Proc. Fla. State Hort. Soc. 118:423-428. 2005.
A REFEREED PAPER
DESIGN OF PERFORATION-MEDIATED MODIFIED ATMOSPHERE PACKAGING
FOR SHREDDED CARROTS: MATHEMATICAL MODELLING
AND EXPERIMENTAL VALIDATION
JULIO MONTANEZ,1 FERNANDA A.R. OLIVEIRA,1* JESUS FRIAS,2
MANUEL PINELO,1 PRAMOD V. MAHAJAN,1 LUÍS M. CUNHA3,4
AND M. CONCEIÇÃO MANSO3,5
1Department of Process and Chemical Engineering
University College
Cork, Ireland
2
School of Food Science and Environmental Health,
Dublin Institute of Technology
Dublin, Ireland
3
Post-Harvest Research Sub-Unit, CECA-ICETA
University of Porto
Porto, Portugal
4
SAECA, Faculty of Sciences
University of Porto
Portugal
5
FCS
University Fernando Pessoa
Porto, Portugal
Additional index words. Daucus carota, MAP, perforationmediated, shredded carrots, produce respiration
Abstract. Perforation-mediated modified atmosphere packaging (PM-MAP) consists of packing fresh produce in an airtight
package perforated by one or more tubes. The interplay between the product respiration rate (RR) and the rate of gas exchange through the tube(s) promotes an increase in CO2 and a
decrease in O2 concentration, the atmosphere eventually levelling off. The objective of this work was to design and validate
a package for shredded carrots, based on mathematical models earlier developed for predicting RR and gas exchange rate.
Different amounts of produce and tube dimensions were selected and experiments were performed at 10 °C (50 °F). Predicted and experimental gas compositions were quite different
and anaerobiosis was observed in almost every package. This
might be explained by an increase of RR during storage, as
earlier reported for shredded carrots stored in air. Another set
of experiments was then performed, halving the amount of
produce, and the equilibrium gas composition was in the recommended range. The RR at steady state was calculated by a
mass balance and it was found that the values were approximately three-fold those obtained with the predictive model,
The authors acknowledge financial support from the Irish Government
under the National Development Plan 2000-2006 and technical assistance
from Mr. Paul Conway. J. C. Montanez acknowledges financial support from
CONACyT, SEP and UAdeC.
Authors L. M. Cunha and M. C. Manso acknowledge financial support
from FCT with the contribution of FEDER funds, through contract POCTI/
AGG/48437/2002, Portugal.
*Corresponding author; e-mail: [email protected]
Proc. Fla. State Hort. Soc. 118: 2005.
which explains the difference between prediction and validation results. The respiratory quotient was however similar, approximately one, which shows that storage time increases RR
but does not influence the underlying mechanisms. It can
therefore be concluded that the design of MAP for shredded
carrots needs to take the effect of storage time on RR into consideration. As a rule of thumb, package design might be based
on the triple of RR predicted by existing models.
Florida is one of the biggest producers of carrots in the
US, being ranked number four in 1997. Almost all carrots
produced in Florida are for the fresh market, with only a
small percentage of the production for processed products
(canned carrots, carrot juice, etc.). Due to changes in consumer lifestyle, it is recommended that the food industry develop new products with added convenience (i.e., time and
work saving, and waste reduction; Moura and Cunha, 2005).
During the last years, development of new types of products,
namely of minimally processed fruits and vegetables, has
been increasing. In the US market sales of minimally processed fruits and vegetables in the year 2000 were estimated
about $10 billion to $12 billion (IFPA/PMA, 1999). The purpose of minimally processing is to deliver to consumers freshlike products with good visual quality (in terms of appearance) while ensuring food safety and maintaining their nutritional and sensory qualities (Wiley, 1994). Minimal
processing involves pre-treatments like washing, shredding,
trimming, peeling or slicing, to which fruits and vegetables
are submitted before packaging. During minimal processing,
fruits and vegetables alter their metabolism due to the breaking of protective surface structures, increased availability of
nutrients, and possible increase of microbial proliferation
(Barry-Ryan and O’Beirne, 2000). In order to extend the
shelf life of minimally processed products a number of technologies are available to control deteriorative processes.
