The dual-porosity
model has been used widely to describe the fracture
network in well test or numerical simulation due to the high computational
efficiency. The shape factor, which can be used to determine the capability
of mass transfer between the matrix and fracture, is the core of the
dual-porosity model. However, the conventional shape factor, which
is usually obtained under pseudo-steady state assumption, has certain
limitation in characterization of the mass transfer efficiency in
a shale/tight reservoir. In this study, a new transient interporosity
flow model has been established by considering the influence of nonlinear
flow, stress sensitivity, and fracture pressure depletion. To solve
this new model, a finite difference and Newton iteration method was
applied. According to the Duhamel principle, the solution for time-dependent
fracture pressure boundary condition has been obtained. The solution
has been verified by using the fine-grid finite element method. Then,
the influence of nonlinear flow, stress sensitivity, and fracture
pressure depletion on shape factor and interporosity flow rate has
been studied. The study results show that constant shape factors are
not suitable for unconventional reservoirs, and the interporosity
flow in the shale/tight reservoir is controlled by multiple factors.
The new model can be used in test interpretation and numerical simulation,
and also provides a new approach for the optimization of the perforation
cluster number.