Abstract: According to characteristic of shale gas reservoir,mathematical description methods of diffusion and desorption are analyzed.Three seepage models controlled by different kinds of seepage mechanisms are built:① a mathematical model which considers diffusion and interporosity of desorbed gas and free gas,② a mathematical model which considers desorption and diffusion,③ a mathematical model which considers desorption and diffusion in organic porosity and interporosity in inorganic porosity.With modified Lord Kelvin point source function pressure solutions are botained.With corresponding transformation for point source functions,formation pressure solutions for vertical fractured well and fractured horizontal well are obtained and typical curves are shown.At last,characteristics of different curves and three mechanisms' influences on pressure are analyzed.

Key words: shale reservoir, seepage mechanism, mathematical model, well test analysis