Modified Atmosphere Packaging (MAP) can be interpreted as dynamic system with two gas fluxes, the respiration rate
of the fresh product and the gas exchange through the barrier (Van de Velde et al., 2002). Traditionally, food companies
have been using polymeric films to package fresh fruits and
vegetables with some success. However, most of the commercial polymeric films are suited to promote low levels of O2 and
high levels of CO2 in the package headspace, thus increasing
the risk of reaching anaerobic conditions, especially when the
packaged product has a high metabolic activity. Due the low
water vapour permeabilities presented by most MAP packaging films, moisture condensation in the inner film surface is a
common occurrence, leading to optimal conditions for microbial growth. There are others factors that make the use of
polymeric films unsuitable for a number of products as Oliveira et al. (1998) have pointed out.
Perforation-Mediated Modified Atmosphere Packaging
(PM-MAP) is an alternative system to conventional MAP with
polymeric films to control the gas exchange rates during the
423
storage of fresh products (Emond and Chau, 1990). It consists of macro perforations attached to gas-tight rigid containers (glass jars, plastic packages or corrugated cardboard
containers with an impermeable liner). It is ideal for products
requiring high levels of CO2 (10-20% v/v) and low levels of O2
(2-10% v/v) (Emond and Chau, 1990). Produce that have potential to be packed in PM-MAP include: avocado, blackberry,
blueberry, cherry, fig, lemon, lime, strawberry, raspberry,
spinach, sweet corn, broccoli, asparagus, mushrooms and
leeks (Baugerod, 1980; Emond and Chau, 1990), and a number of fresh cut produce such as shredded cabbage, shredded
or sliced carrots and carrot sticks, sliced or diced onions and
cubed cantaloupes (Fonseca, 2001).
PM-MAP has been reported to be an optimal packaging
technique for several fruits and vegetables such as leeks
(Baugerod, 1980), strawberries and broccoli (Emond et al.,
1991), shipped mixed loads of snap beans and strawberries
(Silva, 1995), spinach (Chimphango, 1996), broccoli (Ramachandra, 1995), cauliflower (Ratti et al., 1996), cut onion
(Lee and Renault, 1998), bananas (Stewart et al., 2005; Williams et al., 2001), galega kale (Fonseca et al., 1999) and sweet
corn (Riad et al., 2002). Until now, PM-MAP has been applied
mainly for whole fresh produce having high respiration rate,
but not for minimally processed shredded carrots.
The objective of this work was to verify the applicability of
PM-MAP for the storage of shredded carrots at 10 °C by combining the mathematical models previously developed by
(Iqbal et al., unpublished data) and Fonseca et al. (2000) for
RR of shredded carrots and gas permeability, respectively.
Mathematical Modelling
Joining a model developed by Fonseca et al. (2000) for
the kinetics of gas composition in PM-MAP packages with a
model developed by (Iqbal et al., unpublished data) to predict the respiration rate of shredded carrots, and assuming
that the gas exchange takes place through one tube only and
considering that the package contains a respiring product,
the equations obtained for O2 and CO2, are:
s
– yo
y
α xy o
dyo
c2
c ε
b
2
2 - – -----------------------------------------------------2- = a × D × L × ----- × ----------------------------y
2
dt
V
c
Γ
f
φ + y o × [ 1 + ------]
×e
–E
a
1---------- × --1- – ---------E
T T
g
ref
2
2
dy
c o2
-------------- =
dt
ϒ
W
× ----V
f
–E
a
1---------- × --1- – ---------s
E
T T
y
– y co
α xy o
g
W
ref
co 2
ε
2
2
β × a × D × L × ----2 × ------------------------------------- + RQ × -------------------------------------------------------- × e
× ----V
Γ
V
y
f
f
co 2
φ + y o × 1 + ------------ϒ
2
b
c
(1)
i
i
@ t = 0, y o = y o 2 ( 3 ) and @ t = 0, y o = y o 2 ( 4 )
424
2
Materials and Methods
Sample preparation. Carrots (Daucus carota) were purchased at a local supermarket (Tesco, Cork, Ireland). Carrots
were washed and peeled, topped and tailed using a sharp
knife. Carrots were shredded using a Moulinex (model 4400)
vegetable-processing machine equipped with a grating disk.
