The　effective　stress　and　pore　pressure　can　change　the　fracture　aperture,　which　in　turn　can　change　the　methane　Knudsen　number　and　transitions　between　gas　flow　regimes.　A　novel　Knudsen　number　(Kn)　model　for　gas　flow　under　coal　deformation　was　established;　a　revised　permeability　model　was　formulated　and　used　to　obtain　an　equation　for　the　Klinkenberg　coefficient　b.　The　predictions　of　the　revised　permeability　model　were　in　good　agreement　with　experimental　data,　and　the　parameters　used　to　determine　the　gas　Kn　were　obtained.　An　increase　in　the　pore　pressure　under　coal　deformation　causes　the　fracture　aperture　to　increase　and　the　gas　molecular　mean　free　path　to　decrease,　thereby　decreasing　the　Kn.　Thus,　the　critical　pore　pressure　for　the　transition　between　gas　flow　regimes　is　reduced.　The　gas　Kn　for　a　deformed　fracture　is　higher　than　that　for　a　constant　fracture　aperture.　The　critical　fracture　aperture　for　the　transition　between　gas　flow　regimes　increases　under　coal　deformation.　The　Klinkenberg　coefficient　b　for　methane　is　a　variation　value　that　increases　as　Kn　decreases.　The　Kn　variation　is　very　important　for　determining　the　coal　permeability　and　which　can　be　used　to　resolve　problems　in　CBM　recovery.　©　2021　Elsevier　Ltd