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.

The relative humidity depends on the temperature which changes pw,s and the pressure which changes pw in a closed system. The partial pressure for water vapor at saturation is expressed as 3816.44

pw,s = 133.32 · e(18.3036− T +227.03 )

(2)

The partial pressure of water vapor, pw , is described by [2] pw = yH2 O · 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 Packaging material Paperboard consist of fibers transient analysis of the mass transfer is required. which form flocs. Due to the properties of the fiber The general equation for mass transfer is used. and the manufacturing process, there are three differ∂CA ∂CA ∂CA ∂CA ent directions of paperboard. MD which is the ma+ vx + vy + vz = (4) ∂t ∂x ∂y ∂z chine direction of the in-plane surface and CD which  2  ∂ CA ∂ 2 CA ∂ 2 CA is the cross machine direction of the in-plane surface. = DAB + + + RA Finally there is the z-direction which is across the pa∂x2 ∂y 2 ∂z 2 perboard thickness.[1] On the left hand side there is the accumulation and the convective transport in the different directions. The air-water system The concentration of water On the right hand side there are the terms for diffuvapor in air can be expressed by relative humidity. sive transport and chemical reactions. pw (1) RH = pw,s 1

If there is no chemical reaction and transport only occurs in one direction the equation will be [3]   2 ∂CA ∂ CA ∂CA (5) + vx = DAB ∂t ∂x ∂x2 The convective term for mass transfer through a stagnant component where flux is caused by both convection and diffusion is expressed by v=

−DAB dCA Ctot − CA dx

(6)

The equation for mass transfer in one direction, with no chemical reaction will then be [3]   ∂CA −DAB ∂CA ∂CA + = (7) ∂t Ctot − CA ∂x ∂x   2 ∂ CA = DAB ∂x2

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

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.

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, Dair , was estimated to 1.1·10−5 m2 /s, using equation 3.15 in [3]. The background leakage into the test apparatus was estimated to 0.0023 mol/(m2 ·s) using the concentration

2

Table 1: Properties of the packaging material, the thin air layer and the void space Subdomain parameter

Paperboard

Thin air layer

Inside space

Diffusion, D [m2 /s]

D

Dair

Dair

−Dair dc Ctot −c dx

0

−Dair dc Ctot −c dy

0

0

0

0

0.023

Convective flux −D dc -x-direction, Ctot −c dx u [m/s] −D dc -y-direction, Ctot −c dy v [m/s] -z-direction, 0 w [m/s] Reaction, R [mol/(m3 s)]

0

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.

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/m3 , 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. 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

Test 1 Test 2 Test 3 Test 4 Test 5 Ref. test

RH [%] start end 28.7 54.4 30.1 55.1 31.1 56.9 29.9 56.9 32.5 57.3 20.5 32.9

C [mol/m3 ] start end 20.2 38.3 21.1 38.8 21.9 40.1 21.1 40.0 22.9 40.3 14.5 23.2

Figure 3: The simulated concentration change inside the void space of the test apparatus. 3

m2 /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 m2 /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 Figure 4: A COMSOL illustration of the concentra- concentrations are equal which could be explained by the swelling of paper fibers. Furthermore, the tion gradient in the simulated model. background leakage term in the model has no depenThe diffusivity of the paperboard was estimated dence of the autoclave concentration which means it to 4.2 · 10−7 m2 /s with a standard deviation of 2.5 · does not abate as the concentrations levels out. 10−8 m2 /s, as can be seen in table 3. Conclusions Comparisons between the effective diffusivity for the Tetra Recart paperboard and experTable 3: The diffusivities of the Tetra Recart paperimental data for other paperboard materials showed board, obtained by simulation. some differences. It is however diffucult to make any clear conclusions considering that there is no previDiffusivity D [m2 /s] ous data for diffusivities at the elevated temperature Test 1 4.07 · 10−7 and pressures. The obtained diffusivity is however Test 2 4.00 · 10−7 much higher than the diffusivity of water in paperTest 3 4.34 · 10−7 board fibers which suggests that the studied transport Test 4 4.60 · 10−7 mechanism does not occur solely through the fibers. Test 5 4.09 · 10−7 Further tests are needed before any clear concluAverage 4.2 · 10−7 sions can be made regarding the accuracy of this test Standard deviation 2.5 · 10−8 apparatus and the paperboard properties at elevated temperatures. Furthermore, there is need for some improvements to the COMSOL model. The simulated model in figure 4 shows a concentration gradient in the paperboard. This agrees with Nomenclature the moisture profile that could be seen by inspection of the samples just after retorting. C Concentration [mol/m3 ] Earlier studies by Foss et al estimated the diffuDAB Diffusivity, comp. A in comp. B [m2 /s] −14 2 sivity to 3.8·10 m /s for water in paper fibres at Ni Flux of component i [mol/m2 s] ◦ 23 C and atmospheric pressure [4]. The diffusivity Ptot Total pressure [P a] in paper fibers is therefore much lower than the efpw Partial pressure of water vapor [P a] fective diffusivity through Tetra Recart paperboard. pw,s Partial pressure of water vapor at sat.[P a] Most likely, the diffusion in the paperboard does not RA Chemical reaction of component A follow the same mechanisms as pure fiber diffusion. RH Relative humidity [%] Earlier experiments on TBA material at 23.7◦ C t Time [s] and 1 atm gave an effective diffusivity of 7.17·10−6 T Temperature [◦ C] 4

vi yi

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

References [1] Pappersteknik, Fellers, C., Norman B., Avd. f¨or pappersteknik, KTH, 1996 [2] ”Systemet luft-vatten” (literature for the course Sep. FK.), Stenstr¨om, S., Dept. Chem. Eng., Lund University, 2004 [3] ”Transportprocesser” (literature for the course Sep. FK.), Stenstr¨om, 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 best¨amning av diffusionskoefficienter i PaToF-projektet, Andersson E, Dept. Chem. Eng., Lund University (2001)

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