The tight formation has the characteristics of the extremely low permeability and the sensitivity of the permeability to the effective stress. The conventional constant shape factor model cannot accurately characterize the transient inter-porosity flow characteristics. In this paper, a new model is established by considering the effect of the stress sensitivity and the time-dependent fracture pressure boundary condition. The Pedrosa substitution and the perturbation method are applied to eliminate the nonlinearity of the model. The Laplace transformation method is used to obtain the analytical solution in the Laplace domain. Based on the Duhamel principle, the solution under the time-dependent fracture pressure boundary condition is obtained. The results obtained by the new model are compared with those obtained by the model of Hassanzadeh and the finite element analysis to validate the new model. Finally, the influences of the stresssensitivity and the decreasing velocity of the fracture pressure on the shape factor and the velocity of the inter-porosity flow are discussed. It is shown that the larger the stress sensitivity coefficient, the smaller the value of the shape factor and the smaller the velocity of interporosity flow will be. The fracture pressure depletion has a significant effect on the inter-porosity flow. The effects of the matrix stress sensitivity become more pronounced when the effects of the fracture pressure depletion are considered. Moreover, the shape factor and the velocity of inter-porosity flow are different in different stages as the fracture pressure depletion coefficient is not the same. The velocity of the inter-porosity flow will increase first to reach an equilibrium and then decrease when the decreasing rate of the fracture pressure is small, which is different from the results obtained under the constant fracture pressure boundary condition. The estimation of the velocity of the inter-porosity flow would be inaccurate if the effect of the fracture pressure depletion is not take into account. The new model provides a theoretical basis for the development of tight reservoirs and can be used in the study of the well test analysis and the numerical simulation of multi-fractured horizontal wells in a tight formation.

tight reservoir  /  matrix-fracture  /  transient inter-porosity flow  /  time-dependent shape factor  /  fracture pressure depletion