important because it indicates that the increment in toma-to paste production, in this particular case, is restricted only by
mechanical factors like available vapor pressure, maximum speci-
fied holdup, and pump power, etc.
The total cost minimization allows the determination of the
best equipment design (optimum number of effects), but no
information on operating conditions and product quality is ob-
tained. On the other hand, with the NPV approach, it is possible
to optimize the system design and operating conditions simulta-
neously. In addition, the NPV approach considers the final product
quality as an intrinsic parameter of the system.
With the inclusion of lycopene as a quality parameter (NPV), the
optimum number of effects decreases from 4 to 3 when compared
with total cost analysis. In addition, it was also possible to deter-
mine the optimum operating conditions of the 3 effects systemat 260 kPa.
Fig. 10. Optimum number of effects for different input flow rates ton/h according to total cost minimization and Net Present Value maximization.
Table 3
Optimum operating conditions
1st effect 2nd effect 3rd effect
Heat transfer area, m2 209.6 209.2 209.1
Global heat transfer coefficient,
kJ/C/m2/h
4494.5 6767.2 8475.4
Heat transferred, MJ/h 32803.8 30941.1 28727.7
Boiling point raise, C 0.53 0.07 0.03
Holdup, kg 5320 4907 4815
Residence time, h 0.639 0.224 0.141
DTNukiyama 34.8 21.9 16.2
Steady state values
Steam inlet flowr at e, k g/h 1 501 2.9
Steam inlet pressure, kPa 260
Steam inlet temperature, C 129.1
Steam inlet ent halpy , k J/ kg 2 72 5.45Output flowrate, kg/h 8322.5 21930.0 34265.4
Temperature,C 94.26 71.88 55.60
Concentration SS, kg/kg 0.300 0.114 0.073
Lycopene concentration, kg/kg SS 0.0096790 0.0099130 0.0099724
% Lycopene retention 96.79% 99.13% 99.72%
Concentrate enthalpy, kJ/kg 311.3 276.7 220.7
Vapor flowrate, kg/h 13607.5 12335.4 15734.6
Vapor pressure, kPa 81.84 32.9 16.5
Vapor temperature, C 93.73 71.81 55.57
Vapor enthalpy, kJ/kg 2666.3 2629.6 2602.4
Condensed flowrate, kg/h 15012.9 13607.46 12335.4
Condensation temperature, C 129.08 93.7 71.81
Condensed enthalpy, kJ/kg 540.4 392.4 300.7
Table 4
Optimum number of effects for different steam inlet pressures
Pv0, kPa Number of optimum effects
Minimum total cost Maximum NPV
110 4 2
120 4 2
130 4 3
140 4 3
150 4 3
160 4 3
170 4 3
200 4 3
230 4 3
260 5 3
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It appears of extreme relevanceto consider quality as an intrinsic
and integral part of the process design, as it will then be possible to
identify several potential improvements in different food processes.
Acknowledgements
Author Ricardo Simpson is grateful for the financial support
provided by CONICYT through the FONDECYT project number1070946. Author Sergio Almonacid is grateful for the financial sup-
port provided by CONICYT through the FONDECYT project number
1070512.
References
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Himmelblau, D.M., Bischoff, K.B., 1968. Process analysis and simulation:deterministic system. Wiley, New York, USA.
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