Mathematical Modeling of Fluid Flow to Unconventional Oil Wells With Radial Fractures and Its Testing With Field Data

Radial fractures are created in unconventional gas and oil reservoirs in modern well stimulation operations such as hydraulic refracturing (HRF), explosive fracturing (EF), and high energy gas fracturing (HEGF). This paper presents a mathematical model to describe fluid flow from reservoir through radial fractures to wellbore. The model can be applied to analyzing angles between radial fractures. Field case studies were carried out with the model using pressure transient data from three typical HRF wells in a lower-permeability reservoir. The studies show a good correlation between observed well performance and model-interpreted fracture angle. The well with the highest productivity improvement by the HRF corresponds to the interpreted perpendicular fractures, while the well with the lowest productivity improvement corresponds to the interpreted conditions where the second fracture is much shorter than the first one or where there created two merged/parallel fractures. Result of the case studies of a tight sand reservoir supports the analytical model.