Full text of DOI:10.1111/j.1365-2621.2000.tb16028.x

JFS: Food Engineering and Physical Properties
Optimizing Apple Juice Extraction
in Multiple Presses
M.T. GONZÁLEZ, M.P. ELUSTONDO AND M.J. URBICAIN
ABSTRACT: A method was developed to find the optimum hydration flow sheet that maximizes either the profit or
the soluble solids recovery for a given number of presses in an apple concentrate juice plant. The pomace arising
from a press can be wetted with either pure water or dilute juice from downstream presses, or a mixture of both in
any proportion. The mass balance around the presses involving any hydration arrangement was posed as an array
named connectivity matrix. The connectivity matrix and the economical balance were written in computer code in
order to carry out the optimization procedure. The optimization started from a minimum amount of water, and
stepwise increasing levels of hydration were evaluated. The best value of this combinatorial search was retained.
The optimum arrangement was pure countercurrent in most of cases considered.
Key Words: extraction, hydration, apple juice, optimization, press
sugar recovered from the solid matrix, which in turn means a sav-
Introduction
ing in raw material. However, it also means a larger amount of wa-
ter to be evaporated to get the concentrate, increasing the manu-
facturing costs.
N APPLE JUICE MANUFACTURING, IT IS A COMMON PRACTICE TO
I
hydrate the pomace resulting from one press and send it to
the next for further extraction. This procedure can be repeated in
a set of presses in series, and each one can receive the pomace
from the preceding one previously hydrated. However, hydra-
tion has certain limits, because one press may be flooded if hy-
drated in excess, and it should be taken into account that if juice
is to be concentrated, the evaporation cost increases.
It could be expected then to have a break-even point that
makes the whole operation optimal in terms of the profit. In the
analyzed example, the full line on Fig. 1 shows that the best re-
sults are obtained at a relatively low degree of hydration, in this
case at 30%. It must be remarked that the simulation was per-
formed for increments of 10% in the hydration level, finding the
best result for 30%, though the fitting polynomial shows a maxi-
mum at approximately 27%. In a real case, it should be advisable
to perform additional runs between 25% and 30% at 1% intervals
to find the actual maximum.
A plant manufacturing apple juice concentrate (AJC) usually
has 2 different working periods during the year, in accordance
with the raw material supply, because it defines not only the
price but also the way the evaporation costs will be considered.
The evaporation stage is usually the bottleneck, hence if the
apple availability is large, the evaporator will work at full capac-
ity, the involved costs are fixed, and the incidence of apple
costs is lower. Conversely, several months after the harvest sea-
son, apples are supplied from cold storage in smaller quanti-
ties, making the evaporating costs variable in accordance with
the operation time required, and the relative weight of costs is
inverted.
The results show conclusively that the plant management
must be careful in deciding the degree of hydration from the
point of view of the raw material consumption only. A good figure
in the raw material cost component could be a bad one when the
general balance is drawn.
The optimal flow sheet for the selected example with that de-
gree of hydration is shown in Fig. 2. Water wets press 5 at a flow
The objective of this work is to devise a method to find the op-
timum hydration flow sheet for a given number of presses, which
maximizes either the profit or the soluble solids recovery. The
model is posed for 2 alternative situations: The raw material is-
large enough to saturate the plant evaporation capacity or there
is a shortage that makes the evaporator work on demand.
Results and Discussion
HE ALGORITHM DESCRIBED WAS PROGRAMMED IN FORTRAN
Tand tested with different examples of both saturated evapo-
rator and raw material shortage seasons (González 1990;
González and Urbicain 1998).
In Fig. 1, the results of the optimization set of five presses, in
terms of both the net profit and the sugar recovery, are present-
ed as a function of hydration level, expressed as percentage of
the pomace mass processed.
