Changes in the permeability tensor of fabric preforms caused by various modes of fabric distortion and fabric-layers shifting and compacting is one of the key factors controlling resin flow during the infiltration stage of the common polymer-matrix composite liquid-molding processes. While direct measurements of the fabric permeability tensor generally yield the most reliable results, a large number of fabric architectures used and numerous deformation and layers rearrangement modes necessitates the development and the use of computational models for prediction of the preform permeability tensor. The Lattice Boltzmann method is used in the present work to study the effect of the mold walls, the compaction pressure, the fabric-tows shearing and the fabric-layers shifting on the permeability tensor of preforms based on orthogonal balanced plain-weave fabrics. The model predictions are compared with their respective experimental counterparts available in the literature and a reasonably good agreement is found between the corresponding sets of results.