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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 com-

mon method to give the food long term durability and

temperature resilience. Recently, new retorting tech-

niques have enabled new packaging materials, one of

them is Tetra Recart which is paperboard-based. The

Tetra Recart packaging material consists of 65% pa-

perboard which has been laminated with several lay-

ers 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 en-

vironment 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 differ-

ent directions of paperboard. MD which is the ma-

chine 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 pa-

perboard thickness.[1]

The air-water system The concentration of water

vapor in air can be expressed by relative humidity.

RH=pwpw,s

(1)

The relative humidity depends on the temperature

which changes pw,s and the pressure which changespw in a closed system. The partial pressure for watervapor at saturation is expressed as

pw,s = 133.32 e(18.3036 3816.44

T+227.03) (2)

The partial pressure of water vapor, pw, is describedby [2]

pw = yH2O P (3)

Moisture transport Mass transfer by diffusion oc-

curs 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.

CAt

+ vxCAx

+ vyCAy

+ vzCAz

= (4)

= DAB2CA

x2 +

2CA

y2 +

2CA

z2

+ RA

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 diffu-

sive 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]

CAt

+ vxCAx

= DAB

2CAx2

(5)

The convective term for mass transfer througha stagnant component where flux is caused by both

convection and diffusion is expressed by

v =DAB

Ctot CA

dCAdx

(6)

The equation for mass transfer in one direction, with

no chemical reaction will then be [3]

CAt

+

DAB

Ctot CA

CAx

CAx

= (7)

= DAB

2CAx2

Method The goal was to develop a moisture trans-

port test apparatus which allowed diffusivity mea-

surements in the lateral direction, for both the MD

and CD.

Water vapor is transported from the humid auto-

clave, through the paperboard into the apparatus. The

concentration of water vapor inside is measured us-

ing relative humidity, temperature and pressure trans-

mitters. 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 horizon-tally on top of the apparatus in between silicone rub-

ber 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 125C and 3.8 bar for one hour.

A reference test was performed without the packag-

ing material, to see if there was any background leak-

age of moisture. When investigating the diffusion

through the packaging material, a stack of five sam-

ples 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 simulat-

ing the moisture transport to find a corresponding dif-

fusivity. In COMSOL, the 3D convection and diffu-

sion 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 andsilicone 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 consid-

ered. The thickness of polypropylene and alu-

minum was neglected since the diffusivities in

these layers are much smaller than in paper-board. 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 125C.

The properties of the three subdomains are de-

scribed by the parameters in table 1.

The diffusivity in the air, Dair, was estimatedto 1.1105 m2 /s, using equation 3.15 in [3]. Thebackground leakage into the test apparatus was esti-

mated to 0.0023 mol/(m2s) using the concentration

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Figure 4: A COMSOL illustration of the concentra-

tion gradient in the simulated model.

The diffusivity of the paperboard was estimated

to 4.2 107 m2 /s with a standard deviation of2.5 108 m2/s, as can be seen in table 3.

Table 3: The diffusivities of the Tetra Recart paper-

board, obtained by simulation.

Diffusivity D [m2/s]Test 1 4.07 107

Test 2 4.00 107

Test 3 4.34

107

Test 4 4.60 107

Test 5 4.09 107

Average 4.2 107

Standard deviation 2.5 108

The simulated model in figure 4 shows a concen-

tration 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 diffu-

sivity to 3.8

10

14

m

2

/s for water in paper fibres at23C and atmospheric pressure [4]. The diffusivity

in paper fibers is therefore much lower than the ef-

fective 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 23.7C

and 1 atm gave an effective diffusivity of 7.17106

m2/s [5]. This value was recalculated to an estimated

value for 125C and 3.8 bar, using the temperature

proportional dependence for diffusivity, T1.5 to T2.0, and the inversely proportional pressure depen-dence, 1/P. The diffusivity was then 3.0106 m2/s

which is about ten times larger than the measureddiffusivity 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 exper-

imental data shows a non-linear increase, while the

simulated concentrations increase almost linearly.

The concentration curve should have a slightly non-

linear behavior as the difference between the out-

side 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 depen-

dence of the autoclave concentration which means it

does not abate as the concentrations levels out.

Conclusions Comparisons between the effective dif-

fusivity for the Tetra Recart paperboard and exper-

imental data for other paperboard materials showed

some differences. It is however diffucult to make any

clear conclusions considering that there is no previ-

ous data for diffusivities at the elevated temperature

and pressures. The obtained diffusivity is however

much higher than the diffusivity of water in paper-

board fibers which suggests that the studied transportmechanism does not occur solely through the fibers.

Further tests are needed before any clear conclu-

sions 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/m3]DAB Diffusivity, comp. A in comp. B [m

2/s]

Ni Flux of component i [mol/m

2

s]Ptot Total pressure [Pa]pw Partial pressure of water vapor [Pa]pw,s Partial pressure of water vapor at sat.[Pa]RA Chemical reaction of component ARH Relative humidity [%]t Time [s]T Temperature [C]

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vi Convective flow term, i:th direction [m/s]yi Mole fraction of component i

References

[1] Pappersteknik, Fellers, C., Norman B., Avd. for

pappersteknik, KTH, 1996

[2] Systemet luft-vatten (literature for the course

Sep. FK.), Stenstrom, S., Dept. Chem. Eng.,

Lund University, 2004

[3] Transportprocesser (literature for the course

Sep. FK.), Stenstrom, 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 bestamning

av diffusionskoefficienter i PaToF-projektet,

Andersson E, Dept. Chem. Eng., Lund Univer-

sity (2001)

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