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thesis entitled

PREDICTION OF MOISTURE CONTENT OF PACKAGED
DRY FOOD PRODUCTS BY A CALCULATION
BASED ON SIMULATION I

presented by
RANDY A. KLIMENT

has been accepted towards fulfillment
of the requirements for

M.S. degreeinscm’o' of Packaging

”W333

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Major professot I
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A st I , l979
Date ugu 5

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PREDICTION OF MOISTURE CONTENT OF PACKAGED
DRY FOOD PRODUCTS BY A CALCULATION

BASED ON SIMULATION

BY

Randy A. Kliment

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

School of Packaging

1979

ABSTRACT
PREDICTION OF MOISTURE CONTENT OF PACKAGED

DRY FOOD PRODUCTS BY A CALCULATION
BASED ON SIMULATION

BY
Randy A. Kliment

The storage life of packaged dry food products may
depend on a number of factors but one of the most important
is the adsorption of moisture to some critical level.

In real life the temperature and relative humidity are
changing. The purpose of this study was to set up condi-
tions where the temperature and relative humidity are
constant during any storage interval but changed from inter-
val to interval and predict the moisture content during
these intervals. Actual experimental testing was conducted
on three commercially available packaged dry food products
to determine the moisture content during short storage
intervals. Harsher condition changes were used between
intervals than expected in real life. Each packaged product
was subjected to at least one cycle, defined as subjecting
the samples to conditions of low temperature-low relative
humidity, transferring through storage intervals to condi-

tions of high temperature-high humidity, and back down

Randy A. Kliment

again to low temperature-low humidity. A calculation based
on simulation was then used to predict the moisture content
of the three products during short storage intervals corre-
sponding to the same conditions and time periods as used
for the experimental tests. The calculated results were in
good agreement with the actual experimental results.
Because of the extreme conditions the packaged products
were subjected to, it is expected that this method can be
used to calculate moisture content increase during actual

field storage.

Dedication

This thesis is dedicated to my family,
especially my parents, in gratitude for their
encouragement and assistance during this and
all other endeavors.

Also to Mr. John Barnes whose influence
on personal development and career selection

will always be remembered.

ii

ACKNOWLEDGEMENT S

The author wishes to thank Dr. Steven Gyeszly for his
considerable time and effort, encouragement, and guidance
while serving as major adviser. Thanks are also due to
Dr. Hugh Lockhart and Dr. Mark Ubersax for their criticisms
and suggestions as members of the thesis committee.

Also, a special note of appreciation is extended to
General Foods Corporation and in particular Mr. Harry
Topalian. Without his personal involvement and committment

this thesis might never have been completed.

 

iii

TABLE OF CONTENTS
Page
LIST OF TELES O O O O O 0 O O O O O O O 0 v

LIST OF FIGURES D O O O O C O O O O O O O 0 Vi

INTRODUCTION 0 C O O O O O O O O O O O O O 1
LITERATURE REVIEW . . . . . . . . . . . . . 4
DISCUSSION OF CALCULATION BASED ON SIMULATION. . . . 9

EXPERIMENTAL METHODS . . . . . . . . . . . . 18

A. Data Generation For Calculation . . . . . . 18

Initial moisture content. . . . . . . . . l9
Sorption isotherms. . . . . . . . . . 20
Water vapor transmission rate . . . . . . . 22
Surface area of the pouch . . . . . . . . 23
Fill weight of the package . . . . . . . . 23
Headspace volume of the package . . . . . . 23

B. Experimental Testing . . . . . . . . . . 24

Initial moisture content. . . . . . . . . 24
Test conditions of actual experimental testing . 25
Calculation of experimental moisture content . . 31

CAIICULAT ION O O O O O O O O O O O O O O O 3 6
Calculation of Permeability Constant from WVTR. . . 36
Calculation of Slope and Intercept. . . . . . . 37
Determination of Moisture Content by Calculation

Based on Simulation . . . . . . . . . . . 37

RESULTS AND DISCUSSION . . . . . . . . . . . 44

Experimental Error of Actual Testing . . . . . . 50

Experimental Error of Calculation Based on
Simulation 0 O O O O O O O O O O O O O 5 1

S HWY 0 O O O O O O O O O O O O O O O 5 6

REFERENCES . . . . . . . . . . . . . . 58

iv

10.

ll.

12.

LIST OF TABLES

Initial moisture content . . . . . . . .

Pouch surface area, headspace volume, and
package fill weight. . . . . . . . . .

Water vapor transmission rates . . . . . .

Test conditions, salt solutions, and equilibri-
um moisture content results for sorption
isotherms . . . . . . . . . . . . .

Experimental test conditions; results of experi-
mental and calculated moisture contents--
PrOduct A O O O O O O O O O O I O 0

Experimental test conditions; results of experi-
mental and calculated moisture contents--
Product B . . . . . . . . . . . . .
Experimental test conditions; results of experi-
mental and calculated moisture contents--
Product C . . . . . . . . . . . . .

Permeability constant as determined from water
vapor transmission rates . . . . . . . .

Permeability constant at temperatures used in
experimental testing . . . . . . . . .

Slope and intercept from sorption isotherms. .

Greatest percentage difference between calcu-
lated and experimental data . . . . . . .

Overall moisture content increases. . . . .

Page

26

26

26

27

32

33

34

38

38
39

44

45

LIST OF FIGURES

Page
Adsorption isotherms--Product A . . . . . 28
Adsorption isotherms-—Product B . . . . . 29
Adsorption isotherms--Product C . . . . . 30
Permeability constant as a function of
temperature--Package A . . . . . . . . 40
Permeability constant as a function of
temperature--Package B . . . . . . . . 40
Permeability constant as a function of
temperature-—Package C . . . . . . . . 40
Experimental and calculated results--
PrOduCt A O O O O O O O O O O I O 41
Experimental and calculated results--
PrOdUCt B O O I O O O O O O O O O 42
Experimental and calculated results--
PrOduct C C O I C O O C O O O O O 43

vi

INTRODUCTI ON

Stability of packaged dry food products depends
greatly on the protection provided by packaging. The
surrounding environment is detrimental to extended storage.
The amount of protection provided by the package depends on
the package's ability to act as a barrier between the
internal and external environment.

