Producing gas from shale strata has become an increasingly important factor to secure energy over recent years for the considerable volume of natural gas stored. Unlike conventional gas reservoirs, gas transports in shale reservoir is a complex process. In the organic nano pores, slippage effect, gas diffusion along the wall, viscous flow due to pressure gradient, and desorption from Kerogen coexist. In the micro fractures, there exists viscous flow and slippage. Also, with pressure depletion, gas viscosity will decrease. The porosity will increase when the gas desorbs from the pore wall. However, factors such as viscosity decrease and porosity increase have not received enough attention in existing mathematical models. It is important to construct a unified model considering all known mechanisms.
In this paper, based on dual porosity continuum media, mass balance equations in matrix and fracture were constructed using dusty gas model. In the matrix, Knudsen diffusion, Fick diffusion and viscous flow were considered. Gas desorption was characterized by Langmuir isothermal equation. In the fracture, Forchheimer flow was considered. Porosity increase was calculated by the equivalent volume increase due to gas desorption from the pore wall. Gas viscosity was characterized as a function of Knudsen number. Later, equivalent integral weak forms were derived based on constant pressure boundary. And model got solved using finite element method. Finally sensitive factors of shale gas production were analyzed. The results show that considering gas viscosity change increases cumulative gas production by nearly 12% under given reservoir conditions. Considering porosity increase will obtain higher production than without. The matrix and fracture permeability increase with time during production. Ignoring one of these factors such as Knudsen diffusion, slippage effect, desorption, viscosity decrease and porosity increase will obtain less cumulative production. For more accurate shale gas production prediction, it is crucial to incorporate these factors into the model.