Transport in Porous Media

, Volume 126, Issue 2, pp 379–410 | Cite as

Comparative Study of Three Models for Moisture Transfer in Hygroscopic Materials

  • Thomas BusserEmail author
  • Julien Berger
  • Amandine Piot
  • Mickael Pailha
  • Monika Woloszyn


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.


Diffusion Advection Non-equilibrium Model Validation Local sensitivity analysis Hygroscopic material 

List of symbols

Latin symbols

\(a_{\,\mathrm {v}}\)

Advection coefficient (\(\mathsf {s/m}\))


Ratio of gas volume to void volume (–)


Capacity (\(\mathsf {J/kg}\))


Heat capacity at constant pressure [\(\mathsf {J/(kg \, K)}\)]


Diffusivity of phase i (\(\mathsf {m}^\mathsf {2/s}\))


Sorption coefficient (\(\mathsf {s/m}^\mathsf {2}\))


Mass flux (\(\mathsf {kg/s/m}^\mathsf {2}\))


Cost function


Permeability (\(\mathsf {s}\))

\(k_{\mathrm {mat}}\)

Intrinsic permeability (\(\mathsf {m}^\mathsf {2}\))


Thickness of sample (\(\mathsf {m}\))


Mass (\(\mathsf {kg}\))

\(N_{\mathrm {t}}\)

Number of temporal iterations (–)




Pressure (\(\mathsf {Pa}\))

\(P_{\mathrm {sat}}\)

Saturation vapour pressure (\(\mathsf {Pa}\))



\(R_{\mathrm {v}}\)

Water vapour perfect gas constant ((\(\mathsf {J/(kg \, K)}\))


Volumetric source term ((\(\mathsf {kg/(m}^\mathsf {3 \, s)}\))


Temperature (\(^\circ \mathsf {C}\))


Time (\(\mathsf {s}\))

\(v_{\mathrm {g}}\)

Gas velocity (\(\mathsf {m/s}\))


Volume (m\(^3\))


Volumetric concentration of phase i (\(\mathsf {kg/m}^\mathsf {3}\))


Coordinate along the material, depth (\(\mathsf {m}\))


Sensitivity coefficient (–)

Greek symbols

\(\beta \)

Convective mass transfer coefficient (\(\mathsf {s/m}\))

\(\varepsilon \)

Porosity (–)

\(\mu _{\mathrm air}\)

Dynamic viscosity of air (\(\mathsf {Pa \, s}\))

\(\lambda \)

Thermal conductivity [\(\mathsf {W/(K \,m)}\)]

\(\phi \)

Relative humidity (–)

\(\sigma \)

Saturation (–)





bound water


dry air








water vapour




\(\infty \)

ambient air


reference value

\(\star \)

dimensionless parameter



This work was partly funded by the French Environment and Energy Management Agency (ADEME), the “Conseil des Pays de Savoie” (CSMB) and the French National Research Agency (ANR) through its Sustainable Cities and Buildings programme (MOBAIR project ANR-12-VBDU-0009). The authors also acknowledge the Junior Chair Research programme “Building performance assessment, evaluation and enhancement” from the University of Savoie Mont Blanc in collaboration with the French Atomic and Alternative Energy Center (CEA) and Scientific and Technical Center for Buildings (CSTB).


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Univ. Savoie Mont Blanc, CNRS, LOCIEUniv. Grenoble AlpesChambéryFrance
  2. 2.CEA, LITEN, DTS, INESUniversity Grenoble AlpesGrenobleFrance

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