Regarding the sugar recovery, it is apparent that the dotted
line grows monotonically, suggesting hydrating as much as possi-
ble within practical limits. This is not unexpected because the
larger the amount of water introduced, the larger the amount of
Fig. 1—Net profit and sugar recovery as a function of hydration level
for a 5-presses set
© 2000 Institute of Food Technologists
Vol. 65, No. 3, 2000—JOURNAL OF FOOD SCIENCE 461

Optimizing Apple Juice Extraction in Multiple Presses . . .
from press 5 while 100 kg/h of juice collected from presses 1 (60
kg/h) and 2 (40 kg/h) goes to clarification. Juice from presses 3, 4,
and 5 are used to hydrate upstream presses at the rates indicat-
ed in the figure.
Finally, even though most of the examples showed an opti-
mum for a purely countercurrent flow arrangement, as could be
expected, the presented example shows that it is not always true.
The result is a complex function of many economical and techni-
cal variables involved, so each case must be analyzed consider-
ing its cost structure and processing capacity at each particular
season.
Conclusions
SIMPLE ALGORITHM TO OPTIMIZE THE POMACE HYDRATION
Fig. 2—Flow diagram of the 5-presses set for a hydration level of
30% of fresh pulp fed
A
policy before repressing is presented. It is to be applied to an
existing plant having 2 or more presses, either piston or continu-
ous, to determine the amount of water to be added and the con-
rate of 30 kg/h while 100 kg/h of raw material feed the first one. nections flow sheet, in order to maximize the net overall profit of
The exhausted pomace at a rate of 30 kg/h leaves the system the whole plant operation.
Materials and Methods
Nꢁ1
W jꢃ1Xjꢃ1
ꢁ
kꢅjꢁ1
VjkYk ꢅW X ꢁJ Y
(2)
ꢄ
j j j j
Material balance
Let N be the number of presses in a pressing train as
sketched in Fig. 3, where ꢀj is the yield of generic press “j,” the
yield being defined as the mass of juice produced by the unit
mass of fresh pulp. It must be recalled that this definition is
only valid for the pressing of fresh pulp, being meaningless if
hydrated pomace is being pressed.
Taking into account the definition of yield ꢀj given above, it
is ꢀj ꢅ 1ꢃWj, and the calculation of the difference of pomace
mass delivered by 2 consecutive presses is straightforward:
Wjꢃ1 ꢃWj ꢅꢀj ꢃ ꢀ
(3)
jꢃ1
In order to make the calculation general, and assuming the
fresh water inlet is made in the last press, noted N, the water
supply will be considered as a virtual press N ꢁ 1, which obvi-
ously will not produce any juice. With the exception of press 1,
which processes fresh pulp and hence will be not hydrated,
the remaining 2 to N units, can be hydrated in any proportion
by juice provided by one or more of the following presses in the
set, including “press” N ꢁ 1, which means fresh water. In sum-
mary, press j (2 ꢂ j ꢂ N) can receive either water or juice from
anyone between press j ꢁ 1 and N ꢁ 1.
Eq. 1 can be written:
J ꢅꢀj ꢃ ꢀjꢃ1 ꢁVjh
(4)
j
where Vjh is the summation of all wetting streams flowing onto
press j from all presses located downstream it, as given by Eq. 5:
Nꢁ1
Vjh ꢅ Vjk
ꢄ
(5)
kꢅjꢁ1
In what follows all equations are referred to 1 kg of fresh
pulp.