The shelf-life of a product is the length of time a

packaged product will remain of acceptable and saleable
quality when subjected to conditions of the distribution
environment. Dehydrated foods can deteriorate through
several mechanisms such as lipid oxidation, non-enzymatic
browning, enzymatic hydrolysis, degradation of proteins, and
caking leading to toughening or insolubility. Stability is
often determined by more than one environmental factor.
The objective of packaging a dry food product then is to
reduce or eliminate the rate of transport of water vapor
and/or oxygen through the package wall into the internal
environment. This is because the rate of deterioration
depends on the conditions of the internal environment.

Typically, industry methods for selecting an appro-
priate flexible packaging material to insure adequate shelf-

1ife and consumer acceptance have been based on actual

storage tests and experience. Actual long-term field
storage is the most direct method of determining shelf-life
but is expensive, time consuming, and impractical for
immediate introduction of a new product. As an alternative,
the food industry uses an accelerated test technique as a
common shelf-life determining tool.

This technique uses accelerated testing conditions
of temperature and humidity compared to normal distribution
storage conditions. Several packaging structures are
selected which have historically exhibited adequate protec-
tion for "similar" products. From these structures the one
that gives the best protection at accelerated conditions is
chosen as the packaging material for the product. This
method results in wasteful overpackaging and severely impedes
development of new packaging concepts.

Therefore a method is needed for calculating the
amount of packaging protection required that will greatly
reduce or eliminate overpackaging and also be more economical
than the accelerated test technique.

The purpose of this thesis is to apply a calculation
based on simulation to the determination of moisture content.
The calculation has been used previously to predict shelf-
life when storage conditions are constant (Manathunya 1976),
but is applied here in time-steps in which the testing
conditions are constant during any one interval and subse-

quently changed for succeeding intervals. This method has

application for prediction of shelf-lives of mass produced
goods that are dispatched into the real world of consumers
where the temperature and relative humidity fluctuate.

In designing a model to simulate fluctuating condi-
tions, drastic changes were used that are more severe than
those occurring in the course of a normal day. No attempt
has been made to determine actual product shelf-life. The
moisture content as a function of time due to changing
storage conditions was determined experimentally and com-
pared to calculated results for the same time periods and

conditions.

LI TERATURE REVI EW

Consumer acceptance of packaged dry food products
depends in large measure upon their quality at the time of
serving. These products may lose their appeal for a number
of reasons, but one of the most important is the loss of
consumer acceptance resulting from adsorption of moisture
from the atmosphere. Packages that resist water vapor
are used to prevent moisture adsorption by the product.

Deteriorative reactions of dry food products that
depend on moisture content are of two general types. The
first are reactions for which a definite critical moisture
content can be established, below which the rate of spoilage
is insignificant. Typical spoilage mechanisms which fall
into this category are bacteria and mold growth, enzymatic
spoilage reactions, recrystallization of sugars, and caking.
The second general type of reactions proceed at all moisture
contents but the rate of the reaction depends strongly on
the moisture content. Many of the reactions which cause
changes in texture, flavor, and color proceed in a manner
which is not dependent on a critical moisture content.

Storage life prediction for a food-package combina-
tion or the prediction of the package protection required

for a particular food have important application in food

packaging. The shelf—life of a packaged product in any
geographical location can be estimated by actual field
storage or by calculation from laboratory measurements of
the package and product under known atmospheric conditions.

The most direct method is the actual field storage
test because only two assumptions need be made. The first
is that the location chosen for the storage test is typical
of the larger general area and the second, that weather
conditions during the test were normal for the time of year
in that area. Careful selection of test locations will
minimize errors resulting from the test location not being
typical of the geographical area. Most field studies extend
for a long period which will tend to lesson the effect of
day-to-day weather variations. The storage life in a
particular area will be greatly influenced by the time of
the year that the products are placed into storage in that
area. Thus, the accumulation of shelf-life data by actual
field storage tests in all market areas for all seasons
becomes a very expensive and time consuming procedure.

To reduce the testing time and the associated high
costs of direct field storage, an accelerated test technique
was introduced. This technique uses high testing conditions
of temperature and humidity compared to normal distribution
storage conditions. Easter (1953) described how to predict
shelf-life from an accelerated laboratory test technique.

Actual testing of the product is conducted under normal and

accelerated conditions until the product is deteriorated or
unacceptable at the accelerated conditions.

The method typically involves the selection of
several packaging structures which have historically exhibi-
ted adequate protection for "similar" products. From these
several structures the one that gives the best protection
as determined by the accelerated testing conditions is
chosen as the packaging material for the product.

This method results in wasteful over-packaging and
severely impedes development of new packaging concepts. In
addition, the accelerated test technique assumes that
reactions that determine shelf-life proceed in the same
manner at accelerated conditions as they do at room condi-
tions. An assumption is also made that "similar products
will have similar room condition to accelerated condition
time ratios. This assumption is not correct in most cases
(Manathunya 1976).

A more scientific approach was introduced for the
prediction of shelf-life that considered properties of the
product, the package, and the internal and external environ-
ment. Several studies have been made in the past in which
the storage life and/or package protection requirements
have been calculated on the basis of certain properties of

the food or package.

Oswin (1945) developed a method to predict a
product's storage life based on adsorption of water by the
food to some critical level of moisture content. Felt et al.
(1945) extended this to the storage of cereals. Charie
et a1. (1963) used the same method for the prediction of
shelf-life of several dehydrated foods. Mizrahi et al.
(1970a) developed a simple mathematical model for predicting
moisture content change and extent of nonenzymatic browning
of stored dehydrated foods. This method could be applied to
determination of the packaging material to be used for a
desired shelf-life. Labuza et al. (1972) extended this work
to additional food systems. Aguilera et al. (1975) and
Davis (1970) have also done similar work for dried potatoes
and Harrington (1973) extended it to storage of seed.

Labuza (1968, 1971) has reviewed the area of maximum amount
of moisture in a food in terms of stability.

Simon et a1. (1971) introduced the same concepts to
the prediction of the shelf-life of a product which under-
goes oxidation. Quast and Karel (1972a,b) extended this
further to products which deteriorate through two mechanisms.
They studied potato chips which turn soggy from adsorption
of moisture and become rancid from oxidation. Mizrahi et al.
(1970b) and Karel et al. (1971) developed a mathematical
model to study the same effects on dehydrated cabbage.

During the past several years, techniques have been

developed to predict the self-life of packaged foods on the

basis of laboratory tests on kinetics of deterioration and
on mass transfer properties of packaging materials.
Reviews of this subject have been published recently by
Karel (1973, 1975), and Labuza (1972, 1973).

Mizrahi and Karel (1977a) developed a method for
accelerated stability tests which does not require prior
knowledge of the kinetic model of the effect of moisture
on rate of deterioration. This isothermal "no model" method
was later extended to include storage at different tempera—
tures by Mizrahi and Karel (1977b).

