Modeling Transient Behavior of High-Velocity Non-Darcy Flow for a Fractured Vertical Gas Well in a Composite Reservoir

Abstract High-velocity non-Darcy (HVND) effect has been validated to be an important phenomenon that can influence the transient behavior of gas flow in high-conductivity media. Based on Barree–Conway's equation, an HVND flow model for a fractured vertical well in a heterogeneous two-region composite gas reservoir was established. The inner and outer regions were assumed to be a naturally fractured formation and a homogeneous formation, respectively. Mathematical models of reservoir and hydraulic fracture were respectively established and solved using the source function and the Laplace transform. The dimensionless pseudo-pressure solution at the wellbore was derived using the coupled conditions between the reservoir and hydraulic fracture. Then, a series of type curves that can reflect the transient behavior characteristics of gas flow was plotted. Nine main flow stages were recognized from type curves, and parameter sensitivities were analyzed. It is found that the transient behaviors are controlled by the physical properties of the HVND effect, hydraulic fracture, and reservoir. The HVND effect has a significant influence on the early transient behaviors. At the end, the engineering application of an example well was successfully performed, and the property parameters of the reservoir were interpreted. The established HVND flow model has important theoretical significance and applied engineering value.