Mass balance can be completed with the following equa-
tions:
Let Vjk be the juice produced by press k that is sent to hy-
drate the pomace in press j. An elemental material balance
around press j gives Eq. 1:
Jj ꢅ Cj
ꢁ
Bj
(6)
Nꢁ1
where Cj is the fraction of juice following the process and Bj the
W jꢃ1
ꢁ
kꢅjꢁ1
V
ꢅW ꢁJ
j
(1)
ꢄ
jk
j
fraction used for hydration of the preceding presses. Hence:
jꢃ1
B ꢅ
j
V
(7)
A similar balance on soluble solids gives Eq. 2:
ꢄ
kj
2
kꢅ
Fig. 3—Sketch of a set of N presses with a general flow diagram of hydrating steams
462 JOURNAL OF FOOD SCIENCE—Vol. 65, No. 3, 2000

If W0 is the mass flow rate of fresh pulp, assumed to be 1 kg,
the yield of the first press is equal to the juice mass flow rate
produced in that unit:
Yj ꢅ(Wjꢃ1Xjꢃ1 ꢁ Vj,aveYh ꢃ WjXj)/Jj for (ꢀjꢃꢀj-1) ꢇ 0
(16)
Symmetrically, for (ꢀjꢃꢀj-1) ꢆ 0, press j will not extract all the
wetting liquid added, but part of it will remain diluting the pom-
J1 ꢅꢀ1 ꢅW0 ꢃW1
Overall mass balance:
(8)
ace.
Hence:
YꢅY*
for (ꢀjꢃꢀjꢃ1)ꢂ0
(17)
(18)
N
j
j
W0 ꢁBNꢁ1 ꢅWN ꢁ Cj
ꢄ
Overall soluble solids mass balance:
(9)
jꢅ1
Xj ꢅ (Wjꢃ1Xjꢃ1 ꢁ Vj,aveYh ꢃ JjYj)/Wj for (ꢀjꢃꢀjꢃ1)ꢆ0
N
Eq. 11 and 18 are valid for presses 2 to N; for press 1 results
W0X0 ꢅWNXN ꢁ CjYj
ꢄ
(10)
Y1 ꢅ X0 and X1 ꢅ X0.
jꢅ1
To analyze the influence of the hydration in a given press j,
a concept similar to that of equilibrium stages is introduced
(Urbicain and others 1990). When hydration takes place, fresh
water or lean juice is mixed with richer juice trapped in the
pomace, and sugar is expected to diffuse from the juice to the
wetting liquid. Should that mixing be perfect, the final liquid
should have an uniform, theoretical concentration Yteor, j given
by the mass balance expressed by Eq. 11:
Economical balance
Profit, in terms of money units per time unit, is calculated
by Eq. 19:
G ꢅJc (Pv ꢃCT) ꢃCF
(19)
where fixed costs CF and selling price Pv are data, and concen-
trate flow rate Jc and variable costs CT are calculated by the
program as follows:
Yteor, j ꢅ (Wjꢃ1Xjꢃ1 ꢁ VjhYh)/(Wjꢃ1 ꢁ Vjh)
(11)
1) Juice concentrate flow rate, Jc:
and Yj,aveis the average concentration of Vjh, as given by Eq. 12:
Nꢁ1
Jc ꢅJFBF/Bc
(20)
Yj,ave
ꢅ
VjkYk /Vjh
kꢅjꢁ1
(12)
ꢄ
( )
Calculation of juice mass flow rate fed to the evaporator, JF ,
depends of the situation considered, which in turns changes
along the year:
Yteor,j cannot be attained in practical operation, but a lower
equilibrium value Yj* ꢆ Yteor,j will be the actual concentration of
the juice, while the concentration of the liquid originally wet-
ting the pomace, Xjꢃ1, is reduced to a value, Xj* ꢇ Yteor,j in equi-
librium with Yj*.
(a) saturated evaporation (SE), corresponding to a situa-
tion of raw material surplus, usually encountered during har-
vest months season, which makes the evaporator work at full
capacity, and
Let Zj be a diffusion factor, in the form of a dimensionless
concentration given by Eq. 13, as a measure of how efficient
the hydration has been in capturing sugar from the pomace:
(b) evaporation idle capacity (IC), corresponding to a short-
age of raw material, usually encountered during post-harvest
season, making the evaporator work “on demand.”
In the first case JF is a function of the actual evaporation ca-
pacity and is calculated by Eq. 21:
Zj ꢅ (Yj* ꢃYj,ave)/(Yteor,j ꢃYj,ave
)
(13)
In a perfect mixer Yj* tends to Yteor,j, and Zj tends to 1. Yj* can
JFSEꢅ Ev(1 ꢃ BF/Bc )
(21)
be obtained rearranging Eq. 13, with Zj ꢆ1.