More recently, Chirife and Iglesias (1978) and
Boquet et a1. (1978) have reviewed the major equations for
fitting water sorption isotherms of foods. Resnik and
Chirife (1979) studied the effect of moisture content and
temperature on some aspects of nonenzymatic browning in
dehydrated apple.

The scope of this research is concerned with pre-
dicting the moisture content of packaged dry food products
at storage intervals by a calculation based on simulation.
The storage conditions of temperature and humidity change
from interval to interval but are constant during any

particular interval.

DISCUSSION OF CALCULATION

BASED ON SIMULATION

The moisture content--water activity of a food can
be used to predict the storage stability of a food. The
basis of this has been reviewed by Labuza et al. (1970) and
Labuza (1971) from the standpoint of the solvent properties
of water and the degree to which it is bound in food.

The control of water content of a food is a basic
food processing technique based on reducing the water con-
tent to a point that will prevent microbial growth. This
can be accomplished by drying or freezing in which the
water is made unavailable. Other methods involve binding
the water in a food by salting, sugaring, or by use of
chemical agents as used for intermediate moisture foods.

By eliminating the possibility of microbial growth,
the food stability depends on chemical reactions in the
food. The rates of these reactions can be predicted as a
function of the moisture content of the food. very few
reactions can proceed below the monolayer moisture content
value which require the solubilization of reactants and an
aqueous phase for reaction. Above the monolayer hydrolytic
reactions increase with increasing moisture content. Thus,

for prevention of these reactions it is best to keep dry

10

foods as close to the monolayer moisture content as possible
(Labuza 1975).

Since rates of reactions and ultimate storage life
depend on the moisfitre content of packaged dry food products,
a mathematical model that considers the important aspects
of the product, packaging material, and internal and external
environments of the package can be used to predict the
moisture content and shelf-life. Equations relating the
total amount of water in a closed package as functions of
the product, package, and environment have been reported
widely in food packaging.

During experimental storage the internal conditions
of the package are constantly changing in relation to the
constant external environment. By using short time-steps
and assuming the product in the package is in equilibrium
with the internal environment during each time-step, the
moisture content change can be simulated. This is referred
to as the calculation based on simulation.

By knowing the instantaneous internal and external
environmental conditions the change in the weight of the
moisture in the package can be calculated for a short time-
step. As the package gains or loses water the internal
conditions change for the next time-step. Therefore by
using short time-steps and assuming equilibrium the con-
stantly changing experimental conditions can be simulated

and the moisture content calculated based on this simulation.

11

The total amount of water in a closed package (M)
is the sum of the weight of the water in the product (M1)

and the weight of the water in the headspace (M2).

If W is the weight of the dry product in the package

and m is the moisture content (g moisture/100g dry product)

Ml=m'T66. . (2)

Assuming equilibrium in the package (the product
adsorbs the water which penetrated through the package very
rapidly) the moisture content depends on the internal rela-
tive humidity at constant temperature: m = f(Hi) where Hi is
the internal relative humidity. Therefore a relationship
between moisture content and internal relative humidity is
needed. This relationship can be described by the sorption
isotherm of a food.

The sorption isotherm of a food product is best
described as a plot of the amount of water adsorbed or
desorbed as a function of the relative humidity or activity
of the vapor space surrounding the material. This amount
of water is that which is held after equilibrium has been
reached at a constant temperature (Labuza, 1968).

There have been numerous mathematical equations
reported in the literature for describing water sorption
isotherms of food products. Adamson (1960) and Gregg and

Sing (1967) have reviewed the theoretical basis of the major

12

isotherm equations. Labuza (1968) has discussed the use of
these equations within the food field. The commonly used
equations have been summarized by Labuza (1975) and Iglesias
and Chirife (1976a). Additional equations have been suggested
by Iglesias and Chirife (1976b) and Caurie et al. (1976).

In this study the sorption isotherms were
determined for each product. It was found that within the
important range (from initial moisture content to the esti-
mated maximum acceptable moisture content) the curve can be
fitted by a straight line with good agreement. Therefore
in the case of the three products used in this study the
relationship between the equilibrium moisture content and

relative humidity can be expressed by:
m = a + bHi (3)

where a and b are constant. Using these relationships

Equation (2) becomes M1 = (a + bHiIfgfi (4)

By using ideal gas law (water vapor is not an ideal
gas but the error introduced in this case is negligible) the
weight of the water in the headspace can be given by the

equation:

_ 18V Hi
Mz'fiPSI‘OO ‘5’
where
V is the headspace of the package
T is the temperature
R is the gas constant

13

ps is the saturated water vapor pressure at T temperature
18 is the molecular weight of water
M2 is the weight of the water in the headspace

From Equations (4) and (5) the total amount of

water in a closed package at time (t) can be expressed as:
. W 18V H'
M“) = E+bH1<t] TDD + “ITO-'95 TOP (6)

and, the total amount of water in a closed package at time

(t + At) can be defined by:

.1“...

M(t+At)=IE-rbHi(t+A€] 100 + 18V PS HiIg+At2 (7)
RT

The term At is defined as the time-step of the calculation.
The permeation of vapors and gases through polymeric
packages can be described by Fick's laws of diffusion and
Henry's Law of solubility. The basic equation commonly used
by many authors for determining the quantity of moisture vapor
penetrated across a flexible barrier material during a time

period is:

— = g . A . (Pe-Pi) (8)

P is the permeability constant of the film divided by
x the wall thickness, wt/area . time - Aatm

A is the package surface area

Fe is the external water vapor pressure at a temperature,
atm

Pi is the internal water vapor pressure at a temperature,
atm

14

Generally, it is easier to measure the relative
humidity than to measure the water vapor pressure. The rela-
tion between the water vapor pressure and the relative humid-

ity is given by Equation (9).
P
P = I36 - RH (9)

Substituting Equation (9) into Equation (8) and

solving for Q gives (Manathunya 1976):

- E. o ’ s - .
AQ - x A I60 (He H1)At (10)
where
He is the external relative humidity, %
Hi is the internal relative humidity, %

At is the time-step, and At must be very small
AQ is the weight of moisture penetrated through the

container during At

The total moisture of the packaged product at any
subsequent interval (t+At) is the sum of the moisture at
time (t) plus the moisture penetrated through the container

during At. This can be expressed as:

M(t+At)

m(t) + A0 (11)

By knowing the internal relative humidity of the
package at any time the moisture content can be calculated
from the sorption isotherm curve and Equation (3). There-
fore, the moisture content at time (t+At) can be calculated
by knowing the internal relative humidity at time (t+At).

