The impact of diffusion type on multiscale discrete fracture model numerical simulation for shale gas

• Varying-scale flow is taken into account shale gas numerical analysis using DFN.
• Desorption, slippage, diffusion etc. are present in shale gas reservoir depletion.
• Diffusion forms in nano-scale pores include: Knudsen, Fick, transition diffusion.
• The select of diffusion models has a great effect on matrix apparent permeability.
• The small differences in permeability will lead to large difference in results.

The development of unconventional gas reservoirs represents totally distinctive characteristics as compared with the conventional reservoirs. The complex pore structure in shale reservoir determines its special flow mechanism, which can be divided into several categories according to the size and type of pores- non Darcy flow, gas slippage, adsorption-desorption and gas diffusion effect. Based on the gas molecules diffusion form in porous media and combining with the multi-scale distribution structural characteristics of shale gas reservoirs, the shale gas diffusion mechanisms in the shale reservoir space including the diffusion of dissolved gases in the organic kerogen and the diffusion of free gas in the nanopores are analyzed in this paper. Meanwhile, the diffusion in the nanopores consists of Knudsen diffusion (KN ≥ 10), Fick diffusion (KN ≤ 0.1) and transition diffusion (0.1 < KN < 10) according to the Knudsen (KN) number.In this work, we set up new mathematical models for shale gas flow in matrix and fracture networks, and also for their mass transfer in between without neglecting its varying-scale nature following the concept of discrete fracture network (DFN). In addition, we also investigate the different diffusion mechanisms' influences on the production and pressure in the tight shale gas reservoir. Ultimately, concluding that the gas diffusion mechanisms in micro-and nano-scale matrix block have a greater impact on the distribution of shale gas production (especially the production at early time) and reservoir pressure.