A semi-analytical model for horizontal-well productivity in shale gas reservoirs: Coupling of multi-scale seepage and matrix shrinkage

Abstract

Matrix permeability is an important parameter in shale gas productivity prediction. However, the permeability affected by multi-scale seepage is difficult to calculate accurately. The object of this study is to develop an integrated apparent permeability model for multi-scale seepage mechanisms. The apparent permeability model considered shale gas flow from shrinkable matrix to fracture system with slip flow, Knudsen diffusion, and surface diffusion. The transport capacity change with different seepage mechanisms under different conditions was specifically analyzed. The importance of each parameter in the apparent permeability model was qualified using Grey correlation method. In addition, a semi-analytical model for horizontal-well productivity was developed to describe shale gas transport in reservoir. The semi-analytical model was solved using Laplace integral transformation and point source method. According to the results based on Grey correlation method, the effects of pore radius and Langmuir volume on dimensionless-type curves were discussed. Compared with the pore radius, the Langmuir volume had more influences on the shape of typical curve. The slip flow played the most important role in gas transport in mesopores and macropores when the pressure was more than 2 MPa and the surface diffusion was the primary transporting mechanism at any pressure in micropores but it can be negligible in macropores. The research result presented that the multi-scale seepage mechanisms would be considered in well tests and shale gas production.