A technique is proposed that uses a multi-scale approach to calculate transport properties of compressed felts using only image analysis and numerical calculations. From the image analysis fiber diameter distribution and fiber orientation are determined. From a known porosity and the latter two characteristics, two representative elementary volumes (REV) are constructed: one based on the volume-weighted average diameter and one on an inverse volume-weighted average diameter. Numerical calculations on the former showed that it correctly estimates viscous and thermal permeabilities, while the latter correctly estimates tortuosity and viscous and thermal characteristic lengths. From these calculations, micro-macro analytical expressions are developed to estimate the transport properties of polydisperse composite felts based solely on open porosity, fiber diameter polydispersity, and fiber orientation. Good agreements are obtained between analytical predictions and measurements of transport properties. The predicted transport properties are also used in the Johnson–Champoux–Allard–Lafarge (JCAL) equivalent fluid model to predict the sound absorption coefficient of the felts. Excellent agreements are obtained with impedance tube measurements. •Investigating transversely isotropic polydisperse fibrous media.•Modeling fiber microstructures for transport and sound absorbing properties.•Two microscale models established using volume and inverse-volume-weighted diameters.•Semi-analytical model predicts accurately for a wide range of porosities.