Moisture transport in paperboard Test method development

Moisture transport in paperboard
Test method development
Merit Lassing
Department of Chemical Engineering, Lund University
Abstract Paperbased packaging material is used as a container for preserved food. During the retorting
process, problems sometimes occur where the paperbased material absorbs too much moisture and looses
its stability. To find a solution to this problem, the properties of the paperboard must be known at elevated
temperatures and pressure. In this work a test apparatus was developed in order to measure the moisture
transport through the paperboard at the conditions in a retort. The test data was used in a convection and
diffusion model, were the effective diffusivity for water vapor in the paperboard was estimated.
The results were compared to earlier experimental data for paperboards and the diffusivities for water vapor
in air and paper fibers. The effective diffusivity of water vapor in paperboard was found to be higher than
for paper fibers, but lower than for air. Compared to other paperboard materials, the diffusivity for the Tetra
Recart board was somewhat lower.
Introduction Preserving food by canning is a common
method to give the food long term durability and
temperature resilience. Recently, new retorting techniques
have enabled new packaging materials, one of
them is Tetra Recart which is paperboard-based. The
Tetra Recart packaging material consists of 65% paperboard
which has been laminated with several layers
of polypropylene and one layer of aluminium foil
to make the material retortable and provide a sealed
barrier around the food.
When sterilizing the filled paperboard box, steam
and pressurized air is mixed in the retort. The environment
is moist and hot with pressure changes,
not the most suitable for a paperboard material. It
is therefore important to know the properties of the
packaging material at the conditions in the retort.
Packaging material Paperboard consist of fibers
which form flocs. Due to the properties of the fiber
and the manufacturing process, there are three different
directions of paperboard. MD which is the machine
direction of the in-plane surface and CD which
is the cross machine direction of the in-plane surface.
Finally there is the z-direction which is across the paperboard
thickness.[1]
The air-water system The concentration of water
vapor in air can be expressed by relative humidity.
RH = p w
p w,s
(1)
The relative humidity depends on the temperature
which changes p w,s and the pressure which changes
p w in a closed system. The partial pressure for water
vapor at saturation is expressed as
3816.44
(18.3036−
p w,s = 133.32 · e T +227.03)
(2)
The partial pressure of water vapor, p w , is described
by [2]
p w = y H2O · P (3)
Moisture transport Mass transfer by diffusion occurs
when the total pressure is constant while the
concentrations of a certain component are different.
When there is a bulk transport of a component, it is
described by the convective transport.
When the concentrations changes over time, a
transient analysis of the mass transfer is required.
The general equation for mass transfer is used.
∂C A
∂t
= D AB
( ∂ 2 C A
∂x 2
∂C A
+ v x
∂x + v ∂C A
y
∂y
+ v ∂C A
z
∂z = (4)
+
∂2 C A
∂y 2
)
+ ∂2 C A
∂z 2 + R A
On the left hand side there is the accumulation and
the convective transport in the different directions.
On the right hand side there are the terms for diffusive
transport and chemical reactions.
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If there is no chemical reaction and transport only
occurs in one direction the equation will be [3]
(
∂C A ∂C A ∂ 2 )
+ v x
∂t ∂x
= D C A
AB
∂x 2 (5)
The convective term for mass transfer through
a stagnant component where flux is caused by both
convection and diffusion is expressed by
v =
−D AB dC A
C tot − C A dx
(6)
The equation for mass transfer in one direction, with
no chemical reaction will then be [3]
∂C A
∂t
+
(
−DAB ∂C A
C tot − C A ∂x
) ∂CA
∂x = (7)
( ∂ 2 )
C A
= D AB
∂x 2
Method The goal was to develop a moisture transport
test apparatus which allowed diffusivity measurements
in the lateral direction, for both the MD
and CD.
Water vapor is transported from the humid autoclave,
through the paperboard into the apparatus. The
concentration of water vapor inside is measured using
relative humidity, temperature and pressure transmitters.
The volume of the apparatus is known which
means the amount of transported water vapor can be
estimated. Figure 1 shows the principle of the test
apparatus. The packaging material is placed horizontally
on top of the apparatus in between silicone rubber
seals, and the equipment is sealed using a metal
lid and clamps. The only moisture transport into the
apparatus should be through the paperboard.