All the steps were carried out at 10 °C (50 °F) and the instruments used were previously disinfected with ethanol (95% v/
v). After shredding, carrots were packed immediately and
stored in a walk-in controlled temperature room at 10 °C (50
°F). Two experiments were conducted in order to verify the
effect of different amounts of produce on the equilibrium gas
composition. Details of experimental conditions tested are
showed in Table 2.
Perforation-mediated systems. PVC tubes with different
dimensions (Table 2) were used. For each experiments condition, a single tube was inserted in the lid of the glass jars (1.9
L, 0.067 ft3) fitted with stoppers for gas sampling. In order to
support the particles in the tube, a metallic net was placed in
the tube end. The packages were stored in a walk-in controlled temperature room at 10 ± 1 °C (50 ± 1.8 °F).
Gas concentration analysis. The changes in gas concentration (O2 and CO2) with time were measured by taking samples (every 24 h) through a septum of the package and
analyzing them by a gas analyzer (PBI Dansensor, Checkmate
9900, Denmark). Sampling had no influence on gas concentration in the jar, as the sampled volume, 5 - 6 mL (1.76 - 2.12
× 10-4 ft3), was negligible compared to the total volume of the
package.
Simulation study. Simulations to predict the kinetics of
gas composition change regarding O2 and CO2 during the
storage of shredded carrots in PM-MAP were developed using
MATLAB 6.0 (The Math Works Inc., Natick, Mass.).
Statistical analysis. Statistical analysis was performed to
verify how well the model predicted the experimental results
by estimating the root mean square error (RMSE) of the predictions (Yang and Chinnan, 1988):
(2)
where yo 2 and are the volumetric percentages of O2 and CO2,
respectively, Vf is the free volume inside the package, W is the
product weight, a, b and c are constants, β is the permeability
ratio, K co 2 ⁄ K o 2 is the permeability coefficient for O2 and CO2,
ε and Γ are the bed porosity and tortuosity factor, α, φ, and γ
are the Michaelis-Menten model constants, RQ is the respiratory quotient, is the activation energy, is the universal gas constants of the gases, T is the storage temperature and Tref is the
reference temperature. Model parameters for respiration
rate and permeability are reported in the Table 1.
Equations (3) and (4) state the initial conditions defined
by the gas composition of the package at the initial time:
2
Equations (1) and (2) form a system of two non-linear differential equations that simulate the evolution of O2 and CO2
in the package. This system cannot be solved analytically in its
general form and a numerical method is required to solve this
system.
RMSE =
1
--n
n
* 2
∑ ( Mi – Mi )
(5)
i=1
where Mi is the experimental gas concentration (O2 and
CO2), Mi* is the predicted value from the model; and n is the
number of experimental points.
Results and Discussion
First Study
Screening and assessment of metabolic activity state. Figure 1-I shows the changes of headspace composition of O2
and CO2 during the storage of shredded carrots packaged in
PM-MAP at 10 °C (50 °F). From this set of experiments, a rapid change in gas composition was observed during the first 72
h of storage reaching to anaerobic conditions. Carlin et al.
Proc. Fla. State Hort. Soc. 118: 2005.
Table 1. Respiration and permeability model parameters used in designing PM-MAP for shredded carrots.
Design variables
Symbol
Respiration rate-related
Package permeability-related
Value and units
α
γ
φ
Ea
Rg
Tref
RQ
5.88 × 10-9 m3 kg-1 s-1 (9.4374 × 10-8 ft3 lb-1 s)
40.70% v/v
0.44% v/v
69.00 kJ mol-1 (16.42 kcal mol-1)
8.314 × 10-3 kJ mol-1 K (1.987 × 10-3 kcal mol-1 K)
283.15 K
0.89 dimensionless
a
b
c
β
6.42 × 10-6 m2.148 s-1 (8.24 × 10-5 ft2.148 s-1)
1.45 dimensionless
-0.598 dimensionless
0.81 dimensionless
Γ2
1.12 dimensionless
(1990) reported anaerobic conditions after 3 d during the
storage of grated carrots in polymeric films at 10 °C (50 °F).