Substituting Equations (6), (7) into Equation (11)

15

and solving for the internal relative humidity at time

(t+At) gives equation (12).

 

_ - AQ
H(t+At) — H1(t) +—Wb + 1.331 S (12)
100 RT

The calculation uses time-steps for determining the
moisture content of the packaged product during any interval.
An interval is defined as the experimental conditions of
constant temperature and humidity that the package was
subjected to for a time period. The conditions of each
successive interval vary. The internal conditions of the
package at the beginning of the first interval can be cal-

culated by rearranging Equation (3) to:

Hi(o) = 1‘17? (13)
where
Hi(o) is the initial internal relative humidity
mi is the initial moisture content
a is the intercept of the sorption isotherm
b is the slope of the sorption isotherm

By knowing the initial internal conditions of the
package and the constant external conditions at the first
interval, the weight of the moisture penetrated through the
package for a time-step (At) can be determined by Equation
(10) (the external conditions are constant during an interval
with the internal conditions changing with time). The
internal relative humidity will change as moisture penetrates

or leaves the package. The internal relative humidity of

16

the package at time (t+At) will depend on the amount of
water vapor penetrated through the container wall during the
time-step At. The internal relative humidity at (t+At) can
be determined from Equation (12). This new internal rela-
tive humidity at time (t+At) will equilibrate with the food
in the package and change the moisture content of the pro-
duct according to Equation (3).

The change in time (At) in going from (t) to (t+At)
is defined as the time-step. At the end of each time-step
the moisture content of the product will change as a function
of the internal relative humidity. As the internal relative
humidity changes the partial pressure difference (He-Hi) will
also change since the external relative humidity is constant.
The weight of the moisture penetrated through the package
(A0) for the next time-step (t+2At) will change as a function
of this partial pressure difference change.

During experimental storage of the packages the
internal conditions are constantly changing in relation to
the constant external conditions. By selecting a short At
for the time-steps and assuming equilibrium during each time-
step, the internal environment change can be simulated and
the moisture content calculated based on this simulation.

The length of the time-steps will affect the results
of the calculation. The shorter the time-steps the more
accurate the simulation of constantly changing internal con-

ditions. Time-steps of 30 minutes, 15 minutes, and 10

17

minutes were evaluated. The corresponding moisture contents
(g moisture/100 g dry product) at the end of the interval
determined by the calculation for Product A were 4.0428%,
4.0427%, and 4.0427% respectively. Since these values are
very close together, 30 minute timesteps were used.

Products B and C exhibited similar results. A program was
written using Equations (3), (10), and (12) for a T159
programmable calculator and the results of the calculation

based on simulation were determined using this program.

EXPERIMENTAL METHODS

Three different commercially available packaged dry
food products with low initial moisture contents were
selected to be used for this study. All three products are
mixtures of various ingredients with differing compositions.
Thus their abilities to adsorb water vapor from the atmos-
phere are not the same and different shelf-lives can be
expected. With a low initial moisture content (all three
were different and covered a range) water vapor adsorption
from the atmosphere to a maximum acceptable moisture content
is the important criteria in determining shelf-life.

Product A is a gelatin product, B a dessert pudding,
and C a coating mix. These products were tested in their
existing packages which are paper/plastic laminates of vary-
ing degree of water vapor transmission. Packages are
labeled A, B, C to correspond to products A, B, and C. By
using existing packages produced on production equipment,
variables attributed to pouch seals, other machineability

defects, and rough handling are included in this study.

A. Data Generation Eor Calculation

The calculation based on simulation uses certain

properties of the product, package, and environment to

18

l9

predict moisture content. The initial moisture content,
sorption isotherm, water vapor transmission rate of the
packaging material, and surface area, fill weight, and

headspace volume of the package are required.

Initial moisture content

 

Many methods are available for determining the
moisture content of a food. Moisture content means the
determination of the water held in the food. A common
method of determining moisture content is to remove the
water from the food and measure the weight change.

This can be accomplished by drying the food at some
temperature for a time period and measuring the weight
change. The air oven technique generally uses high tempera-
tures for a long period of time. This high temperature can
cause chemical reactions in the food affecting the change
in weight and at the same time volatiles may be lost.

The vacuum oven technique uses a lower temperature
and shorter drying time than conventional oven techniques.
The rate of diffusion of water is faster by drying in a
vacuum. However, there is still the possibility of weight
loss due to evolution of volatiles from the food.

Other methods include freeze-drying at room tempera-
ture, drying with P205 desiccant, extracting or volatilizing
the water in the food by means of an organic solvent, and
methods based on the physical-chemical properties of bound

and free water.

20

After reviewing the available methods, it was
decided to use the vacuum oven technique. This method is
widely used for food products because it is an efficient
method.

Three samples of each product containing approxi-
mately 3 grams of product (each sample was obtained from a
different package) were placed in a vacuum oven at 60°C for
4 hours. The average percentage of moiSture content on a
dry basis was determined by the loss of weight of the

samples due to loss of moisture and expressed in units of

gg moisture

100 g dry product . Results are in Table l.

Sorption isotherms

 

The sorption isotherms were determined for each
product by placing samples of known initial moisture content
in contact with a range of relative humidities at three
constant temperatures and measuring the weight gain or loss.

Constant humidities can be created by materials
whose affinity for water regulates the water vapor pressure
in the atmosphere surrounding the material. A saturated
aqueous salt solution in contact with an excess of a
definite solids phase at a given temperature will remain a
constant humidity within any enclosed space around it. By
properly selecting the salt to be used a wide range of

humidities can be obtained and controlled.

21

There has been numerous data published relating
relative humidity at a constant temperature for particular
salts in a closed environment. The attainment of stable
relative humidities is possible if certain procedures are
followed.

Chemically pure salts and distilled water must be
used as small amounts of contaminants can seriously affect
the determination of the equilibrium humidity condition.

The preparation of the salt solution should be a
slush with excess undissolved crystals. Too much water will
produce a higher humidity than expected and solid crystals
sticking above the surface of the solution can reduce the
humidity.

The surface area of the solution should be as large
as possible and the vapor space as small as possible. The
air should also be circulated over the solution by some
means.

The sorption isotherms for the three products were
determined at three temperatures and eleven relative
humidities by using saturated aqueous solutions of salts.
The salts used and their corresponding relative humidities
at the three temperatures are listed in Table 4.