Xj* is given by the amount of soluble solids contained in Wj, and
calculated by difference
In case b) JF is calculated as a function of the mass flow rate
of processed pulp, by means of Eq. 22:
Xj* ꢅ(Wjꢃ1Xjꢃ1 ꢁVjh Yj,ave ꢃ Yj*Vjh)/Wjꢃ1
(14)
JIFC ꢅ PRc(W0X0 ꢃ WNXN)
(22)
however, actual values Xj and Yj leaving the press are equal to
equilibrium ones in the particular case of (ꢀj ꢃ ꢀjꢃ1) ꢅ 0 only.
Should it be the case, press j is expected to produce the same
amount of pomace than press (j ꢃ 1), independent of the de-
gree of hydration, so if no water is added, no juice is produced.
Otherwise, any amount of water added should leave the press
as juice Jj and the final concentrations in the juice and the
pomace liquid would be Yj ꢅ Yj* and Xj ꢅ Xj* respectively.
If (ꢀjꢃꢀj-1) is not equal to 0, concentrations are to be calcu-
lated in a different manner. Let (ꢀjꢃꢀjꢃ1) be ꢇ 0. That means
that press j will extract all the liquid added plus some of the liq-
uid entering with the pomace. In this case:
When JF is calculated by means of Eq. 21, the pulp mass
flow rate that can be processed is obtained by rearranging Eq.
22 and using the found value of JF:
P ꢅ JSFE/Rc(W0X0 ꢃ WNXN)
(23)
If, alternatively, JF is calculated by Eq. 22, the dependent
parameter is the water to be evaporated, and it is calculated as
the difference between the juice flow rate fed to the evapora-
tor and the concentrate:
Ev ꢅ JIFC ꢃ Jc
(24)
X ꢅX*
for (ꢀjꢃꢀjꢃ1)ꢈ0
(15)
2) Variable costs, CT:
Factor CT in Eq. 19 is the summation of 4 terms:
j
j
Vol. 65, No. 3, 2000—JOURNAL OF FOOD SCIENCE 463

Optimizing Apple Juice Extraction in Multiple Presses . . .
jꢃ1
(hij ꢁ cj) ꢅ 1
j ꢅ 3, …, Nꢁ1
(34)
CT ꢅ CMꢁ Cp ꢁ Cz ꢁ CE
(25)
ꢄ
iꢅ2
where
Coefficients cj can be related to pitch p by means of factors
kjj with a relationship similar to Eq. 32:
CM ꢅ PMRj
(26)
the parameter Rj being the ratio between pressed pulp and-
concentrate produced:
cjj ꢅ kij/p
(35)
(36)
Then Eq. 34 becomes:
Rj ꢅP/Jc
(27)
j
kij ꢅ
p
Cp is a datum entered by the user.
ꢄ
iꢅ2
Cz is the cost of enzyme treatment, which could be done to
the pulp before pressing in order to increase the yield and de-
pends on the enzymes price, Cz, and the applied doses, Dz,
and it is calculated by Eq. 28:
kij is also a natural number such that 0 ꢂ kij ꢂ p and Eq. 36
must be satisfied N ꢃ 1 times, namely for j ꢅ 3, …, N ꢁ 1.
Calculations to be performed are all material and economi-
cal balances for all possible combinations of kij. It must be not-
ed that for a given p, there are (j ꢃ 2) degrees of freedom in
each press, excepting the fresh water supply, virtual press N ꢁ
1, for which element kN+1,N+1 is always 0, making (j ꢃ 3) degrees
of freedom.
