Center for Light and Environmentally-Friendly Structures ZELUBA®

Research project

Simulation model for numerical calculation of the resistance during steam diffusion in wood-based materials

This research project, funded by the German Federal Ministry of Economics and Technology, was carried out to investigate why the parameters for vapour diffusion resistance (µ value) for individual, largely comparable wood-based materials deviated to an enormous degree – in some cases more than the power of ten. The literature research prior to the application being submitted provided no explanation for this, so a systematic investigation of the influences of each parameter seemed necessary.

© Fraunhofer WKI
Fig. 1: Measured values for the diffusion resistance (µ value) of test specimens from particles with a ratio variable of < 0.001 (fibres), applied to the raw density of the test specimen.

During the project it became clear that certain parameters (e.g. the type of binding agent) had no recognizable influence while others had a considerable influence. The raw density, for example, has an exponential effect. This, combined with the fact that the raw density of wood-based materials has a relatively large - for construction purposes inconsequential - variance, explains why there were great differences in the specified values. The results of the investigations in this project also show that the µ-values measured cannot be reliably interpreted if the raw density of the test specimen is not accounted for at the very least. Besides the raw density, the particle size and the level of adhesive content also have a considerable influence under each different set of conditions. 

© Fraunhofer WKI
Fig. 2: Measured values for the diffusion resistance (µ value) of test specimens from particles with a ratio variable of < 0.1 (fine strands), applied to the raw density of the test specimen.

The exponential influence of the raw density on the diffusion resistance can be clearly recognised in Figures 1 and 2. In the raw density range of approx. 450 kg/m³ to 600 kg/m³, an over-proportional increase in resistance can be seen. In fibreboards widely used in construction, particle boards and OSB are produced with raw densities in the range of approx. 550 kg/m³ to approx. 700 kg/m³. As, however, the raw density has a significant influence on the diffusion resistance within this range, it is obvious that the test results are difficult to interpret if details concerning the raw density of the test specimens are unknown.

Whilst the raw density correlates very well with the µ value, the logarithmical influence of the particle size is very difficult to model, so specific models were created in this project for common particles such as fibres, chips and strands. The influence of the level of adhesive content, however, correlates with the raw density and the particle size such that the models for describing the µ value display two summands.

The first describes as

the exponential influence of the raw density. The second, as

describes the influence of the level of adhesive content in relation to the raw density.

The individual factors a to g for each wood-based material type are listed in Table 1. The raw density should always be entered in kg/m³ and the level of adhesive content as a percentage. The proportion of hydrophobic agents should be added to the adhesive content. As wood-based materials can possess different particle sizes, raw densities and adhesive contents in the individual layers, the models are differential in practice, i.e. have to be applied specific to each layer.

Tabelle 2: Factor Values

Factor Factor values for panels made up of
Fibres Chips Rough chips / fine strands Rough strands / veneer
a 5 10 70 120
b 0,1 0,2 0,3 0,4
c 150 150 130 145
d 0,1 0,1 0,2 0,2
f 10 5 4 3
g 100 50 50 30


The models are not precise mathematical physical models. They have been empirically calculated on the basis of test results. Error estimation has shown that the results have an error level of around +/-10% and that measurements show a similar error range. As the adhesive content in a diffusion sample and within a layer cannot be precisely ascertained and the particle sizes can differ greatly even within a layer, the difference between the measurement and the calculation can be even greater than that stated above. However, a µ value as shown above can be expected on average, meaning that the µ value can be predicted with sufficient precision for a production batch.

Comparing the results of the diffusion measurements with small samples with a diffusion face of around 54cm² to those with a 250cm² diffusion face, it can be seen that the smaller test specimens produce greater deviations from the average (especially when there are inhomogeneous materials in the face) than their larger counterparts. ISO 12572 specifies that the diffusion resistance value has to be the (arithmetic) average from 5 samples. This approach, however, does not take into account that the process involves parallel-“connected” resistances from a physical point of view. Face (Ages) of a wood-based material consists of many small aligned faces (Ai). Thus, the face

Ages = ∑Ai .                                                                                         

Each partial face has its own diffusion resistance. As these partial faces lie next to each other, the diffusion resistance of the overall face (Rges) is ascertained as the total resistance of several “parallel-connected” resistances. The equation is


This equation shows that the partial faces with a very low resistance can significantly impair the total resistance. In the case of fibre panels, these (microscopic) partial faces with very low diffusion resistance are very evenly distributed across the face due to the particle structure. The bigger a particle’s face (fibre – chip – strand – veneer), the more likely it is that partial faces occur which have a very low diffusion resistance.

Whilst the results of the investigations do not enable us to forego measuring the diffusion resistance, they do allow considerably improved interpretation of the measurement results. Due to the relatively large raw density deviations in wood-based materials, it would appear to be advisable to determine the raw density of each individual test specimen and to standardise the measured values against the nominal raw densities of the measured wood-based material. The requirement to determine the raw density of each individual test specimen should be embedded in the ISO 12572 standard. Relevant parameters for standardisation of the measured values against the nominal raw densities will be compiled in the near future for each of the wood-based material forms fibreboards, particle boards, OSB and plywood boards. These should not, however, be embedded in the aforementioned standard. These parameters are, presumably, better suited to placement in the EN 13986 standard.

The ISO 12572 should, however, stipulate that the diffusion resistance of the respective material is no longer formed from the average values of the measurement results, but instead through observation of parallel-connected resistances.

In addition to the prospect of uniform, realistic values for diffusion resistance, the results of these investigations also provide the wood-based material industry with a tool with which the effects of alterations to the production process on the diffusion resistance can be realistically estimated. 



Bundesministerium für Wirtschaft und Technologie (Federal Ministry of Economics and Technology, BMWi) via the Arbeitsgemeinschaften industrieller Forschungsvereinigungen (Federation of Industrial Research Associations, AiF), represented by the Internationaler Verein für Technische Holzfragen e.V. (International Association for Technical Issues Related to Wood, iVTH)

Wood-based products industry