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# Comparative Study of Three Models for Moisture Transfer in Hygroscopic Materials

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Prediction of moisture transfer within material using a classic diffusive model may lack accuracy, since numerical simulations underestimate the adsorption process when a sample is submitted to variations of moisture level. Model equations are always established with assumptions. Consequently, some phenomena are neglected. This paper therefore investigates the impact of improving traditional diffusive models by taking into account additional phenomena that could occur in moisture transport within hygroscopic fibrous materials such as wood-based products. Two phenomena in the porous material are investigated: (1) non-equilibrium behaviour between water vapour and bound water, and (2) transport by air convection. The equations of each model are established by starting from averaging conservation equations for the different species considered within material (water vapour, bound water and air). In addition, the validity of assumptions currently used in the models is verified. Then the three models are compared with experimental data to highlight their capacity to predict both the vapour pressure and the mass of adsorbed water. This comparison tends to show a slight improvement in predictions with the new models. To increase our understanding of these models, the influence of the main parameters characterising phenomena (sorption coefficient, intrinsic permeability, Péclet number and Fourier number) is studied using local sensitivity analysis. The shape of the sensitivity coefficients shows that the first kinetics period is only impacted a little by the non-equilibrium. In other periods, the influence of the diffusion phenomenon represented by the Fourier number is much greater than that of the two other phenomena: advection and sorption. Nevertheless, the sensitivity study shows that these two phenomena have some influence on vapour pressure.
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Transport in Porous Media (2019) 126:379–410
https://doi.org/10.1007/s11242-018-1161-8
Comparative Study of Three Models for Moisture Transfer in
Hygroscopic Materials
Thomas Busser1,2 ·Julien Berger1·Amandine Piot2·Mickael Pailha1·
Monika Woloszyn1
Received: 26 March 2018 / Accepted: 19 September 2018 / Published online: 26 September 2018
Abstract
Prediction of moisture transfer within material using a classic diffusive model may lack
accuracy, since numerical simulations underestimate the adsorption process when a sample
is submitted to variations of moisture level. Model equations are always established with
assumptions. Consequently, some phenomena are neglected. This paper therefore investi-
gates the impact of improving traditional diffusive models by taking into account additional
phenomena that could occur in moisture transport within hygroscopic ﬁbrous materials such
as wood-based products. Two phenomena in the porous material are investigated: (1) non-
equilibrium behaviour between water vapour and bound water, and (2) transport by air
convection. The equations of each model are established by starting from averaging con-
servation equations for the different species considered within material (water vapour, bound
water and air). In addition, the validity of assumptions currently used in the models is veriﬁed.
Then the three models are compared with experimental data to highlight their capacity to
predict both the vapour pressure and the mass of adsorbed water. This comparison tends to
show a slight improvement in predictions with the new models. To increase ourunderstanding
of these models, the inﬂuence of the main parameters characterising phenomena (sorption
coefﬁcient, intrinsic permeability, Péclet number and Fourier number) is studied using
local sensitivity analysis. The shape of the sensitivity coefﬁcients shows that the ﬁrst kinetics
period is only impacted a little by the non-equilibrium. In other periods, the inﬂuence of the
diffusion phenomenon represented by the Fourier number is much greater than that of the
two other phenomena: advection and sorption. Nevertheless, the sensitivity study shows that
these two phenomena have some inﬂuence on vapour pressure.
Keywords Diffusion ·Advection ·Non-equilibrium ·Model ·Validation ·Local sensitivity
analysis ·Hygroscopic material
BThomas Busser
thomas.busser@univ-smb.fr
1Univ. Savoie Mont Blanc, CNRS, LOCIE, Univ. Grenoble Alpes, 73000 Chambéry, France
2CEA, LITEN, DTS, INES, University Grenoble Alpes, 38000 Grenoble, France
123
... Numerical hygrothermal models [28][29][30] have been developed in the literature, which take into account, at best, internal processes (vapor transport, sorption, etc.), but they also generally involve some unknown parameters concerning the sorption-desorption dynamics. Finally, significant discrepancies subsist between the predictions of these models and macroscopic measurements [31,32], suggesting the need of progress concerning the description of physical processes in these model. ...
... Here, the thermal equilibrium is presumed. In addition, the gradient of total pressure is assumed as negligible [20,21]. With this assumption, the heat and mass flows are driven only by diffusion processes. ...
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