Approximately 3 grams of each product were weighed
into aluminum dishes then placed over a saturated salt solu-
tion in a closed container. Three 3 gram samples were used

for each product at each condition.

22

Samples were periodically weighed on an analytical
balance until no weight gain or loss was obtained indicat-
ing equilibrium had been reached. At the time equilibrium

was attained, the equilibrium moisture content was calcu-

g moisture
100 g dry product '

tain the sorption isotherms the average equilibrium moisture

To ob-

 

lated and expressed in units of

content of the three repeat samples was plotted against the
corresponding relative humidity at three temperatures.
Results are in Table 4 and plots of the sorption isotherms

are in Figures 2, 3, and 4.

Water vapor transmission rate

The water vapor transmission rates were determined
in the laboratory of the manufacturer that supplied the
three products. Water vapor transmission rates were deter-
mined using ASTM Standard Method F372-73 which is a rapid
procedure for determining WVT of flexible barrier materials
in film or sheet form using an infrared detection technique.
This method covers the use of the MoCon IRD-2 Infrared
Diffusometer.

In this method a dry chamber is separated from a
wet chamber of known temperature and humidity by the barrier
material to be tested. The time for a given increase in
water vapor concentration of the dry chamber is measured by
monitoring the differential between two bands in the infra-

red spectral region, one in which water molecules adsorb

23

and the other where they do not. This information is then
used to calculate the water vapor movement through a known
area of barrier material.

The water vapor transmissions were determined at
three temperatures--100, 92, and 83°F with use of ZNSO -

4

7H20 as the saturated salt solution. This solution gives a
relative humidity of 90% at the three temperatures mentioned

above. Results are in Table 3.

Surface area of the pouch

 

Surface area measurements were made by measuring
the web width of each pouch structure and multiplying by
the cutoff length. The average of three pouch area measure-

ments for each packaging structure are listed in Table 2.

Fill weight of the package

 

The package fill weight for each product was deter-
mined by subtracting the pouch weight from the total package
weight and averaging the values of three samples. Results

are in Table 2.

Headspace volume of the package

 

The headspace volume of flexible packages is diffi-
cult to determine due to the fact that flexible packages do
not have three independently fixed dimensions so the volume
cannot be reliably calculated. Also, flexible packages can

change shape and volume with changes in pressure.

24

Therefore the headspace volume should be calculated to
standard temperature and pressure.

There is a method for determining the headspace
volume resembling that of Griffin (1972) that uses
Archimedes Principle, Boyle's Law, and the combined gas law.
An attempt was made to use this method in determining the
headspace volume but was found to be inadequate due to the
nature of the pouch material.

The only alternative was to make an estimate of the
headspace volume by determining the approximate dimensions
of the headspace. By substituting various headspace values
higher and lower than the estimated value into the equation
for calculation of moisture content, it was determined that
the headspace measurement had little effect on the calcu-
lated results. This was due to the fact that the water
vapor that permeates the package equilibrates with the food
inside the package faster than the permeation across the
barrier. There is a small portion of the total moisture in
the headspace compared to the moisture in the product.

Results are in Table 2.

B. Experimental Testing

 

Initial moisture content
Initial moisture contents of Products A and B are
reported in Table 1. It was necessary to redetermine the

moisture content of Product C since there was a time lapse

25

between the previous determination as used for the sorption
isotherms and the time when the experimental testing was
conducted. This value is listed in Table 1.

Test conditions of actual
experimental testing

 

 

Three temperatures were established, two in con-
trolled atmosphere walk-in cabinets and one in a controlled
condition laboratory. Four relative humidities were set-up
at each temperature. The relative humidities were estab-
lished by placing beakers of saturated salt solutions with
an excess of the definite solids phase in closed containers.

Five packages of Product A, B, and C were weighed on
an analytic balance and placed over a saturated salt solu-
tion at a temperature for a certain time period. At the
end of the time period the weight of each pouch was deter-
mined and the moisture content calculated.

After the pouches were weighed they were transferred
to another previously set—up condition where the temperature,
relative humidity, or both were changed. At the end of this
second interval the pouches were again weighed, the moisture
content calculated, and then transferred to another interval.
In this manner the conditions were constant during any one
interval but constantly changed from interval to interval.

Each product was subjected to at least one full
cycle defined as transferring the samples from low tempera-

ture-low humidity through intervals up to conditions of

26

Table 1.--Initia1 moisture content.

 

% Moisture - for
sorption isotherms
( g moisture )

100g dry product

 

% Moisture - for
experimental test
( g moisture )
100g dry product

 

 

Product A 0.725
Product B 4.042
Product C 3.555

0.725
4.042
3.690

 

Table 2.--Pouch surface area, headspace volume,
fill weight.

and package

 

 

 

 

 

 

 

Headspace Package
Surface area(cm2) volume(cm3) fill wt(g)
Package A 206 25 84.5
Package B 281 70 102.4
Package C 292 35 66.8
Table 3.--Water vapor transmission rates.
Temp.(°F) RH(%) WVTR(g/100in2°24 hrs)
Package A 100 90 0.23
92 90 0.12
83 90 0.08
Package B 100 90 0.68
92 90 0.37
_ 83 90 0.24
Package C 100 90 0.19
92 90 0.10

83 90 0.06

 

27

Table 4.--Test conditions, salt solutions, and equilibrium
moisture~content results for sorption isotherms.

 

(

g moisture

Equilibrium Moisture Content

 

)

 

 

 

 

Temper— Sa1t(*) Relative 100g dry product
ature Solution Humidity
(°F) (%) Product
A B C

90 (NH4)ZSO4 79.5 11.33 30.64 35.25
NaCl 75.2 3.54 21.58 25.49
NaNOz 62.9 1.55 6.35 7.87
NaBr 55.5 1.04 5.01 6.52
Mg(N03)2 50.8 0.90 4.82 5.82
KN02 46.9 0.75 4.63 5.32
K2C03 43.6 0.78 4.40 4.95
Cr03 40.1 0.76 4.22 4.49
MgC12 32.2 0.64 3.90 3.80
KC2H302 21.7 0.63 1.83 3.06
LiCl 11.1 0.42 1.29 2.25

76 (NH4)2SO4 80.0 6.01 32.73 37.96
NaCl 75.4 3.11 13.11 15.08
NaNOz 64.5 1.92 6.49 8.56
NaBr 58.0 1.35 5.50 7.10
Mg(N03)2 53.1 1.20 5.21 6.48
KN02 48.2 1.06 4.81 5.52
K2C03 43.8 0.86 4.90 5.10
Cr03 39.5 0.82 4.47 4.44
MgClz 32.8 0.83 4.38 3.98
KC2H302 22.9 0.68 3.96 3.37
LiCl 11.1 0.59 1.75 2.68

62 (NH4)ZSO4 80.6 4.92 21.43 35.01
NaCl 75.6 3.61 11.64 19.33
NaNOz 66.2 1.90 9.99 9.27
NaBr 60.5 1.48 5.53 7.65
Mg(N03)2 55.4 1.31 5.29 6.94
KN02 49.6 1.20 4.99 5.95
K2C03 44.1 0.98 4.78 5.27
Cr03 37.6 0.90 4.57 4.84
MgClz 33.3 0.80 4.18 4.22
KC2H302 23.0 0.76 4.13 3.78
LiCl 11.1 0.58 2.96 2.80

 

*Wink and Sears (1950).

