A rigorous model that describes the transient flow of a polymer solution displacing a reservoir fluid was developed as a means to account for leakoff phenomena and net pressure during frac&pack treatments. An exact solution with a moving interface problem was derived in terms of the pressure profiles from the fracture face into the reservoir, in turn determining the fluid leakoff rate. The results show that the leakoff rate is dependent on the fracture net pressure, fluid and rock properties and injection conditions. The concept of a constant bulk property such as the leakoff coefficient is no longer necessary (or physically meaningful) in high-permeability reservoir stimulation. The developed leakoff model has been incorporated into a fracture propagation model to predict fracture dimensions, net pressure and the interactions between leakoff and created fracture during the propagation, packing stage and fracture closing. The variation of the slope behavior of the net pressure with time at a constant injection rate suggests a new method to diagnose fracture tip screenout.
Traditionally, hydraulic fracturing has been used to stimulate the production or injection of low-permeability reservoirs. During a treatment, part of the fracturing fluid fills the fracture and part leaks off into the formation driven by the pressure gradient between the fracture and formation. The rate of fluid leakoff controls the fracture dimensions and determines the fracturing fluid efficiency. The prediction of fluid leakoff behavior is crucial for the proper design of pumping schedules and the interpretation of pressure profiles during the fracture treatments.
A commonly used solution for fracturing fluid leakoff was obtained by Carter, using assumptions of constant fracture width and pressure. The leakoff model was presumed to be inversely proportional to the square root of time with a proportionality constant called the fluid loss coefficient. A number of studies since Carter have evaluated experimentally and modeled theoretically leakoff behavior. Some authors examined two-dimensional flow in the containing both fluid fluid.
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