The test apparatus was placed in the autoclave
where the retort programme held the temperature and
pressure constant at 125 ◦ C and 3.8 bar for one hour.
A reference test was performed without the packaging
material, to see if there was any background leakage
of moisture. When investigating the diffusion
through the packaging material, a stack of five samples
with 10 mm diffusion length were used.
Obtained relative humidity data was recalculated
to concentrations of water vapor. The concentrations
were used in COMSOL Multiphysics when simulating
the moisture transport to find a corresponding diffusivity.
In COMSOL, the 3D convection and diffusion
model was found to be suitable, which uses the
general equation for mass transfer.
Figure 1: Test apparatus - moisture transport is
shown by the arrows. 1. packaging material and
silicone seals, 2. RH and temperature transmitter 3.
pressure transmitter 4. pressure equalizer
Due to symmetry, 1/4 of the actual test apparatus
geometry was drawn in the model, which consisted
of three subdomains.
• The packaging material. Only the paperboard,
with a total thickness of 1.5 mm, was considered.
The thickness of polypropylene and aluminum
was neglected since the diffusivities in
these layers are much smaller than in paperboard.
The length of the packaging material
was 10mm.
• The thin air space between the lid and the test
apparatus was assumed to have the thickness
of the packaging material and silicone seals,
which meant a total thickness of 4 mm. The
length of this layer was 20 mm.
• The void space inside the test apparatus was
assumed to be rectangular, with 1/4 of the test
apparatus volume at 3.8 bar and 125 ◦ C.
The properties of the three subdomains are described
by the parameters in table 1.
The diffusivity in the air, D air , was estimated
to 1.1·10 −5 m 2 /s, using equation 3.15 in [3]. The
background leakage into the test apparatus was estimated
to 0.0023 mol/(m 2·s) using the concentration
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Table 1: Properties of the packaging material, the
thin air layer and the void space
Subdomain Paper- Thin air Inside
parameter board layer space
Diffusion, D D air D air
D [m 2 /s]
Convective flux
−D dc −D
-x-direction,
air dc
C tot−c dx C tot−c dx
0
u [m/s]
−D dc −D
-y-direction,
air dc
C tot−c dy C tot−c dy
0
v [m/s]
-z-direction, 0 0 0
w [m/s]
Reaction, R 0 0 0.023
[mol/(m 3 s)]
data from the reference test. It was expressed as a reaction
parameter in the void space in the model. The
initial concentration inside the test apparatus was decided
by each experiment. The water vapor concentration
in the autoclave was assumed to be 70.4
mol/m 3 , which is the concentration of water vapor at
3.8 bar and 125 ◦ C when RH is is 100%. The initial
concentration of water in the packaging material was
assumed to be the same as inside the test apparatus.
The diffusivity was assumed to be isotropic.
Figure 2: Concentration change in the experiments.
The background leakage also seemed to be repetetive,
since similar results were obtained on different
occasions. When the leakage was taken into consideration,
the water vapor increase due to diffusion
through the packaging material could be measured.
Simulation was performed on each experiment.
The time span was 3340 s, the same time as the test
apparatus had held 125 ◦ C at 3.8 bar pressure during
the retort tests. Simulated results can be seen in
figures 3 and 4. The initial concentration of water
vapor inside the test apparatus and the outer concentration
in the autoclave was given as boundary conditions
in COMSOL. The effective diffusivity in paperboard
was estimated to a value where the simulated
end concentration was the same as the obtained end
concentration in the experimental data.
Results The experimental concentrations of water
vapor can be seen in figure 2. The results from the
experiments were found to be similar.
Table 2: Relative humidity and concentration inside
the test apparatus at the start and end of the tests
RH [%] C [mol/m 3 ]
start end start end
Test 1 28.7 54.4 20.2 38.3
Test 2 30.1 55.1 21.1 38.8
Test 3 31.1 56.9 21.9 40.1
Test 4 29.9 56.9 21.1 40.0
Test 5 32.5 57.3 22.9 40.3
Ref. test 20.5 32.9 14.5 23.2
Figure 3: The simulated concentration change inside
the void space of the test apparatus.
