Abstract Though much of the theoretical literature on reactions in porous catalyst pellets is concerned with special cases, such as binary mixtures at the Knudsen diffusion limit, in situations of industrial interest the reaction mixture usually contains several substances. There is often more than one independent chemical reaction, and pore sizes may correspond to a diffusion law anywhere between the extremes of Knudsen diffusion and bulk diffusion. A method of calculating the behavior of porous catalyst pellets in these more difficult but realistic circumstances has recently been developed, and its practicability has been demonstrated by applying it to an isothermal catalyst pellet. In the present paper this method is extended to deal with non-isothermal pellets and is applied to the industrially important SNG-process (low temperature, high pressure methanation on a shift-type catalyst). The computed results are compared with those obtained when a simple Knudsen type diffusion model is used.