28

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29

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31

high temperature-high humidity and back down again. Actual
conditions that each product were subjected to and the
corresponding time periods are listed in Tables 5, 6, and 7.

Calculation of experimental
moisture content

 

 

The moisture content calculations at each weighing
were based on first determining the dry weight of the
product at time t=0 which has a moisture content equal to
the initial moisture content. The dry weight at time t=0

is determined by:

where
W0 is the weight of the product in the pouch at
t=0, grams mi is the initial moisture content of

the product,

9 moisture
100 g dry product

 

Do is the dry weight of the product at time

t=0, grams.

The moisture content at any weighing can now be

determined by:

32

 

 

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33

 

 

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0:00:00 0:00:00 0:00:00 0:00:00 .0050:. .0.. .0. 0
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34

 

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500.0 000.0 005.0 000.0 0.000 05 0.05 00
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005.0 500.0 005.0 000.0 00.000 00 0.00 00
005.0 000.0 005.0 000.0 50.000 00 0.00 00
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35

Mc =U x100
where
Wt is the weight of the product in the pouch at
time t, grams
Do is the dry weight of the product at time
t=0, grams
Mct is the moisture content at any weighing at

time t,

g moisture
10W 9 dry product

 

Results are in Tables 5, 6, and 7.

CALCULATION

The calculation based on simulation requires the
permeability constant of the packaging material and a

mathematical expression for the sorption isotherm.

Calculation of Permeability Constant from WVTR

As discussed previously the water vapor transmission
rates were determined by an infrared detection technique at
three temperatures and one relative humidity for each struc-

ture. These values were converted to permeability constant

 

over thickness (3) having units‘3f(xEL§$?Aatm’ by assuming

that the partial pressure of water vapor in the dry chamber
is zero atm. This assumption is based on the fact that the
dry chamber is purged with dessicated air.

The permeability constants were determined at three
temperatures that were different from the experimental
storage temperatures used. The logarithm of the permeabil-
ity constant was plotted against the inverse of the testing
condition temperature in degrees Kelvin. By referring to
this plot the permeability constant at other temperatures

can be determined. Results of the permeability constants

determined from the WVTR's and the extrapolated values at

36

37

experimental test temperatures are in Tables 8 and 9. The
permeability constants as a function of temperature are in

FiguresJP, 6, and *fi

Calculation of Slope and Intercept

 

As discussed previously it was determined the sorp-
tion isotherm could be described by a straight line and

expressed mathematically as:
m = a + bH

The slope and intercept was determined between the
initial moisture content and estimated maximum allowable

moisture content. Results are reported in Table 10.

Determination of Moisture Content by Calculation
Based on Simulation

 

 

The moisture contents versus time for the same con-
ditions corresponding to those used in the experimental
determination were calculated using Equations (3), (10),
and (12). A program utilizing these equations was written
for a T159 programmable calculator. Appropriate values were
entered into the program and moisture contents calculated.
Results are in Tables 5, 6, and 7. These values were plot-
ted on the same graph as the experimentally determined
values so a direct visual comparison can be made. These

plots are illustrated in Figureélfi, 9, and $6.

38

Table 8.--Permeability constant as determined from water
vapor transmission rates.

 

Permeability constantéfilm thickness

 

 

 

 

Temp. (°F)
P 90120)
I
X (cmz) (hr) (AATM)
Package A 100 0.000255
92 0.000170
83 0.000151
Package B 100 0.000755
92 0.000525
83 0.000453
Package C 100 0.000211
92 0.000142
83 0.000113

 

Table 9.--Permeability constant at temperatures used in
experimental testing.

 

Permeability constantéfilm thickness

 

 

 

 

Temp.(°F)
P 9(H20)
—I
X (cmz) (hr) (AATM)
Package A 90 0.000163
76 0.000147
62 0.000140
Package B 90 0.000500
76 0.000426
62 0.000400
Package C 90 0.000133
76 0.000103

62 0.000092

 

39

Table 10.--Slope and intercept from sorption isotherms.

 

 

 

 

Product Temperature Slope Intercept

(°F) b a

A 62 0.00388 0.6707
76 0.00799 0.5224
90 0.02143 -0.1581

B 62 0.0492 2.564
76 0.0424 2.988
90 0.0405 2.596

C 62 0.0642 2.091
76 0.0616 1.959

90 0.0773 1.360

 

 

 

 

 

 

 

 

 

 

 

109 E (9/Cm2°hr-Aatm)
2.0x10’4
1.0x10'4 °-°°§25 0.00335 0.00345
I l
1
, , , . T(°K)
Figure 4. Permeability constant as a function of
temperature--Package A.
log §'(g/cm2-hr-Aatm)
1.0x10’3-
5.0x10"4
3.0X10-4 0.00325 0.00335 0.00345
1 I I 1
Figure 5. Permeability constant as a function of TZ‘KS
temperature--Package B.
P 2
log ; (g/cm -hr-Aatm)
2.0x10-4
1.0::10'4
7.0x10-5 0.00325 0.00335 0.00345
l I l
1
Figure 6. Permeability constant as a function of TI‘KS

temperature--Product C.

 

41

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mean. 123.09
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RESULTS AND DISCUSSION

The moisture content results at the end of each
interval as determined through time-steps by the calcula-
tion method compared very well with the moisture content
results determined experimentally. The greatest percentage
difference for each product is in Table 11.

Table 11.—-Greatest percentage difference between calcu-
lated and experimental data.