Cz ꢅ PzDzRj
(28)
Regarding the evaporation cost CE, when raw material is the
process bottleneck (situation b) as mentioned above), it is cal-
culated by means of Eq. 29:
As an example, let it be a set of 4 presses, hence Eq. 36 can
be posed 3 times. Let it be p ꢅ 2, which means that the juice
delivered by any press is to be divided in 2 equal streams, one
going to another press and the remaining half going either to
clarification or to a third press. The resulting equations are:
CE ꢅ EvCv/JC
(29)
where Cv is the cost of evaporate 1 kg of water.
Conversely, when the evaporator is saturated, evaporation
cost is a constant included in CP and CE ꢅ 0.
k23ꢁk33 ꢅ2
k24 ꢁk34 ꢁk44 ꢅ2
k25 ꢁ k35 ꢁ k 45 ꢅ 2
Optimization
(37)
Optimization seeks the best hydration flow sheet, among
all possible arrangements between presses, having as objec-
tive either the maximum profit or the maximum sugar recov-
ery.
MATRIX A
With reference to Fig. 1, Vij is a fraction of Jj and can be ex-
pressed as:
Vij ꢅ hijJj
(30)
where hij is a factor between 0 and 1.
Considering Eq. 6 and 7, inequality Eq. 31 must be true:
jꢃ1
h
iꢅ2
1
(31)
ꢄ
ij ꢂ
Coefficients hij are the elements of a triangular superior
matrix, named connectivity matrix because its elements define
the amount of juice from press k that goes to wet press j. This
matrix has Nꢃ1 rows, representing the hydrated presses from
2 to N, and N ꢃ 1 columns, identifying the source presses,
from 3 to N ꢁ 1.
We define a variable named “pitch,” noted p, a natural
number equal or larger than 1, to determine the minimum
amount of juice allowed to flow from one press to another. The
pitch is related to hij by a simple expression, valid for i ꢆ j:
MATRIX B
hij ꢅKij/p
Fractions of juice going to clarification are defined as:
cj ꢅ Cj/Jj
(32)
(33)
The cj’s can be added to RHS of inequality Eq. 32 to make it
an equation:
464 JOURNAL OF FOOD SCIENCE—Vol. 65, No. 3, 2000

The possible values of the kij are 0, 1, and 2 respectively,
while k33, k44, and k45 result from the values assigned to k23, k24
34, k25 and k35
The complete set of cases to be studied are represented by
Matrix A.
In this case 108 alternatives will be evaluated. For example,
which is the minimum amount of water required for all the
presses to produce some juice.
,
k
.
Hence, the program evaluates all possible configurations,
starting with the critical hydration as the minimum value, se-
lecting the best of them on the basis of the selected criteria,
the hydration level is increased in a certain arbitrary, and the
procedure is repeated until the maximum selected hydration
is reached.
if we assume k23 ꢅ 1, k33 ꢅ 1, k24 ꢅ 1, k34 ꢅ 1, k44 ꢅ 0, k25 ꢅ 0, k35
ꢅ 2, k45 ꢅ 0, the hij’s and cj’s will be those shown in Matrix B.
Elements of Matrix B show that fresh water will wet press 3
only, juice from press 4 will wet presses 2 and 3 in equal parts,
while 50% of the juice from press 3 will go to press 2, and the re-
maining 50% will go to clarification. If p ꢅ 4, the number of cas-
es to evaluate rises up to1125, and for p ꢅ 10, 47916 calcula-
tions will be required.
It is worth to mention that not all calculated configurations
are physically or practically feasible, so some heuristics are in-
troduced to discard them immediately. For example, the total
hydration could be larger than the critical but could be dis-
tributed in such a way that for some particular press it is not.
In that case the configuration is eliminated. Another case is
when the amount of liquid entering to a given press is such
that the unit would be flooded; it is also discarded.
If the train has 5 presses, for p ꢅ 1, cases evaluated will be
96, for p ꢅ 2, 1800, for p ꢅ 4, 91875, and for p ꢅ 5, 395,136. This
means an exponential growth in the number of calculations as
p increases.
