In a secondary biogenic methane reservoir, closed pores may enclose thermogenic methane formed during diagenesis, whereas open pores carry biogenic methane. To assess this possibility, the isotopic compositions of desorbed and residual gas from the Eocene Harutori (coals and sedimentary rocks) and Paleocene Shiomi (sedimentary rocks) formations in the Kushiro Coal Mine were analyzed assuming that the desorbed and residual gas were derived mainly from open and closed pores, respectively. Values of δ13C(CH4) for residual gas from the Shiomi (−54.6‰ to −39.9‰) and Harutori (−77.9‰ to −60.5‰) formations were higher than those for desorbed gas (−80.9‰ to −71.9‰ and − 81.2‰ to −68.9‰, respectively), and ∆13C(CH4) values (δ13C(CH4)residual gas − δ13C(CH4)desorbed gas) were greater for the Shiomi Formation (18.5‰ to 37.5‰) than the Harutori Formation (3.3‰ to 14.4‰). The relatively high δ13C(CH4) values for residual gas and the large ∆13C(CH4) value for the Shiomi Formation imply preservation of thermogenic gas in some closed pores in this formation. The bulk diffusion coefficient of methane in minerals is lower than that of kerogen by more than two orders of magnitude. Therefore, methane in the closed pores of minerals should be preserved for longer periods than that in the closed pores of kerogen. The closed pores enclosing thermogenic methane in the Shiomi Formation are likely developed in the mineral matrix of this formation.