O2 decreased linearly until 72 h and after that the equilibrium
was reached at very low concentrations. CO2 concentration
increased linearly during the experiments, reaching to 20%
v/v after 80 h of storage. Fermentation was found in packages
A, B and D, which have lower permeability values for O2 and
CO2. For package C having a high permeability value (see Fig.
1-I-c) the gas compositions for O2 and CO2 at 96 h of storage
were 6.7% and 15.7% v/v, respectively. An equilibrium gas
composition was not reached in this package, even after 100
h of storage.
From Figure 1-I (a, b and d) it is possible to conclude that
RR of shredded carrots was higher than permeability values,
showing a faster depletion of O2 and a CO2 accumulation during the storage. It could also be inferred that RR of shredded
carrots might be higher than predicted by equations (1) and
(2). This effect may be possible due to changes of metabolites
available during storage of carrots. This would make that
batches of carrots stored for different periods of time before
the shredding and PM-MAP storage will present different
availability of nutrients and therefore will exhibit a different
respiration capacity.
While this effect produces a high variability between
batches of carrots stored during the harvest year, it would be
reasonable to expect that it does not affect the general metabolic behaviour of the carrot and its response to variations of
O2 and CO2. In this way, it would be expected that the main
assumptions and coefficients of equations (1) and (2) hold
valid and that the only effect that the storage time would have
is increasing the maximum respiration rate, and therefore affecting the α parameter in equation (1). This hypothesis was
further validated by the fact that the respiratory quotient of
these experiments was the same as the one predicted by the
model (data not shown). Moreover the effect of time on RR
for shredded carrots at ambient temperature has already
been reported (Iqbal et al., 2005).
After this first screening experiment, the analysis of experimental and predicted gas composition showed that the
experimental RR was higher than the predicted from the
equation (1) increasing the parameter α by a factor of 2.98.
In order to study the suitability of the model for PM-MAP,
now with the correction factor on α, a new experiment was
designed. To reduce the risk of anaerobiosis, the amount of
produce in the package was halved.
Second Study
Assessment of the model predictions with the corrected model. Figure 1-II shows the changes in O2 and CO2 compositions during the storage of shredded carrots at 10 °C. The
experimental conditions for the second part of the experiments are presented in the Table 2 (column 5). Figure 1-II
also shows RR changes predicted by equations (1) and (2).
There is a large deviation between experimental and predicted values of O2 and CO2 gas concentrations. Changes in experimental gas composition in the packages were faster than
those predicted by the model. An analysis of the experimental
and the predicted gas composition (data not shown) showed
that the experimental RR is higher than the predicted from
the model 2.98 times. This effect may be possible due to an
increment of the metabolic activity during the storage of carrots. Fonseca (2001) also observed these deviations in the kinetics of gas composition during the storage of shredded
galega kale, but when considering a time effect on the respiration rate model, the predictions were successfully in agreement with the experimental data. If such a time effect occurs,
it must be considered in the design of MAP packages.
Table 2. Experimental conditions used to test the applicability of PM-MAP to extend the shelf life of shredded carrots.
Perforation dimensions
Package
A
B
C
D
Weight of produce, kg
Diameter, mm
Length, mm
Experiment 1
Experiment 2
7 (0.022 ft)
7 (0.022 ft)
9 (0.029 ft)
9 (0.029 ft)
23.5 (0.077 ft)
31.5 (0.103 ft)
15.5 (0.050 ft)
31.5 (0.103 ft)
0.38 (0.837 lb)
0.29 (0.628 lb)
0.30 (0.661 lb)
0.38 (0.837 lb)
0.19 (0.419 lb)
0.14 (0.314 lb)
0.30 (0.661 lb)
0.19 (0.419 lb)
Proc. Fla. State Hort. Soc. 118: 2005.
425
Fig. 1. Changes in gas composition during the storage of shredded carrots in PM-MAP. The symbols represent the experimental data values and the solid
lines predicted values by equations (1) and (2) (, O2 and , CO2). I—Data from the first study (conditions shown in Table 1— experiment 1); II—Data
from the second study (Table 1— experiment 2); III - Data from the second study, showing simulations using a correction factor of 2.98 for α. a) Package A
(packed tube with ε = 0.32); b) Package B (ε = 0.32); c) Package C (ε = 0.37); d) Package D (ε = 0.37).
