Comparative analysis of predictive equations for transfer processes in different porous structures

Research on transfer processes in various types of porous media has become important for the optimization of high technology engineering devices and processes. In this study the micro-structural parameters of different types of porous media, namely granular media, foamlike media and fibre beds, are characterized and quantified. Existing analytical modelling procedures for the three different types of porous media have been unified and refined to improve their predictive capabilities. Deterministic equations are proposed for predicting the streamwise pressure gradient, permeability and inertial coefficient of each type of porous medium. The equations are applicable over the entire porosity range and steady laminar flow regime and well suited as drag models in numerical computations. It is shown that the improved granular model can be regarded as qualitative and quantitative proof of the extensively used semi-empirical Ergun equation. The proposed model is used to provide physical meaning to the empirical coefficients. An Ergun-type equation is also proposed for foamlike media by remodelling the interstitial geometric configuration and accompanying flow conditions. The range of applicability of the existing foam model has been extended by incorporating the effect of developing flow in the pressure drop prediction. An equation is proposed in which the variation in the cross-sectional shape of the fibres can be incorporated into the interstitial form drag coefficient used in the foam model. This serves as an improvement on the constant value previously used. The existing foam model is also adapted to account for anisotropy resulting from compression. Two case studies are considered, namely compression of a non-woven glass fibre filter and compression of a soft polyester fibre material. The significant effect of compression on permeability is illustrated. In each case study the permeability values range over more than an order of magnitude for the narrow porosity ranges involved. The pressure drop prediction of the foam model is furthermore adapted to account for the combined effects of compression and developing flow. The newly proposed model diminishes the significant over-prediction of the existing foam model. An equation is furthermore proposed for predicting the permeability of Fontainebleau sandstones in which the effect of blocked throats is accounted for. Lastly, equations are proposed for predicting diffusivity ratios of unconsolidated arrays of squares and cubes. The prediction of the diffusivity ratio proposed in the present study, as opposed to model predictions from the literature, takes into account diffusion that may take place in stagnant fluid volumes. It is shown that a specific weighted average model proposed in the literature is not adequate to predict the diffusivity ratio of fully staggered arrays of squares, since it is shown not to be applicable to rectangular unit cells. Instead a new weighted average model is proposed which is applicable over the entire porosity range and for both staggered and non-staggered arrays of solid squares and cubes. The proposed weighted average model provides satisfactory agreement with experimental data from the literature and numerical data generated in the present study. ii Stellenbosch University http://scholar.sun.ac.za