The effects of directional compaction, non-Darcy flow and anisotropic swelling on the extraction of natural gas in coal seam reservoirs are important but not well understood so far. This paper investigated these combined effects through a numerical model which fully couples the interactions of coal seam deformation, anisotropic gas flow in fractures, and anisotropic absorption/adsorption of natural gas in coal matrix. In the sorption process, the Langmuir isotherm is extended by including some microstructure information to describe sorption induced anisotropic swelling strain (called anisotropic swelling). The Forchheimer equation is reformulated to consider the non-Darcy effect in directional flows (called non-Darcy flow). A strain ratio of matrix to fractured element is introduced for the directional compaction induced evolution of permeability (called directional compaction). The effect of anisotropic swelling strain is also converted into anisotropic swelling body forces in the mechanical deformation process. This model is verified by the experimental results of single fracture flow under compaction. This verified model is used to quantify the relative importance of directional compaction and matrix swelling through a block model containing a single fracture. It is found that directional compaction of the single fracture can reduce the permeability by 70% and matrix swelling can reduce the permeability by over 30%. This example illustrates the important contribution of matrix swelling to the anisotropy of permeability. This fully-coupled model is applied to a production well in a coal seam gas reservoir to investigate the combined effects of directional compaction, non-Darcy flow and anisotropic swelling on well production rates. It is found that both directional compaction and anisotropic swelling can significantly induce the anisotropy of permeability, forming a skin damaged zone and largely affecting the production rate of natural gas extraction. Directional compaction and anisotropic swelling can significantly accentuate the non-Darcy effect near wellbore for unconventional coal seam gas reservoirs. Thus, the anisotropic evolution of permeability near wellbore cannot be ignorable for the evaluation of production data. (C) 2013 Elsevier B.V. All rights reserved.