An unsteady seepage flow model considering kickoff pressure gradient for low-permeability gas reservoirs

Kickoff pressure gradient occurs when gas flows in a low permeability reservoir. In order to describe the issue of unsteady seepage flow in this kind of reservoir, an unsteady-state seepage flow mathematical model which takes kickoff pressure gradient into consideration is built up based on previous research and the characteristic of start-up pressure gradient existing in low velocity non-Darcy percolation flow (the fluid flow boundary expands outwards constantly). Combining the Laplace space analytic solution by using Green function method with the numerical approximation, the nonlinear mathematical model can be resolved. An equation for calculating single-well control radius is established, and a single-well control radius chart board is drawn up which can be used to calculate single well control radius. Case study indicates that the unsteady seepage flow model taking kickoff pressure gradient into account can correctly present the percolation mechanism and real production performance of a low-permeability gas reservoir.