Simulation experiment and mathematical model analysis for shale gas diffusion in nano-scale pores

Gas diffusion in nano-scale porous media of deeply burried shale includes bulk diffusion (Fick and Knudsen diffusions) and surface diffusion. To reveal the migration mechanism of this process, the influence of temperature and pressure on diffusion coefficient needs to be quantitatively evaluated. A case study was made with the Cambrian Niutitang Formation in the Maoping area, Zigui, western Hubei, South China. Gas diffusion was simulated by isobaric diffusion experiments under different temperature and pressure conditions. The results indicated that: (1) The diffusion coefficient DF decreases with increasing of pressure (when the pressure is higher than 30 MPa, DF tends to be constant), and increases with increasing of temperature; (2) In the high temperature-pressure setting, DF is affected significantly by pressure and generally tends to decrease. Moreover, the impacts of temperature, pressure, porosity and lithology were quantitatively calculated, and a mathematical model of gas diffusion was established, which had comparable results with simulation experiment. The following conclusions were thus drawn: (1)Higher temperature will cause stronger molecular kinetic energy, resulting in increasing bulk and surface diffusion coefficients, while higher pressure will slightly strengthen the Fick and surface diffusions, but significantly limit the Knudsen diffusion, and cause lower total diffusion coefficient; (2) Larger pore size leads to stronger bulk diffusion, but weaker surface diffusion. Finally, according to the studies of a specific research block, high pressure setting is conducive to the preservation of nano-scale porous gas reservoir in shale, while the uplift accompanied by pressure release is the main stage of shale gas loss.