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In order to investigate the influence on shale
gas well productivity caused by gas transport in nanometersize
pores, a mathematical model of multi-stage fractured
horizontal wells in shale gas reservoirs is built, which
considers the influence of viscous flow, Knudsen diffusion,
surface diffusion, and adsorption layer thickness. A discrete-
fracture model is used to simplify the fracture modeling,
and a finite element method is applied to solve the
model. The numerical simulation results indicate that with
a decrease in the intrinsic matrix permeability, Knudsen
diffusion and surface diffusion contributions to production
become large and cannot be ignored. The existence of an
adsorption layer on the nanopore surfaces reduces the
effective pore radius and the effective porosity, resulting in
low production from fractured horizontal wells. With a
decrease in the pore radius, considering the adsorption
layer, the production reduction rate increases. When the
pore radius is less than 10 nm, because of the combined
impacts of Knudsen diffusion, surface diffusion, and
adsorption layers, the production of multi-stage fractured
horizontal wells increases with a decrease in the pore
pressure. When the pore pressure is lower than 30 MPa, the
rate of production increase becomes larger with a decrease
in pore pressure.