Nꢁ1
One heuristic adopted is that ꢄVjk in press j must be lower
kꢅjꢁ1
Optimization can be performed with either the net profit or
the maximum sugar recovery as objective function. One con-
straint to be taken into account is the amount of fresh water
added to the last press: It can not be unlimited so a certain
maximum hydration must be defined. A practical way is to
take it as a fraction of the total amount of pulp to be processed,
selected with some heuristic criterion.
than 1.5 the mass flow rate of pomace fed to the press. If at a
certain level of hydration all configurations are neglected be-
cause that condition is not satisfied, it means that no further
hydration is possible, and the iteration stops.
In any case, once all best configurations have been select-
ed at each level of hydration, the program selects the best
among them, with it the corresponding hydration flow rate
and reports the result.
In the other end, it is the “critical hydration,” a concept pre-
sented in a former paper (Elustondo and Urbicain, 1992),
Nomenclature and units
Pv
Pz
Rc
V
Concentrate selling price [U$S / kg concentrate]
Enzyme price [U$S / kg enzyme]
Bc
BF
Brix degrees of concentrate [kg sol.solids / kg concentrate]
Brix of juice fed to evaporator [kg sol.solids / kg concen-
trate]
Clarification yield [kg of raw material / kg. conc.]
Juice flow rate wetting press j from press k [kg / kg of
raw material]
jk
Bj
Juice flow rate from press J [kg / kg of raw material)
Concentrate evaporation cost [U$S / kg concentrate]
Water evaporation cost [U$S / kg vapor produced]
Juice flow rate to clarification from press j [kg / kg of raw
material]
W
Pomace from press j [kg / kg of raw material]
Sugar concentration in pomace from press j [kg / kg
pomace]
CE
CV
Cj
j
X
j
*
X
Sugar equilibrium concentration in pomace from press
j, [kg /kg pomace]
j
CM Raw material cost [U$S / kg concentrate]
Y
Sugar concentration in juice from press j [kg / kg juice]
Cp
CT
Cz
Dz
Ev
G
Processing cost [U$S / kg concentrate]
Total cost [U$S / kg concentrate]
Enzymes treatment cost [U$S / kg concentrate]
Enzymes addition [kg / kg of raw material]
Water evaporated [kg/h]
j
References
Elustondo MP, Urbicain MJ. 1992. Critical hydration in a series of presses for apple juice
manufacture. J Food Engineering 17: 217–224.
González MT. 1990. Programa Hidrat, PLAPIQUI.
Net profit [U$S / h]
González MT, Urbicain MJ. 1998. Optimización de la hidratación en un tren de prensas. II
Congreso Iberoamericano de Ingeniería de Alimentos, Bahía Blanca March.
Urbicain MJ, Elustondo MP, Ramos MA. 1990. Computer Simulation of an ACJ Plant. Sym-
posium of the International Federation of Fruit Juice Producers; May 17; Paris.
MS 19990608 received 6/1/99; revised 1/4/00; accepted 3/30/00.
GF
hij
Jc
Fixed costs [U$S / h]
Fraction of juice from press j wetting press i [ - ]
Concentrate mass flow rate [kg/h]
Juice fed to the evaporator [kg/h]
Juice from press j [kg / kg of raw material]
Factor in equation (32)
JF
Authors express their acknowledgment to the National Research Council of Argentina
(CONICET) and to Universidad Nacional del Sur for their support to this work.
Jj
kij
p
Authors are with the Planta Piloto de Ingenieria Qui9mica (UNS-CONICET)
Camino La Carrindanga Km 7, C.C. 717, (8000) Bahia Blanca, Argentina.
Address inquiries to M.J. Urbicain (e-mail: alurbica@criba.cdu.ar).
Pitch, variable in equation (32)
Fresh pulp mass flow rate [kg/h]
P
PM Raw material price [U$S / kg of raw material]
Vol. 65, No. 3, 2000—JOURNAL OF FOOD SCIENCE 465