 

% Difference

 

 

Product (Mex - Mcalc x 100)
Mex
A 10.0
B 4.1
C 1.5

 

Because the times the packages were subjected to the
conditions at each interval were relatively short, the incre-
mental moisture content changes between intervals were rela-
tively small. The overall increases between initial and
final moisture contents were most significant. The overall

increase results are in Table 12.

44

45

Table 12.-~0vera11 moisture content increases.

 

Overall experimental Overall calculated
moisture content moisture content
Product increase (%) increase (%)

 

ave low high

 

’1; 17.2 15.6 20.4 8.8
C 4.8 3.2 7.0 7.3
2.8 2.1 3.4 3.5

 

The experimental moisture content results of the five
samples of each product varied significantly from low to high
values. The overall variations are listed in Table 12 and
illustrated graphically in Figures 7, 8, and 9. The overall
calculated moisture content results compared very well to the
range of the experimental results for Products B and C and not
as well for Product A.

The results of the calculation did not follow the
graphs of the experimental results exactly as seen in Figures 7,
8, and 9. For instance, when the package was subjected to a
lower relative humidity at the same temperature as the previous
interval, the moisture content decreased. The calculated
results was not able to follow the experimental decrease in
moisture content. The reason for this can be attributed to
the fact that the calculation is based on the erroneous assump-
tion that the product in the package is in equilibrium with

the relative humidity of.the internal environment.

46

One factor in the calculation is the internal relative
humidity of the package at the beginning of any interval.
Assuming equilibrium in the package, the change of the weight
of the moisture penetrated through the container for a period

of time is defined as:

-A--25 (He-Hi)At (8)

A0 = 100

xlw

For any specific interval the temperature and external relative
humidity are constant. Therefore, the only variable in the
above equation is the internal relative humidity (Hi). The
direction of the penetration of water vapor will depend on the
value of (He-Hi). If this value is positive water vapor will
penetrate into the package. But, when this value is negative
the internal relative humidity is greater than the external
relative humidity and the concentration gradient (partial
pressure difference) is such that there will be a net loss of
water vapor from the package to the external environment.
This results in a lower calculated moisture content than the
previous interval.

The relationship between the equilibrium moisture
content and relative humidity can be expressed by the sorption
isotherm or as: m = a + bHi, where a and b are constant for

each product at a temperature.

m - a
b I
internal relative humidity can be determined at any time as

the

 

By rearranging this equation to Hi =

47

a function of the moisture content and the slope and inter-
cept of the sorption isotherm.
The sorption isotherm of a product is determined at
a constant temperature. At various temperatures the
sorption isotherm will be different and thus the relation-
ship between the internal relative humidity and moisture
content will change as the temperature changes. This can
be illustrated for Products A, B, and C in Figures 2, 3,
and 4 which show the sorption isotherm at three temperatures.
The calculation is based on the assumption of equi-
librium between the product and the internal humidity of
the package. When a package was transferred from one temper-
ature to another, the internal conditions changed greatly
according to the relationship between the moisture content
and relative humidity as a function of the sorption iso-
therm. The product and internal environment will require a
certain time to equilibrate. Since equilibrium is assumed
for the calculation, the theoretical internal relative humid-
ity will be lower than the actual internal relative humidity.
Therefore, when the experimental moisture content
decreases, the internal relative humidity must be greater
than the external relative humidity according to Equation
(8). Since the theoretical internal relative humidity is
lower than the actual internal relative humidity because of
the assumption of equilibrium, the calculation did not give
decreased moisture content values corresponding to

decreased experimental moisture content values.

48

Proof that equilibrium had not been reached can be
illustrated by the experimental results of intervals 16 and
17 in Table 5. Even though the external relative humidity
decreased from 75.4% to 64.5%, the product still adsorbed
water vapor and thus the moisture content increased. If the
product and internal conditions had reached equilibrium in
storage interval 16, the relative humidity inside the package
would have been greater than the external relative humidity of
storage interval 17. The result would have been a concentra-
tion gradient (partial pressure difference) such that the
product loses water vapor to the lower external relative
humidity. The same situation can be illustrated by intervals
20 and 21.

One reason why equilibrium had not been reached was
the short time periods the packages were subjected to the
conditions at each interval before transferring to the next
storage interval. Secondly, the packaging materials which
were used are good water vapor barriers, therefore the moiSture
transfer during short time-periods is relatively small. .&5

As can be seen in Figures 7, 8, and 9, although the
calculated moisture content values never decreased, the trends
of the calculated values did follow the trends of the experi-
mental values very well for Products B and C and to a lesser
extent for Product A.

This differencejxxtrend for Product A can be seen in
Figure 7 in which the trend of the calculated values followed

the trend of the experimental values up to a point. Between

49

intervals 15 and 16 in Table 5 the experimental moisture
content increased sharply while the calculated value increased
much slower. The test conditions during this interval changed
drastically from 90°F/55.5%RH to 76°F/75.4%RH. Because of the
drastic condition change and the assumption of equilibrium this
calculated value was not able to follow the experimental value.
Drastic condition changes such as these are not common in the
course of a normal day.

Figures 8 and 9 illustrate that the trends of the
calculated values followed the trends of the experimental
values very well for Products B and C. This can be attributed
to the fact that the change of conditions between intervals
for these two products were smoother and less severe than for
Product A. The model was designed this way to determine the
effect of severity of condition change on the results of the
calculation. It was discovered that as the change of con-
ditions became more severe, the deviation of the calculated
to experimental results increased.

The experimental conditions the products were subjected
to are much more severe than what would be expected in normal
distribution. During the course of a normal day the weather
conditions change at a gradual and smoother rate. For instance,
the temperature does not ordinarily jump from 76 to 90°F in a
matter of minutes or the relative humidity change from 60% to
80% in the same time period. The experimental model was
designed to subject the products to drastic changes of tempera-

ture and humidity. Thus, since the calculation based on

50

simulation adequately predicted the moisture content for drastic
changes over a short time period it can be assumed that this
method can be used to predict the moisture content over a longer
time period where the conditions change gradually and the

product is closer to equilibrium with the environment.

Experimental Error of Actual Testing

In the determination of the initial moisture content
evolution of volatile components of the food may have occurred
even though the vacuum oven method was used to minimize these
effects. If this was the case the loss of weight may have been
more than just loss of moisture resulting in a higher moisture
content determination than the actual moisture content. This
measurement is critical since all subsequent moisture content
values are based on the initial moisture content.

