Limited entry is used in multistage fracturing to attempt to distribute fracture fluid among multiple perforation clusters evenly. As the slurry is pumped through perforations, the perforation holes can be eroded because of abrasion by the proppant, and therefore become enlarged, resulting in less effective limited entry and lower efficiency of the fracture treatment. Distributed Acoustic Sensing (DAS) is a method used for monitoring of fluid flow during hydraulic fracturing. By evaluating the changing DAS responses at perforation cluster locations during fracture pumping, DAS can be used to evaluate perforation erosion. DAS is a measurement of acoustic energy induced by fluid movement with fiber optic sensing cables. A raw acoustic signal recorded by the interrogator is transformed into an energy response (Frequency Band Energy), which is used for further interpretation of fluid volume distribution among perforated clusters on each stage of the fracturing treatment.
Based on previous laboratory experiments and computational simulations, there is a correlation between the Frequency Band Energy and fluid flow rate. As the flow rate is a function of fluid velocity and perforation area (diameter of perforation), the same flow rate could be attained with a combination of different velocities and areas, leading to a non-unique solution when interpreting DAS measurements. We transferred the correlation into the relationship between velocity and Frequency Band Energy, using the perforation area as an additional parameter. It enforces avoiding non-unique solutions in the interpretation process.
Perforation diameter is a function of erosion rate, which depends on the proppant concentration and velocity of fluid passing through the perforation. In order to connect correlation parameters with the diameter of perforations, computational simulations of fluid injection were conducted with different perforations geometries. Based on these simulations, a function that connects the area of perforation with a correlation parameter was obtained. It allows us to include the diameter of perforation in the analytical equation explicitly.
The application of the enhanced correlation in the interpretation process leads to increased accuracy of the fluid distribution calculation. For each time step, the velocity of the fluid, the mass of proppant, and the diameter of the perforations are computed, allowing the calculation of the flow rate in each perforation cluster. Perforation erosion is included in the model. Examples using field data are presented in the paper.