Modelling and validation of wood permeability: combining fractal theory with mercury intrusion porosimetry method

The permeability of wood materials significantly affects wood modification, drying and further processing of wood-based building materials, and there is a need for a better understanding and evaluation of the permeability of wood materials. This paper presents a novel method for estimating the macroscopic permeability in wood by combining mercury intrusion porosimetry (MIP) data with the fractal theory. The characterization of wood’s structural parameters through MIP provides essential geometric data for the subsequent modelling process. A computational model for permeability was established based on principles of fractal geometry and seepage flow theory. This model aimed to elucidate the relationship between the structural characteristics of wood and its permeability behaviour. By deriving an explicit expression for permeability, the model incorporated critical structural parameters, e.g., minimum and maximum pore size, pore size distribution, porosity, fractal dimension, and the fractal dimension associated with tortuosity. The permeability of the three wood species studied, i.e., Scots pine, white birch, and oak, was 28.6, 13.6 and 1.4 mD, respectively. To validate the model, the calculated permeability values were compared with experimentally measured data, showing a strong correlation and confirming that the model accurately reflects the permeability behaviour of wood based on its structural characteristics. Notably, the model demonstrated the effectiveness of utilizing MIP data in conjunction with fractal theory, thus, the computational efficiency of this method significantly surpassed that of traditional numerical simulations, which allowed a better understanding of the interplay between structure and permeability in wood.