Five samples of each product were used in the actual
testing at each interval. The results of the determination of
moisture content at each interval varied throughout these
five samples. This can be explained by material variations
of the laminates, either variations in thickness or variations
in the construction of the laminate. The quality of the seal
may also have affected these results as long as it was not a
defective seal resulting in a defective pouch. A leaker would
cause extreme variation in the experimental moisture content
determination.

During the course of the actual testing, the test

condition containers were opened and closed periodically in

51

order to weigh the samples. Because of this the relative
humidity above the saturated salt solutions required time to
equilibrate. Therefore for a certain time period the actual
relative humidity inside the test container may have been
different than the desired relative humidity.

While one package was being weighed the other
packages remained in the test container. Because the con-
tainer had to be opened each time another package was
weighed the conditions inside the container varied slightly
which may have affected the moisture content of the product.
To minimize this effect the order of weighing the samples
was rotated.

Experimental Error of Calculation
Based on Simulation

 

 

8/{As was the case in the actual testing; the initial
moisture content determination isialso critical in the calcu-
lation method. The calculation depends on the sorption
isotherms which are determined by the equilibrium moisture
content at different relative humidities. The equilibrium
moisture content at each relative humidity is calculated
from the total weight gain or loss at equilibrium and the
initial moisture content. Any error in the initial moisture
content determination would directly affect the sorption
isotherms and thus affect the calculated results.

Also, the initial moisture content is used to deter-

mine the initial interval relative humidity of the package

52

at the beginning of the first interval. All subsequent
calculated moisture contents depend on this initial internal
relative humidity.

// In determining the sorption isotherms, samples were
placed over a saturated salt solution in a closed container.
Periodic weighings were made until equilibrium was estab-
lished. In order to weigh the samples the containers were
periodically opened and closed thus causing the relative
humidities inside the test containers to fluctuate.
Therefore the equilibrium moisture content may have been
determined at a relative humidity other than the stated
value.

V//Saturated salt solutions can provide a stable humid-
ity condition but the condition created is not necessarily
the relative humidity cited in the literature. (Also, the
various references disagree as to the humidity created.)00cc
No attempt was made to measure the actual relative humidity
inside the test container. ~b

./ Obtaining stable humidities depends on the purity
of the salt, the purity of the water, the preparation of
the salt solution, and the temperature.

Chemically pure salts and distilled water were used
in the preparation of the solutions. Any excess salt crys—
tals sticking above the surface of the solution or any
excess of the aqueous phase will affect the humidity estab-

lished.

53

\//The temperature used for the determination of the
sorption isotherms were average values over the course of
the experiment. Fluctuations in temperature will affect the
sorption isotherm determination. According to the litera-
ture a temperature difference of only 2°F between the solu-
tion and vapor causes an error of approximately 5% relative
humidity. The temperature is also assumed constant for the
calculation.

Determination of the water vapor transmission rates
is another area of possible error. The MoCon instrument is
a fast method for determining water vapor transmissions but
introduces some error over the dish method.

Also the water vapor transmission rates were deter-
mined for a flat sheet of material. This value may differ
somewhat from the water vapor transmission rate of the
package itself. During machining of the pouch the laminated
structure may be damaged and the moisture barrier properties
reduced slightly. This is particularly evident for Products
A and B packaged in gusseted pouches. The plow used to form
the gusset may damage the laminated structure or a gusset
fold may not be properly heat sealed resulting in a small
air channel formed in the fold.

V/ Surface area was determined by measuring the flat
sheet dimensions of a pouch and averaging the values of
three pouches. Possible errors result from the accuracy of

the measuring instrument and the measurement itself.

54

Since the packaging materials are laminates, varia-
tions in their construction will result in experimental
error. A 5 to 10% variation in thickness is not uncommon
in the packaging industry and any defects in the laminating
layers will add to this error.

Manufacturers are faced with the question of the
degree to which he must protect his product to get it to the
consumer in an acceptable condition. One method of deter—
mining this is actual field storage which is both time con-
suming and expensive. An alternative is the accelerated
test technique but to assume that "similar” products will
have similar shelf-lives is inaccurate. This method has
severe limitations and is still relatively expensive and
time consuming. The method presented in this paper is not
intended to replace actual field storage, accelerated test
techniques, or other mathematical methods. It is a practi-
cal tool that can be used by a packaging engineer in package
development when a new product has to be introduced in a
short lead time and the package's performance must be known
for a particular set of environmental conditions.

The shelf-life of packaged dry food products depends
greatly upon the geographical location and time of year at
which the packaged product is placed into that location.
Because of this it may be economical to package differently
for various geographical areas or even package differently

in the same area during various times of the year.

55

By obtaining weather data for a geographical region
the calculation based on simulation can be used to predict
a package's performance in that region. Conversely, for a
desired shelf-life in any particular region the required
package protection can be determined thus reducing the
possibility of overpackaging.

V//Considering all of the possible errors in this study,
the calculated results are in good agreement with the experi—
mental results. The change of conditions used in the experi-
ment were much more severe than those expected in the course
of a normal day. The trends of the calculated results were
able to follow the trends of the experimental results even
though the conditions changed drastically between intervals.

\//’This calculation method is a quick, inexpensive, and
reasonably accurate method for introduction of a product
with short lead times but should be verified by actual
storage monitoring during the course of the introduction.
Verification is a common practice in food packaging no

matter what method is used to predict storage life.

SUMMARY

The determination of a products' shelf-life is
important to food packaging. Reactions that determine
storage life of packaged dry food products depends mostly
on the moisture content of the product.

A calculation based on simulation was proven to
adequately predict moisture content, with certain limita-
tions, during short constant condition storage intervals
when the conditions change from interval to interval.
Condition changes between intervals were more severe than
those expected during the course of a normal day.

The calculation can be used as a practical tool by
the packaging engineer in package development for introduc-
tion of a new product in short lead times. The development
time can be reduced along with reducing the possibility of
overpackaging or underpackaging. The performance of a
package can be predicted in a particular geographical region
by obtaining weather data for the region and applying it to
the calculation. This type of determination is important
because the shelf-life of packaged dry food products depends
upon the geographical location and time of year the product

is placed into that location. Determining the shelf-life of

56

57

a product by actual field storage in all market locations
for introduction during all seasons of the year is expensive
and time consuming.

Future work in this area should include actual field
storage with constant monitoring of the environmental
changes and periodic moisture content determinations. The
recorded environmental conditions can then be used in the
calculation to predict the moisture content with comparison
to experimental moisture content. By actual field storage
the change of conditions is gradual and smoother and there
is a better chance of the product in the package being close

to equilibrium with the internal environment.

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