Considering such time effect and adding the factor of
2.98, as mentioned earlier, the mathematical model was modified. Figure 1-III shows the new simulations, considering the
426
correction factor in the respiration rate. It can be seen that
the model describes better the kinetics of O2 and CO2 changes. When decreasing the weight/volume ratio in the package,
Proc. Fla. State Hort. Soc. 118: 2005.
the equilibrium gas compositions reached levels close to the
optimal recommended for shredded carrots (O2 levels from 1
to 5% v/v and CO2 levels from 15 to 20% v/v). All the tube
dimensions tested leaded to conditions on the optimal gas
composition range at steady state. By analyzing the Figure 1III, it can be observed that the predicted transient changes in
gas composition were faster than those of experimental values, independently of the tested package. With this observation one can assume that the respiration rate of shredded
carrots increases with time.
Equilibrium gas compositions were reached after 100 h of
storage independently of the tube dimensions inserted in the
packages. In packages with tubes of 9 mm diameter (0.029 ft)
and 15.5 mm (0.050 ft) length (package C), the equilibrium
gas composition of O2 was higher (7% v/v) than the recommended value (Fig. 1-III-c). However, the CO2 gas composition was 16% v/v, being in the recommended range. To reach
the optimal gas levels in this package an increment in the
ratio weight/volume or a decrease in permeability values
(reducing tube diameter or increasing tube length) could decrease the O2 levels. However care must be taken due to possible temperature fluctuations during the storage, as these
fluctuations when above the recommended temperature
could lead to a decrease of O2 levels and an increase of CO2
levels inside the package, tending to anaerobic conditions
that will decrease the marketability and the safety of the product. Figure 1-III showed that the model predicted satisfactorily the changes in gas composition during storage of shredded
carrots in PM-MAP.
Temperature is a very important factor to control during
the storage of fresh produce in MAP and PM-MAP systems. In
experiments reported in this paper, the temperature values
inside the packages were higher than the external temperature (set point), being this difference in the range of 1 to 2 °C
(33.8 to 35.6 °F) (data not showed). This difference in temperature could be attributed to the heat generated during
respiration of shredded carrots along storage.
RMSE values (equation 5) calculated from experimental
and predicted values for changes in gas composition during
storage of shredded carrots are given in the Table 3. From
this table it can be seen that the model used to predict the
headspace changes of O2 and CO2 in the package provides adequate predictions over the wide range of experimental conditions under the present study.
On overall, differences between the experimental and
model predictions were in the range of 1.43 to 2.48% v/v for
O2 and 1.84 to 2.81% v/v for CO2, with this values being much
smaller closer to the equilibrium conditions.
Table 3. Root mean square error, RMSE (equation (5)), between the experimental and predicted O2 and CO2 (using equations (1) and (2)) during the
storage of shredded carrots in perforation-mediated MAP at 10 °C (50 °F).
Tube dimensions
D, mm
7 (0.022 ft)
7 (0.022 ft)
9 (0.029 ft)
9 (0.029 ft)
Gas
L, mm
O2, % v/v
RSME
CO2, % v/v
RSME
23.5 (0.077 ft)
31.5 (0.103 ft)
15.5 (0.050 ft)
31.5 (0.103 ft)
1.79
1.43
1.52
2.48
2.81
1.84
2.16
1.94
Proc. Fla. State Hort. Soc. 118: 2005.
Conclusions
A mathematical model describing the kinetic changes of
gas composition during the storage of shredded carrots was
applied. Perforation-mediated modified atmosphere packages
were tested experimentally for the storage of shredded carrots
at 10 °C (50 °F). From the experimental results it was observed
that for this particular batch of produce the respiration rate
(RR) values were 2.98 times that those obtained with the predictive model, which explains the difference between prediction and validation results. New simulations were developed to
include this effect on the respiration rate model, and the simulations showed very good fit to the experimental data. It can
therefore be concluded that the design of MAP for shredded
carrots needs to take the effect of storage time on RR into consideration. As a rule of thumb, package design might be based
on the triple of RR predicted by exiting models.
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