A computational model of a vertical well with waterflooding fracturing for pressure transient analysis

A new computational model for a vertical well with waterflooding fracturing is presented, which accounts for changes in the fracture half-length during the interpretation of pressure transient analysis (PTA) parameters. The model is based on a numerical algorithm derived from an analytical solution, utilizing a proposed relationship between the fracture half-length, process time, and its geometric dimensions. This functional dependence is developed using available PTA data.
The model employs the infinite-conductivity fracture equation and the superposition principle to describe changes in fracture geometry. The superposition principle is implemented through a series of activations and deactivations of fictitious wells with varying fracture half-lengths, where each well operates for a specific time interval before being shut down.
It is demonstrated that the change in fracture half-length during the closure stage follows a functional dependence on the initial and final fracture half-lengths, as well as the well operation time. The results obtained from the proposed model, incorporating the fracture half-length dependence function, show good agreement with experimental data when calculating pressure in a well with waterflooding fracturing.
A numerical analysis of the vertical well model with waterflooding fracturing is conducted using the developed algorithm. The influence of the final fracture half-length and the duration of fracture closure on pressure changes and the pressure derivative in the well is established. The use of the proposed fracture half-length dependence in calculating well operating conditions is shown to be justified. The application of this model allows for a more accurate description of parameter changes during PTA interpretation in wells with fractures of variable length.