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Figure 4: A COMSOL illustration of the concentration
gradient in the simulated model.
The diffusivity of the paperboard was estimated
to 4.2 · 10 −7 m 2 /s with a standard deviation of 2.5 ·
10 −8 m 2 /s, as can be seen in table 3.
Table 3: The diffusivities of the Tetra Recart paperboard,
obtained by simulation.
Diffusivity
Test 1
Test 2
Test 3
Test 4
Test 5
Average
Standard deviation
D [m 2 /s]
4.07 · 10 −7
4.00 · 10 −7
4.34 · 10 −7
4.60 · 10 −7
4.09 · 10 −7
4.2 · 10 −7
2.5 · 10 −8
The simulated model in figure 4 shows a concentration
gradient in the paperboard. This agrees with
the moisture profile that could be seen by inspection
of the samples just after retorting.
Earlier studies by Foss et al estimated the diffusivity
to 3.8·10 −14 m 2 /s for water in paper fibres at
23 ◦ C and atmospheric pressure [4]. The diffusivity
in paper fibers is therefore much lower than the effective
diffusivity through Tetra Recart paperboard.
Most likely, the diffusion in the paperboard does not
follow the same mechanisms as pure fiber diffusion.
Earlier experiments on TBA material at 23.7 ◦ C
and 1 atm gave an effective diffusivity of 7.17·10 −6
m 2 /s [5]. This value was recalculated to an estimated
value for 125 ◦ C and 3.8 bar, using the temperature
proportional dependence for diffusivity, ∼ T 1.5 to ∼
T 2.0 , and the inversely proportional pressure dependence,
1/P. The diffusivity was then 3.0·10 −6 m 2 /s
which is about ten times larger than the measured
diffusivity for the Tetra Recart material.
Finally it should be noted that the COMSOL model
is simplified and could be improved. When test data
is compared to simulated concentrations, the experimental
data shows a non-linear increase, while the
simulated concentrations increase almost linearly.
The concentration curve should have a slightly nonlinear
behavior as the difference between the outside
and inside concentration decrease. However, the
measured concentration curve levels out before the
concentrations are equal which could be explained
by the swelling of paper fibers. Furthermore, the
background leakage term in the model has no dependence
of the autoclave concentration which means it
does not abate as the concentrations levels out.
Conclusions Comparisons between the effective diffusivity
for the Tetra Recart paperboard and experimental
data for other paperboard materials showed
some differences. It is however diffucult to make any
clear conclusions considering that there is no previous
data for diffusivities at the elevated temperature
and pressures. The obtained diffusivity is however
much higher than the diffusivity of water in paperboard
fibers which suggests that the studied transport
mechanism does not occur solely through the fibers.
Further tests are needed before any clear conclusions
can be made regarding the accuracy of this test
apparatus and the paperboard properties at elevated
temperatures. Furthermore, there is need for some
improvements to the COMSOL model.
Nomenclature
C Concentration [mol/m 3 ]
D AB Diffusivity, comp. A in comp. B [m 2 /s]
N i Flux of component i [mol/m 2 s]
P tot Total pressure [P a]
p w Partial pressure of water vapor [P a]
p w,s Partial pressure of water vapor at sat.[P a]
R A Chemical reaction of component A
RH Relative humidity [%]
t Time [s]
T Temperature [ ◦ C]
4

v i
y i
Convective flow term, i:th direction [m/s]
Mole fraction of component i
References
[1] Pappersteknik, Fellers, C., Norman B., Avd. för
pappersteknik, KTH, 1996
[2] ”Systemet luft-vatten” (literature for the course
Sep. FK.), Stenström, S., Dept. Chem. Eng.,
Lund University, 2004
[3] ”Transportprocesser” (literature for the course
Sep. FK.), Stenström, S., Dept. Chem. Eng.,
Lund University, 2004
[4] Simultaneous heat and mass transport in paper
sheets during moisture sorption from humid air,
Foss, W.R. et al, Int. J. Heat and Mass Transfer
(2003) vol 46. p.2875 − 2886
[5] Diffusion i kartong, experimentell bestämning
av diffusionskoefficienter i PaToF-projektet,
Andersson E, Dept. Chem. Eng., Lund University
(2001)
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