In the traditional well test models, the quadratic gradient term of nonlinear partial differential equation was neglected according to the assumption of slightly compressible fluid, which could lead to error when the well test time was too long. As time went by, the fluid flowing boundary of low permeability reservoirs extended outwards continuously. In order to study the flowing law of low permeability reservoirs with deformed media, the flow model of low permeability reservoirs of deformed media was built, which considered the influence of starting pressure gradient, moving boundary and quadratic gradient term. The numerical solution of the flow model was obtained by the fully implicit finite difference method. The pressure dynamic curves were drawn to analyse the seepage law of different starting pressure gradient, deformed media and moving boundary. The influence of the quadratic gradient term on the pressure dynamic curves was analyzed. The results could help people understand the seepage mechanism of low permeability reservoirs and provide the theoretical basis for exploring the low permeability reservoirs.
Key words: The quadratic gradient term, moving boundary, starting pressure gradient, deformed media, low permeability reservoirs.