||The slow discharge process of a methane tank filled with porous carbonaceous adsorptive material is modelled and solved by the Integral Transform Method, yielding a hybrid numerical-analytical solution of the related energy equation. A transient one-dimensional nonlinear formulation is adopted, which includes the compressed and adsorbed gas thermal capacitances, the reservoir wall thermal capacitance effect and the gas compressibility influence. The overall mass balance is employed to determine the pressure field evolution, here assumed as spatially uniform. A thorough covalidation analysis is performed, with both numerical and experimental data available in the literature, and the relative importance of some terms in the energy equation formulation is inspected. Finally, different possibilities for the reduction of the adverse effect of the heat of adsorption on storage capacity are proposed and investigated.